ms_id int64 5 216k | instruction_seed stringlengths 33 5.18k | generated_text stringlengths 20.2k 88k | conversations listlengths 2 2 | answer_extracted stringclasses 5
values | other_model_answer stringlengths 1 111 | answers_match bool 2
classes | source_model stringclasses 1
value |
|---|---|---|---|---|---|---|---|
5 | Let $S$ denote the sum of the areas of the squares formed by joining the consecutive points $(n^2, n)$ in the coordinate plane, for all positive integers $n$. Determine the value of $S$. | <think>
Okay, so I need to figure out the sum of the areas of squares formed by joining consecutive points (n², n) for positive integers n. Let me start by understanding the problem step by step.
First, let me visualize what these points look like. Each point has coordinates (n², n). So for n=1, the point is (1,1); fo... | [
{
"from": "human",
"value": "Let $S$ denote the sum of the areas of the squares formed by joining the consecutive points $(n^2, n)$ in the coordinate plane, for all positive integers $n$. Determine the value of $S$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the sum of... | null | \infty | null | qwen3-32b |
6 | "A circle centered at (1, 2) has radius r, where r is a positive integer. The circle partitions the (...TRUNCATED) | "<think>\nOkay, so I need to find the smallest integer radius r for a circle centered at (1, 2) such(...TRUNCATED) | [{"from":"human","value":"A circle centered at (1, 2) has radius r, where r is a positive integer. T(...TRUNCATED) | null | 1 | null | qwen3-32b |
12 | "Consider the following equation:\n$$x^2 + \\frac{1}{4} x + 1 = 0.$$\nDetermine the value of\n$$2x^3(...TRUNCATED) | "<think>\nOkay, so I need to figure out the value of this infinite series: 2x³ + 4x⁶ + 6x⁹ + 8x(...TRUNCATED) | [{"from":"human","value":"Consider the following equation:\n$$x^2 + \\frac{1}{4} x + 1 = 0.$$\nDeter(...TRUNCATED) | null | -\dfrac | null | qwen3-32b |
16 | "Let $f(x)$ be a function defined as $f(x) = x^2 + 2x$. Find $a$ so that $f(f(f(-2))) = f(f(f(a)))$,(...TRUNCATED) | "<think>\nOkay, so I need to find a positive number $ a $ such that $ f(f(f(-2))) = f(f(f(a))) $, wh(...TRUNCATED) | [{"from":"human","value":"Let $f(x)$ be a function defined as $f(x) = x^2 + 2x$. Find $a$ so that $f(...TRUNCATED) | null | -2 | null | qwen3-32b |
17 | "In a triangular prism, the lateral faces meet at a right angle. The area of the base is 72 square u(...TRUNCATED) | "<think>\nOkay, so I need to find the volume of a triangular prism. The problem says that the latera(...TRUNCATED) | [{"from":"human","value":"In a triangular prism, the lateral faces meet at a right angle. The area o(...TRUNCATED) | null | 432 | null | qwen3-32b |
19 | "A triangle with vertices (a, 0), (0, b), and (0, 0) is cut by a line through the point (c, c) into (...TRUNCATED) | "<think>\nOkay, so I need to find the slope of a line that goes through the point (c, c) and cuts th(...TRUNCATED) | [{"from":"human","value":"A triangle with vertices (a, 0), (0, b), and (0, 0) is cut by a line throu(...TRUNCATED) | null | -\dfrac | null | qwen3-32b |
23 | "If\n$$\\frac{f(x)}{g(x)}=\\frac{ax^2-2x+1}{bx^2+3x-2},$$\nwhere $f(x)$ and $g(x)$ are linear functi(...TRUNCATED) | "<think>\nOkay, so I need to find f(x)/g(x) given that it's equal to (ax² - 2x + 1)/(bx² + 3x - 2)(...TRUNCATED) | [{"from":"human","value":"If\n$$\\frac{f(x)}{g(x)}=\\frac{ax^2-2x+1}{bx^2+3x-2},$$\nwhere $f(x)$ and(...TRUNCATED) | null | \dfrac | null | qwen3-32b |
