Dataset Preview
problem string | prompt string | generation string | extracted_answer string | gt_answer string | passed_gt_match bool | domain string | source string | difficulty int64 | label_char_len int64 | dataset_name string | task_type string | task_format string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Let $g(m)$ be the product of the positive integer divisors of $m$. For how many values of $m$, where $1 \le m \le 30$, is $g(m)$ a perfect square? | <|im_start|>system
You are a careful problem solver. Think step by step and put your final answer inside \boxed{} at the end of your response.<|im_end|>
<|im_start|>user
Let $g(m)$ be the product of the positive integer divisors of $m$. For how many values of $m$, where $1 \le m \le 30$, is $g(m)$ a perfect square?<|im... | <think>
Okay, so I need to figure out how many numbers between 1 and 30 inclusive have their product of positive divisors, denoted as g(m), be a perfect square. Hmm, let me start by recalling some properties of divisors and perfect squares.
First, I remember that for any number m, the product of its positive divisors ... | 23 | 13 | false | math | ai2-adapt-dev/openmath-2-math | null | 42,650 | self_distill_openthoughts | reason | generation |
Find the number of triangles with integer sides that have one side equal to the arithmetic mean of the other two sides. | <|im_start|>system
You are a careful problem solver. Think step by step and put your final answer inside \boxed{} at the end of your response.<|im_end|>
<|im_start|>user
Find the number of triangles with integer sides that have one side equal to the arithmetic mean of the other two sides.<|im_end|>
<|im_start|>assistan... | <think>
Okay, so I need to find the number of triangles with integer sides where one side is the arithmetic mean of the other two. Let me start by recalling what an arithmetic mean is. If I have two sides, say a and b, their arithmetic mean is (a + b)/2. So, the third side, which is supposed to be the arithmetic mean, ... | finite, and I need to check again | \infty | false | math | ai2-adapt-dev/openmath-2-math | null | 46,563 | self_distill_openthoughts | reason | generation |
A circle of radius $r$ is inscribed in a square. Two circles of radius $r$ are inscribed in two of the triangles formed by the center of the square and two of its adjacent vertices. These two circles are tangent to each other and to the original circle.
What is the length of the segment $PQ$, which is the diameter of... | <|im_start|>system
You are a careful problem solver. Think step by step and put your final answer inside \boxed{} at the end of your response.<|im_end|>
<|im_start|>user
A circle of radius $r$ is inscribed in a square. Two circles of radius $r$ are inscribed in two of the triangles formed by the center of the square an... | <think>
Okay, so there's this problem about a square with an inscribed circle of radius r. Then there are two more circles of the same radius r inscribed in two of the triangles formed by the center of the square and two adjacent vertices. These two circles are tangent to each other and to the original circle. We need ... | 2r | 2r(1 + \sqrt{2}) | false | math | ai2-adapt-dev/openmath-2-math | null | 54,103 | self_distill_openthoughts | reason | generation |
A circle is inscribed in an isosceles triangle, whose vertex angle is 60 degrees and whose base measures 8 units. Determine the perimeter of the triangle if one of its legs is a tangent to the inscribed circle at a point which divides the leg into two segments, whose lengths are in the ratio 1:3. | <|im_start|>system
You are a careful problem solver. Think step by step and put your final answer inside \boxed{} at the end of your response.<|im_end|>
<|im_start|>user
A circle is inscribed in an isosceles triangle, whose vertex angle is 60 degrees and whose base measures 8 units. Determine the perimeter of the trian... | <think>
Okay, so I need to find the perimeter of an isosceles triangle. The triangle has a vertex angle of 60 degrees and a base of 8 units. Also, one of its legs is tangent to the inscribed circle at a point that divides the leg into two segments with lengths in the ratio 1:3. Hmm, let me try to visualize this.
