id stringlengths 16 16 | problem stringlengths 17 1.85k | generated_solution stringlengths 1.28k 76.4k | expected_answer stringlengths 1 1.87k | problem_type stringclasses 1
value | problem_source stringclasses 4
values | generation_model stringclasses 2
values | pass_rate_72b_tir stringclasses 32
values | difficulty_bin stringclasses 3
values | inference_mode stringclasses 1
value | used_in_kaggle bool 2
classes | source_dataset stringclasses 1
value | source_split stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
da517d197326517d | A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere? | <think>
Okay, so I need to find the radius of a sphere that's tangent to the top, bottom, and lateral surface of a truncated cone. The truncated cone has radii 18 and 2 at its bases. Hmm, let me visualize this. A truncated cone is like a frustum, right? So it's a cone with the top cut off. The sphere touches the top ba... | 6 | has_answer_extracted | aops_c4_high_school_math | DeepSeek-R1 | 0.6875 | easy | cot | false | nvidia/OpenMathReasoning | cot |
fa9c5673c534226a | Find all continuous functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) such that \( f(2x) = f(x) + x \). | <think>
Okay, so I need to find all continuous functions f from the real numbers to the real numbers such that f(2x) = f(x) + x. Hmm, functional equations can be tricky, but let me think step by step.
First, maybe I can try some examples. Let's see if a linear function works. Suppose f(x) = kx, where k is a constant. ... | \( f(x) = x + a \) for any \( a \in \mathbb{R} \). | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.90625 | easy | cot | true | nvidia/OpenMathReasoning | cot |
e161c8face9ec0a3 | For which values of \( n \) is the polynomial \( x_1^n + x_2^n + \cdots + x_n^n - nx_1x_2 \cdots x_n \) reducible, where \( x_1, x_2, \ldots, x_n \) are \( n \) variables? | <think>
Okay, so I need to figure out for which values of n the polynomial \( x_1^n + x_2^n + \cdots + x_n^n - nx_1x_2 \cdots x_n \) is reducible. Hmm, reducible means it can be factored into the product of two non-constant polynomials, right?
First, let me check for small values of n. Maybe start with n=1. Then the p... | \( n = 2, 3 \) | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.375 | medium | cot | true | nvidia/OpenMathReasoning | cot |
50e9102727c6c964 | Find complex numbers \(a\), \(b\), and \(c\) such that \(|a|=|b|=|c|=1\) and \(a^3 + b^3 + c^3 = 2abc\). | <think>
Okay, so I need to find complex numbers a, b, and c such that each has an absolute value of 1 (so they lie on the unit circle in the complex plane) and they satisfy the equation a³ + b³ + c³ = 2abc. Hmm, let me think about how to approach this.
First, since all three numbers have absolute value 1, their recipr... | \(\left(e^{i\frac{\pi}9}, e^{-i\frac{\pi}9}, 1\right)\) | has_answer_extracted | aops_c6_high_school_olympiads | QwQ-32B | 0.0 | hard | cot | false | nvidia/OpenMathReasoning | cot |
3eaa508cf2ea65fa | There exists a line \( L \) with points \( D \), \( E \), \( F \) with \( E \) in between \( D \) and \( F \). Point \( A \), not on the line, is such that \( \overline{AF} = 6 \), \( \overline{AD} = \frac{36}{7} \), \( \overline{AE} = \frac{12}{\sqrt{7}} \) with \( \angle AEF > 90^\circ \). Construct \( E' \) on ray \... | <think>
Okay, so I have this geometry problem here, and I need to solve it step by step. Let me read through it again to make sure I understand all the parts.
There's a line L with points D, E, F, and E is between D and F. Point A is not on line L. We have some distances: AF is 6 units, AD is 36/7 units, and AE is 12/... | 112 | has_answer_extracted | aops_c5_contests_amp_programs | QwQ-32B | 0.0 | hard | cot | false | nvidia/OpenMathReasoning | cot |
92ce7648bc9b87c3 | Determine the largest natural number that is a multiple of 25 and has all distinct digits. | <think>
Okay, so I need to find the largest natural number that's a multiple of 25 and has all distinct digits. Let's start by understanding the problem.
First, a natural number is a positive integer (1, 2, 3, ...). The number must be a multiple of 25, which means it has to end with 00, 25, 50, or 75. But since the di... | 9876432150. | has_answer_extracted | aops_c4_high_school_math | DeepSeek-R1 | 0.3125 | medium | cot | true | nvidia/OpenMathReasoning | cot |
6794ae8d29653c2a | "Bob starts with the number $0$ and adds $111$ (i.e., $7$ in base $2$) to it one hundred times to ob(...TRUNCATED) | "<think>\nOkay, so Bob is starting with the number 0 and adding 111 (which is 7 in decimal, right?) (...TRUNCATED) | 294 | has_answer_extracted | aops_c6_high_school_olympiads | QwQ-32B | 0.21875 | medium | cot | false | nvidia/OpenMathReasoning | cot |
8fac6271cb1f44c5 | "Find all continuous functions \\( f: \\mathbb{R}^+ \\to \\mathbb{R} \\) such that \\( f(x^2) = \\fr(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem where I need to find all continuous functions \\( f:(...TRUNCATED) | \( f(x) = \frac{a}{x} \) | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.625 | easy | cot | true | nvidia/OpenMathReasoning | cot |
8325dd3d4ed67efe | "Let \\(a, b, c > 0\\) and \\(a + b + c \\leq 3\\). Find the minimum value of \n\\[ P = \\sum \\frac(...TRUNCATED) | "<think>\nOkay, so I have this problem here: given positive real numbers a, b, c such that their sum(...TRUNCATED) | 1 | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.96875 | easy | cot | true | nvidia/OpenMathReasoning | cot |
93bb3c537f721b8c | "Calculate the exact value of the series $\\sum_{n=2}^\\infty \\left(\\log (n^3 + 1) - \\log (n^3 - (...TRUNCATED) | "<think>\nOkay, let's try to tackle this series problem. The question is to find the exact value of (...TRUNCATED) | \(\log \frac{3}{2}\) | has_answer_extracted | aops_c7_college_math | DeepSeek-R1 | 0.375 | medium | cot | true | nvidia/OpenMathReasoning | cot |
End of preview. Expand in Data Studio
YAML Metadata Warning:empty or missing yaml metadata in repo card
Check out the documentation for more information.
OpenMathReasoning filtered subset
Filtered from nvidia/OpenMathReasoning split cot in streaming mode.
Filters:
problem_type == has_answer_extracted: True- excluded
problem_source == MATH_training_set: True - max problem chars: 2500
- min/max solution chars: 200/240000
- difficulty mix:
0.3,0.4,0.3usingpass_rate_72b_tir
Counts:
{
"hard": 30000,
"medium": 28296,
"easy": 30000
}
This dataset is intended for student-native reasoning-trace compression experiments.
- Downloads last month
- 34