conversations listlengths 2 2 | question stringlengths 12 5.4k ⌀ | source stringclasses 8
values | id int64 50 49.9k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 1.36k ⌀ | prompt_type stringclasses 2
values | model_responses__example_annotation listlengths 2 2 | model_responses__example_annotation__finish_reason_length_flags listlengths 2 2 | model_responses__example_annotation__length_partial_responses listlengths 2 2 | prompt__example_annotation__metadata dict | model_responses__example_annotation__metadata dict |
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"value": "There are three individuals named A, B, and C standing on a stairway that has 7 steps. If each step can have at most 2 people, and the positions of the people on the same step are not distinguished, the number of different ways they can stand is ( )."
},
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"from": "assist... | There are three individuals named A, B, and C standing on a stairway that has 7 steps. If each step can have at most 2 people, and the positions of the people on the same step are not distinguished, the number of different ways they can stand is ( ). | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | 336 | original_rationalized | [
"To find the total number of different ways the three individuals can stand on the 7-step stairway, we need to consider how many people can occupy each step and the possible distributions.\n\n1. **Case Analysis**:\n - All three individuals on different steps.\n - Two individuals on one step, and one individual ... | [
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"",
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"value": "In a regular $n$-sided polygon, each exterior angle measures $45^{\\circ}$. Find the value of $n$.\n\nA: $7$\n\nB: $8$\n\nC: $9$\n\nD: $10$"
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"value": "<think>\nOkay, so I need to find the number of sides in a regular polygon where each exteri... | In a regular $n$-sided polygon, each exterior angle measures $45^{\circ}$. Find the value of $n$.
A: $7$
B: $8$
C: $9$
D: $10$ | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | B | original_rationalized | [
"To find the number of sides \\( n \\) of a regular polygon where each exterior angle measures \\( 45^\\circ \\), we can use the property of polygons which states that the sum of all exterior angles of any polygon is always \\( 360^\\circ \\). \n\nFor a regular polygon, all exterior angles are equal. Therefore, if ... | [
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"",
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[
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"value": "Let $S$ be a set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3,~x+2,$ and $y-4$ are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for $S?$\n$\\textbf{(A)}\\ \\... | Let $S$ be a set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3,~x+2,$ and $y-4$ are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for $S?$
$\textbf{(A)}\ \text{a single point} \qquad\textbf{(B)}\ \te... | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | E | original_rationalized | [
"To determine which of the given options correctly describes the set \\( S \\), we need to analyze the conditions provided:\n\n1. Two of the three quantities \\( 3, x+2, y-4 \\) are equal.\n2. The third quantity is no greater than this common value.\n\nWe can consider the possible cases where two of these quantitie... | [
false,
false
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"",
""
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[
{
"from": "user",
"value": "If the solution set of the inequality $|\\,x - 1| < kx$ regarding $x$ contains exactly three integers, find the range of the real number $k$."