First... | 24 | \dfrac{56}{3} | false | math | ai2-adapt-dev/openmath-2-math | null | 29,529 | self_distill_openthoughts | reason | generation |
"Let $A,$ $B,$ $C$ be the angles of a triangle. Evaluate\n\\[\\begin{vmatrix} \\sin A & \\cos B & \(...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, so I need to evaluate the determinant of this 3x3 matrix:\n\n$$\n\\begin{vmatrix} \n(...TRUNCATED) | -0.375 | null | null | math | ai2-adapt-dev/openmath-2-math | null | 44,599 | self_distill_openthoughts | reason | generation |
"Consider the sequence $2000, y, 2000 - y,\\ldots$, where each term after the first two is obtained (...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, so I need to find the positive integer y such that the sequence 2000, y, 2000 - y, .(...TRUNCATED) | 2000 | 1236 | false | math | ai2-adapt-dev/openmath-2-math | null | 32,982 | self_distill_openthoughts | reason | generation |
"I'm trying to understand the wave function of two identical particles with spin but unfortunately m(...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, let me try to work through this. So, the user is asking about the wave function for (...TRUNCATED) | the same as for fermions | "\\text{The degeneracy increases due to the orbital spin components combined symmetrically or anti-s(...TRUNCATED) | false | science | stackexchange-physics | null | 12,736 | self_distill_openthoughts | reason | generation |
"Find the sum of all positive integers that can be expressed as a palindrome in both base 2 and base(...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, so I need to find all positive integers that can be expressed as palindromes in both(...TRUNCATED) | valid | 1 | false | math | ai2-adapt-dev/openmath-2-math | null | 34,295 | self_distill_openthoughts | reason | generation |
"The sum of the volumes of all tetrahedrons whose vertices are also vertices of a regular octahedron(...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, so I need to find the sum of the volumes of all tetrahedrons whose vertices are also(...TRUNCATED) | 8*(1/3) + 7*0 = 8/3 | null | null | math | ai2-adapt-dev/openmath-2-math | null | 47,859 | self_distill_openthoughts | reason | generation |
"A rectangular prism has a total of 16 vertices. Each face of the prism is a rectangle and has eithe(...TRUNCATED) | "<|im_start|>system\nYou are a careful problem solver. Think step by step and put your final answer (...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, we have a rectangular prism with 16 vertic(...TRUNCATED) | 8 | null | null | math | ai2-adapt-dev/openmath-2-math | null | 56,958 | self_distill_openthoughts | reason | generation |
End of preview.
Qwen3-0.6B Self-Distillation on OpenThoughts3 (1k)
Self-distillation trajectories generated by Qwen/Qwen3-0.6B on problems
sampled from the deduplicated OpenThoughts3 pool
(hyunseoki/openthoughts3-dedup-index).
The intended use is reasoning retention supervision in selective-forgetting
experiments: the model's own generation distribution is preserved under
distillation because the label sequence was produced by the same base model.
See the upstream research repo
memory_reasoning_split for
training-loop integration.
How it was built
- Streamed the full 1.2M rows of
open-thoughts/OpenThoughts3-1.2M. - Deduplicated by normalized problem text → 65,047 unique questions.
- Uniformly sampled 1,000 unique problems (seed=13) across all three upstream domains (math, code, science).
- Rendered prompts with the Qwen3 chat template + an explicit solver system
prompt, then generated one trajectory per problem with vLLM using Qwen3's
recommended thinking-mode sampling:
temperature=0.6, top_p=0.95, top_k=20, min_p=0.0, max_new_tokens=16384. - Extracted a final answer from each generation via
\boxed{...}/ "final answer" heuristics. - Compared the extracted answer against the upstream solver's boxed GT when available.
Schema
| Field | Type | Notes |
|---|---|---|
problem |
str | Original problem text |
prompt |
str | Chat-templated prompt actually fed to the model |
generation |
str | Raw model output (the label_text / distillation target) |
extracted_answer |
str | Final-answer extraction from generation |
gt_answer |
str or null | \boxed{...} extracted from the upstream solver's response; null when absent |
passed_gt_match |
bool or null | true/false when gt_answer is present; null when no GT was available (e.g. code-golf problems) — this is not a correctness signal, it means "could not be compared" |
domain |
str | math / code / science |
source |
str | Upstream source (e.g. ai2-adapt-dev/openmath-2-math) |
difficulty |
str or null | Upstream difficulty |
label_char_len |
int | Character length of generation |
dataset_name |
str | self_distill_openthoughts |
task_type |
str | reason |
task_format |
str | generation |
Summary statistics
- Total rows: 1000
- By domain:
math: 803science: 105code: 92
passed_gt_matchvalues:true: 144false: 560blank: 296
- Pass rate by domain (within rows that have GT):
math: 134/600 = 22.3% (+ 203 rows without GT)science: 8/83 = 9.6% (+ 22 rows without GT)code: 2/21 = 9.5% (+ 71 rows without GT)
Notes
- No train/eval split is shipped; downstream consumers should split as needed. The whole 1,000-row corpus is intended as one coherent distillation set for the 0.6B self-retention experiments.
passed_gt_matchis a nullable boolean column:true,false, ornull.nullmeans "could not be compared" (no upstream boxed GT available) — it is not a correctness signal. In particular mostcoderows and any math/science row whose upstream solver response lacks a boxed target will benull.- For a sandboxed code-correctness evaluation see the discussion in the research repo — not included here.
Reproducibility
- Sampling seed:
13 - Base model:
Qwen/Qwen3-0.6B - Sampling config: Qwen3 thinking-mode defaults
- Upstream dedup index:
hyunseoki/openthoughts3-dedup-index(commit-pinned on HF)
License / Attribution
Problems and GT answers are derived from
open-thoughts/OpenThoughts3-1.2M;
please follow its license terms. The generated trajectories are model output
from Qwen/Qwen3-0.6B.
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