problem stringlengths 737 3k | answer stringlengths 2 36 | tokenized_prompt stringlengths 787 3.05k | responses listlengths 4 4 | rewards listlengths 4 4 | mean_reward float64 0 1 |
|---|---|---|---|---|---|
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | 159 | <|im_start|>user
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final... | [
"<think>weise\nOkay, let me try to figure out how to solve this equation: (1/5) log₂x = sin(5πx). The partial response already set up the domain and split it into two intervals, (0,1] and (1,32]. I need to check both of these intervals and count the number of real solutions.\n\nFirst, I remember that the sine funct... | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 64 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think> strife\nOkay, so I need to find a two-digit number x such that for any natural number n, m(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | \frac{2\sqrt{3}}{3} | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>lington\nOkay, let's try to figure out the area of region R. So the problem is about a rhom(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 103 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>geb\nOkay, so I need to figure out the expected value of the rank of the winner in this ten(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 27 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>ucci\nOkay, let's try to solve this problem step by step. First, let me understand what the(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | \frac{4}{3} | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>ғ\nOkay, let me try to figure out how to solve this problem. The problem says that the nat(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 26 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>ucci\nOkay, so I need to find the number of tubular numbers less than 100,000. First, let m(...TRUNCATED) | [
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1,
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] | 0.25 |
"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 103 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>geb\nOkay, let's see. I need to find the expected value of the rank of the winner in this t(...TRUNCATED) | [
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"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | 15 | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>obbled\nOkay, let's see. The problem is about finding the sum of the absolute values of the(...TRUNCATED) | [
1,
1,
0,
1
] | 0.75 |
"You are given a problem and a partial solution.\n\nYour task is to carefully study the partial resp(...TRUNCATED) | \frac{2 + 3\sqrt{2}}{7} | "<|im_start|>user\nYou are given a problem and a partial solution.\n\nYour task is to carefully stud(...TRUNCATED) | ["<think>ยาว\nOkay, so I need to solve this trapezium problem. Let me start by understanding t(...TRUNCATED) | [
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