prompt stringlengths 174 1.03k | ground_truth stringlengths 1 6 | verifier_name stringclasses 1
value | rollout_text stringlengths 10 33.1k | rollout_tokens listlengths 3 8.19k | rollout_is_correct bool 2
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<|im_start|>user
Determine the number of all positive integers which cannot be written in the form $80k + 3m$, where $k, m \in \mathbb{N} = \{0, 1, 2, \ldots\}$.
Please reason step by step, and put your final answer within \boxed{}<|im_end|>
<|im_start|>assistant
| 79 | math | Assistant: Alright, I have this problem to solve:
**Determine the number of all positive integers which cannot be written in the form \(80k + 3m\), where \(k, m \in \mathbb{N} = \{0, 1, 2, \ldots\}\).**
First, let's understand what's being asked. We need to find all positive integers that **cannot** be expressed as \... | [
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"text": "Assistant: Alright, I have this problem to solve:\n\n**Determine the number of all positive integers which cannot be written in the form \\( 80k + 3m \\), where \\( k, m \\in \\mathbb{N} = \\{0, 1, 2, \\ldots\\} \\).**\n\nFirst, let's understand what the problem is asking. We... | [
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"<|im_start|>user\nDetermine the number of all positive integers which cannot be written in the form(...TRUNCATED) | 79 | math | "Assistant: Alright, I have this problem to solve:\n\n**Determine the number of all positive integer(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,311,11625,1447,334,35,24308,279,1372,315,678,6785,25780,892,4157(...TRUNCATED) | false | [{"is_correct":true,"text":"Assistant: Alright, I have this problem to solve:\n\n**Determine the num(...TRUNCATED) | [
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"<|im_start|>user\nA cube with $3$-inch edges is made using $27$ cubes with $1$-inch edges. Nineteen(...TRUNCATED) | 14 | math | "Assistant: Alright, I have this problem about a larger cube made up of smaller cubes. Let's break i(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,911,264,8131,23739,1865,705,315,9155,54104,13,6771,594,1438,432,(...TRUNCATED) | true | [{"is_correct":false,"text":"Assistant: Alright, I have this problem about a larger cube made up of (...TRUNCATED) | [
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"<|im_start|>user\nA cube with $3$-inch edges is made using $27$ cubes with $1$-inch edges. Nineteen(...TRUNCATED) | 14 | math | "Assistant: Alright, I have this problem about a larger cube made up of smaller cubes. Let's break i(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,911,264,8131,23739,1865,705,315,9155,54104,13,6771,594,1438,432,(...TRUNCATED) | false | [{"is_correct":true,"text":"Assistant: Alright, I have this problem about a larger cube made up of s(...TRUNCATED) | [
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"<|im_start|>user\nSuppose $P(x)$ is a degree $n$ monic polynomial with integer coefficients such th(...TRUNCATED) | 50 | math | "Assistant: Alright, I have这个问题要解决。首先，我需要理解题目的意思。\n\n**(...TRUNCATED) | [71703,25,97593,11,358,614,105073,30534,100638,1773,101140,3837,35946,85106,101128,33872,100466,1003(...TRUNCATED) | true | [{"is_correct":false,"text":"Assistant: Alright, I have this problem to solve:\n\n*Suppose \\( P(x) (...TRUNCATED) | [
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"<|im_start|>user\nSuppose $P(x)$ is a degree $n$ monic polynomial with integer coefficients such th(...TRUNCATED) | 50 | math | "Assistant: Alright, I have this problem to solve:\n\n*Suppose \\( P(x) \\) is a degree \\( n \\) mo(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,311,11625,1447,9,10048,2900,17767,393,2075,8,1124,8,374,264,8381(...TRUNCATED) | false | [{"is_correct":false,"text":"Assistant: Alright, I have this problem about a polynomial \\( P(x) \\)(...TRUNCATED) | [
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"<|im_start|>user\nFind the number of ordered triples of integers \\((a, b, c)\\), with \\(a \\ge 2\(...TRUNCATED) | 2 | math | "Assistant: Alright, I have this problem to solve:\n\n**Find the number of ordered triples of intege(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,311,11625,1447,334,9885,279,1372,315,11457,88561,315,25780,1124,(...TRUNCATED) | true | [{"is_correct":true,"text":"Assistant: Alright, I have this problem to solve:\n\n**Find the number o(...TRUNCATED) | [
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"<|im_start|>user\nFind the number of ordered triples of integers \\((a, b, c)\\), with \\(a \\ge 2\(...TRUNCATED) | 2 | math | "Assistant: Alright, I have this problem to solve:\n\n**Find the number of ordered triples of intege(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,311,11625,1447,334,9885,279,1372,315,11457,88561,315,25780,1124,(...TRUNCATED) | false | [{"is_correct":true,"text":"Assistant: Alright, I have this problem to solve:\n\n**Find the number o(...TRUNCATED) | [
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"<|im_start|>user\nA \\(4\\times 4\\times h\\) rectangular box contains a sphere of radius \\(2\\) a(...TRUNCATED) | 11 | math | "Assistant: Alright, I have this problem about a \\(4 \\times 4 \\times h\\) rectangular box contain(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,911,264,17767,19,1124,15136,220,19,1124,15136,305,57758,51424,37(...TRUNCATED) | true | [{"is_correct":true,"text":"Assistant: Alright, I have this geometry problem about a \\(4 \\times 4 (...TRUNCATED) | [
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"<|im_start|>user\nA \\(4\\times 4\\times h\\) rectangular box contains a sphere of radius \\(2\\) a(...TRUNCATED) | 11 | math | "Assistant: Alright, I have this problem about a \\(4 \\times 4 \\times h\\) rectangular box contain(...TRUNCATED) | [71703,25,97593,11,358,614,419,3491,911,264,17767,19,1124,15136,220,19,1124,15136,305,57758,51424,37(...TRUNCATED) | false | [{"is_correct":true,"text":"Assistant: Alright, I have this problem about a \\(4 \\times 4 \\times h(...TRUNCATED) | [
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