Datasets:

kushasareen
/

openmath-hard-64

prompt listlengths 2 2	system stringclasses 1 value	data_source stringclasses 1 value	ability stringclasses 1 value	reference_solution stringlengths 923 4.04k	reference_solution_full stringlengths 6.98k 31.1k	reward_model dict	extra_info dict	solution_tokens int64 2.43k 8.19k	mean_response_chars float64 8.82k 35.7k
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "For how many positive integers $n$ is $n^{18/n}$ a whole number?", "role": "user" } ]	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To determine the number of positive integers $ n $ for which $ n^{18/n} $ is a whole number, we need to find $ n $ such that $ n^{18/n} $ is an integer. This means $ \frac{18}{n} $ must be an integer or a rational number that results in an integer when $ n $ is raised to that power. ### Step-by-Step Soluti...	<think> Okay, let's tackle this problem: "For how many positive integers $ n $ is $ n^{18/n} $ a whole number?" Hmm, interesting. So I need to find all positive integers $ n $ such that when you take $ n $ and raise it to the power of $ 18/n $, the result is an integer. Let me think step by step. First off, ...	{ "ground_truth": "9", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.09375, "problem_source": "aops_c4_high_school_math" }	7,494	21,356.6875
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "In a mathematics competition with 25 problems, each problem awards 3 marks for a correct answer, deducts 1 mark for a wrong ans...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To determine the minimum number of candidates needed to ensure that at least two candidates have the same total score in a mathematics competition with 25 problems, we use the pigeonhole principle. Each problem awards 3 marks for a correct answer, deducts 1 mark for a wrong answer, and gives 0 marks for a blank answer....	<think> Okay, so I need to figure out the minimum number of candidates required to ensure that at least two of them have the same total score in this math competition. Let me start by understanding the problem step by step. First, the competition has 25 problems. Each problem can either be answered correctly, incorrec...	{ "ground_truth": "99", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0, "problem_source": "aops_c6_high_school_olympiads" }	7,664	22,869.1875
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "Generalize the problem for an \$ n \\times n \$ board. If the lower left-hand corner square has the number 10, what are all t...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To solve the problem of finding all possible values of the upper right-hand square on an $ n \times n $ board where the lower left-hand corner is 10, we need to follow these steps: 1. Determine the starting number $ k $: - The lower left-hand corner of the board is at position $(n, 1)$. - The number at...	<think> Okay, so I need to figure out all possible values of the upper right-hand square on an n x n board where the lower left-hand corner is 10. Hmm. Let's start by recalling how numbering works on such boards. Wait, the problem doesn't specify the type of numbering. Is it a magic square, a chessboard, or something e...	{ "ground_truth": "10", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.09375, "problem_source": "aops_c6_high_school_olympiads" }	3,371	28,645.3125
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "How many finger-countable functions $ f $ satisfy $ f( f(1)) = 1 $ and $ f(3) = 2 $?", "role": "user" } ]	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To determine the number of finger-countable functions $ f $ that satisfy $ f(f(1)) = 1 $ and $ f(3) = 2 $, we consider the domain and codomain as the set $ S = \{1, 2, 3, 4, 5\} $. 1. Condition $ f(3) = 2 $: - This condition fixes $ f(3) = 2 $, leaving the mappings for $ f(1) $, $ f(2) $, \( f(4...	<think> Okay, so I need to figure out how many functions f satisfy the conditions f(f(1)) = 1 and f(3) = 2. The problem mentions that these functions are "finger-countable," which I think means they're functions from the set {1, 2, 3, 4, 5} to itself, since that's a common scenario where you can count the number of fun...	{ "ground_truth": "200", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0, "problem_source": "aops_c4_high_school_math" }	3,326	12,085.75
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "Five men and nine women stand equally spaced around a circle in random order. The probability that every man stands diametrical...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To solve the problem of finding the probability that every man stands diametrically opposite a woman when five men and nine women are arranged equally spaced around a circle, we can follow these steps: 1. Total Number of Arrangements: There are 14 positions arranged in 7 pairs of diametrically opposite seats. T...	<think> Alright, so I have this probability problem here: Five men and nine women stand equally spaced around a circle in random order. The probability that every man stands diametrically opposite a woman is m/n, where m and n are coprime. I need to find m + n. Hmm, okay, let me think step by step. First, let me try t...	{ "ground_truth": "191", "style": "math_dapo" }	{ "generation_model": "QwQ-32B", "pass_rate_72b_tir": 0, "problem_source": "MATH_training_set" }	6,694	29,559.6875