24 | "A circle is inscribed inside a regular octagon (an 8-sided polygon). If two sides of the octagon ar(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that if I randomly choose two sides of a regular o(...TRUNCATED) | [{"from":"human","value":"A circle is inscribed inside a regular octagon (an 8-sided polygon). If tw(...TRUNCATED) | null | \dfrac | null | qwen3-32b |
26 | "A standard deck of 52 cards is shuffled and 5 cards are drawn at random. What is the probability th(...TRUNCATED) | "<think>\nOkay, so I need to figure out the probability that when I draw 5 cards from a standard dec(...TRUNCATED) | [{"from":"human","value":"A standard deck of 52 cards is shuffled and 5 cards are drawn at random. W(...TRUNCATED) | null | \dfrac | null | qwen3-32b |
29 | "A curve defined by the equation $y = \\sin x$ has a rectangle inscribed in it, with the vertices of(...TRUNCATED) | "<think>\nOkay, so I need to find the ratio of the width to the height of a rectangle inscribed in t(...TRUNCATED) | [{"from":"human","value":"A curve defined by the equation $y = \\sin x$ has a rectangle inscribed in(...TRUNCATED) | null | \dfrac | null | qwen3-32b |
End of preview. Expand in Data Studio
OpenThoughts4 5K Math - Qwen3-32B Only 235B Has Boxed Answer
Overview
This dataset contains 5,441 samples from the OpenThoughts4 math dataset where only Qwen3-235B-A22B produced a valid \boxed{} answer (Qwen3-32B did not). This dataset contains the Qwen3-32B reasoning traces (which lack valid boxed answers).
Relationship to Other Datasets
This is one of 10 child datasets derived from two parent datasets:
Parent datasets (29,963 samples each):
marin-community/open-thoughts-4-30k-math-qwen3-32b-annotated-16384-tokensmarin-community/open-thoughts-4-30k-math-qwen3-235b-a22b-annotated
Child datasets (partitioned by answer availability and agreement):
| Category | 32B Dataset | 235B Dataset | Samples |
|---|---|---|---|
| Both have answer, agree | open-thoughts-4-11k-math-qwen3-32b-agreed-answers |
open-thoughts-4-11k-math-qwen3-235b-a22b-agreed-answers |
10,953 |
| Both have answer, disagree | open-thoughts-4-6k-math-qwen3-32b-disagreed-answers |
open-thoughts-4-6k-math-qwen3-235b-a22b-disagreed-answers |
5,982 |
| Neither has answer | open-thoughts-4-6k-math-qwen3-32b-neither-has-boxed |
open-thoughts-4-6k-math-qwen3-235b-a22b-neither-has-boxed |
6,110 |
| Only 32B has answer | open-thoughts-4-1k-math-qwen3-32b-only-32b-has-boxed |
open-thoughts-4-1k-math-qwen3-235b-a22b-only-32b-has-boxed |
1,477 |
| Only 235B has answer | This dataset | open-thoughts-4-5k-math-qwen3-235b-a22b-only-235b-has-boxed |
5,441 |
| Total | 29,963 |
The ms_id values are unique across all child datasets and match between paired 32B/235B datasets.
Dataset Schema
| Field | Type | Description |
|---|---|---|
ms_id |
int64 | Unique sample identifier |
instruction_seed |
string | Original math problem |
generated_text |
string | Full reasoning trace from Qwen3-32B |
conversations |
list | Multi-turn conversation format |
answer_extracted |
string | Extracted answer from Qwen3-32B (None for this dataset) |
other_model_answer |
string | Answer from Qwen3-235B-A22B |
answers_match |
bool | Whether answers match (None for this dataset) |
source_model |
string | "qwen3-32b" |
Use Cases
- Studying cases where the larger model succeeds but the smaller model fails
- Analyzing the 32B model's failure modes (often due to token limit truncation)
- Understanding format compliance differences between model sizes
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