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"value": "<think>\nOkay, so I need to solve this inequality |x - 1| < kx and find the range of k su... | If the solution set of the inequality $|\,x - 1| < kx$ regarding $x$ contains exactly three integers, find the range of the real number $k$. | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \left( \dfrac{2}{3}, \dfrac{3}{4} \right] | original_rationalized | [
"To determine the range of \\( k \\) such that the inequality \\( |x - 1| < kx \\) has exactly three integer solutions, we need to analyze the inequality for different values of \\( x \\).\n\nFirst, consider the two cases for the absolute value expression:\n\n**Case 1:** \\( x \\geq 1 \\)\n\nHere, \\( |x - 1| = x -... | [
false,
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"",
""
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[
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"value": "If the terminal side of angle $\\theta$ passes through the point $\\left(-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)$, then $\\sin\\theta=$ （ ）\nA: $\\frac{1}{2}$\nB: $\\frac{1}{3}$\nC: $\\frac{\\sqrt{3}}{2}$\nD: $\\frac{\\sqrt{2}}{2}$"
},
{
"from": "assistant",
"val... | If the terminal side of angle $\theta$ passes through the point $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$, then $\sin\theta=$ （ ）
A: $\frac{1}{2}$
B: $\frac{1}{3}$
C: $\frac{\sqrt{3}}{2}$
D: $\frac{\sqrt{2}}{2}$ | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | A | original_rationalized | [
"To find \\(\\sin \\theta\\) given that the terminal side of angle \\(\\theta\\) passes through the point \\(\\left(-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)\\), we can use the definition of sine in terms of coordinates on the unit circle.\n\nThe sine of an angle in a coordinate system is defined as the y-coordin... | [
false,
false
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"",
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[
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"from": "user",
"value": "Return your final response within \\boxed{}. Determine all positive integers $n>1$ such that for any divisor $d$ of $n,$ the numbers $d^2-d+1$ and $d^2+d+1$ are prime.\n\n*Lucian Petrescu*"
},
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"value": "<think>\nOkay, so I need to find... | Determine all positive integers $n>1$ such that for any divisor $d$ of $n,$ the numbers $d^2-d+1$ and $d^2+d+1$ are prime.
*Lucian Petrescu* | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \text{No such positive integers exist} | original_rationalized | [
"To determine if there exist positive integers \\( n > 1 \\) such that for any divisor \\( d \\) of \\( n \\), both \\( d^2 - d + 1 \\) and \\( d^2 + d + 1 \\) are prime, we can start by examining small values of \\( n \\).\n\nFirst, let's consider \\( n = p \\), where \\( p \\) is a prime number. The divisors of \... | [
false,
false
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"",
""
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[
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"from": "user",
"value": "Given $a^{m}=2$ and $a^{n}=8$, find the value of $a^{m}a^{n}$."
},
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"value": "<think>Okay, let's see. The problem says that \\( a^m = 2 \\) and \\( a^n = 8 \\), and we need to find the value of \\( a^m \\times a^n \\). Hmm, so first, let me recal... | Given $a^{m}=2$ and $a^{n}=8$, find the value of $a^{m}a^{n}$. | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | 16 | original_rationalized | [
"We are given \\( a^m = 2 \\) and \\( a^n = 8 \\). We need to find the value of \\( a^m a^n \\).\n\nFirst, let's express \\( a^m a^n \\) using the properties of exponents:\n\\[ a^m a^n = a^{m+n}. \\]\n\nNow we know from the problem statement that:\n\\[ a^m = 2 \\]\nand \n\\[ a^n = 8. \\]\n\nSo,\n\\[ a^m a^n = 2 \\c... | [
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[{"from":"user","value":"Return your final response within \\boxed{}. Given positive integers $m$ (...TRUNCATED) | "Given positive integers $m$ and $n$ so there is a chessboard with $mn$ $1 \\times 1$ grids.(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | "\n\\begin{cases}\n\\sqrt{(m-1)^2 + (n-1)^2} & \\text{if } m \\text{ and } n \\text{ are both even o(...TRUNCATED) | original_rationalized | ["To solve this problem, we need to understand the coloring pattern of the chessboard and how it aff(...TRUNCATED) | [
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"",
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] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
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"n_responses": 2
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[{"from":"user","value":"Return your final response within \\boxed{}. Let \\( f: \\mathbb{Q} \\right(...TRUNCATED) | "Let \\( f: \\mathbb{Q} \\rightarrow \\mathbb{Q} \\) be a function such that for any \\( x, y \\in \(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | Yes | original_rationalized | ["To determine if there must exist a constant \\( c \\) such that \\( f(x) - cx \\) is an integer fo(...TRUNCATED) | [
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"backend": "litellm",
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[{"from":"user","value":"There are 10000 students in the particular school out of that 60% students (...TRUNCATED) | null | tiger_lab_math | 31,371 | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | C | original_rationalized | ["Let's break down the problem step by step:\n\n1. First, we need to find the total number of studen(...TRUNCATED) | [
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"",
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] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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