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "Find the number of ways to select 5 people out of 15 people sitting on a round table such that exactly two of the selected peop...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To find the number of ways to select 5 people out of 15 sitting on a round table such that exactly two of the selected people are consecutive and no other two selected people are consecutive, we can follow these steps: 1. Identify Consecutive Pairs: - In a circular arrangement of 15 people, there are 15 possibl...	<think> Okay, so I need to find the number of ways to select 5 people out of 15 sitting around a round table, with the condition that exactly two of the selected people are consecutive and no other two are consecutive. Hmm, let me think through this step by step. First, since the table is round, the problem is circula...	{ "ground_truth": "1260", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.09375, "problem_source": "aops_c4_high_school_math" }	5,106	31,421.5625
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "How many ways are there to trace out \"1, 2, 3, 4, 5, 6, 7\" by traversing the following diamond, starting at the top and alway...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To solve the problem of finding the number of ways to trace out "1, 2, 3, 4, 5, 6, 7" by traversing the given diamond structure, starting at the top and always moving to an adjacent number, we can use a dynamic programming approach. Each step must move to the next number in the sequence and to an adjacent position in t...	<think> Okay, let's see. I need to find the number of ways to trace the sequence "1, 2, 3, 4, 5, 6, 7" on this diamond structure by moving to adjacent numbers each time. The starting point is the top 1. Hmm. So, each step I have to go from the current number to the next in the sequence by moving to an adjacent position...	{ "ground_truth": "20", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.03125, "problem_source": "aops_c4_high_school_math" }	5,901	27,569.8125
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "A lighthouse facing East sends out a fan-shaped beam of light extending from S.-E to N.-E. An observer sailing due North contin...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To solve the problem, we need to determine the speed of a ship sailing due north that continues to see a fan-shaped beam of light extending from southeast to northeast for $10\sqrt{2}$ minutes after meeting the beam. When the ship leaves the fan of light, it is 10 miles from the lighthouse. 1. **Define the coordinat...	<think> Okay, so I need to find the speed of a ship that's sailing north. The problem says there's a lighthouse facing east with a fan-shaped beam from southeast to northeast. The observer on the ship continues to see the light for 10√2 minutes after passing the beam. When the ship leaves the fan of light, it's 10 mile...	{ "ground_truth": "60", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.0625, "problem_source": "aops_c4_high_school_math" }	4,327	33,019.25
[ { "content": "You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \\boxed{}.", "role": "system" }, { "content": "Find the largest possible value of $n$ such that there exist $n$ real numbers $x_1, \\ldots, x_n$ which satisfy $\|x_i - x_j\| > ...	You are a careful mathematician. Solve the following problem. Show your work, then give the final answer inside \boxed{}.	math_dapo	math	To find the largest possible value of $ n $ such that there exist $ n $ real numbers $ x_1, x_2, \ldots, x_n $ which satisfy $ \|x_i - x_j\| > \frac{1 + x_i x_j}{100} $ for all $ i \neq j $, we proceed as follows: 1. Substitution and Transformation: Let $ x_i = \tan \theta_i $ for \( \theta_i \in \lef...	<think> Okay, let me try to work through this problem step by step. The question is asking for the largest possible value of n such that there exist n real numbers x₁, x₂, ..., xₙ satisfying \|x_i - x_j\| > (1 + x_i x_j)/100 for all i ≠ j. Hmm, that seems a bit complex, but maybe I can break it down. First, let's unders...	{ "ground_truth": "315", "style": "math_dapo" }	{ "generation_model": "DeepSeek-R1", "pass_rate_72b_tir": 0.0625, "problem_source": "aops_c6_high_school_olympiads" }	5,667	24,172.625
[{"content":"You are a careful mathematician. Solve the following problem. Show your work, then give(...TRUNCATED)	"You are a careful mathematician. Solve the following problem. Show your work, then give the final a(...TRUNCATED)	math_dapo	math	"To solve the problem, we need to find the set \$ S \$ of all complex numbers \$ a \$ such that (...TRUNCATED)	"<think>\nOkay, let's see. I need to solve this problem where we have two equations involving comple(...TRUNCATED)	{ "ground_truth": "111", "style": "math_dapo" }	{"generation_model":"DeepSeek-R1","pass_rate_72b_tir":0.0,"problem_source":"aops_c4_high_school_math(...TRUNCATED)	5,278	23,887.25

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openmath-hard-64

64 competition-style math problems with integer answers, taken from nvidia/OpenMathReasoning (CC-BY-4.0), split cot.

How the problems were chosen

From the cot split, keep problems with an extracted integer answer, a low pass_rate_72b_tir, and an answer that the math_dapo scorer grades correctly when it is given back in \boxed{}; deduplicate by problem text. This gives a pool of candidates, of which 400 were scored.
Score each candidate with Qwen/Qwen3-4B (thinking on, 8192 tokens, 16 samples). 84 of the 400 were never solved.
Draw 64 of those 84.

Step 2 samples, so rebuilding the set gives a different draw. This file is the one copy to use.

Columns

prompt (chat messages), reward_model.ground_truth (the integer answer, scored with the math_dapo style), reference_solution and reference_solution_full (from the source), extra_info (source metadata: generating model, pass_rate_72b_tir, problem source), n_correct (correct out of 16 in step 2, always 0) and mean_response_chars.

Checking a copy

The content hash is md5 over each row's prompt and reward_model as sorted JSON, in row order, first 12 hex characters: cc49109b0cb4.

Downloads last month: 40

Number of rows:

Total file size:

627 kB