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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[
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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 ( )."
},
{
"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.",
"role": "system"
},
{
"content": "There are three individuals nam... | 336 | original | [
"To determine the number of different ways three individuals (A, B, and C) can stand on a 7-step stairway where each step can hold up to two people, we need to consider all possible distributions of these three people across the seven steps.\n\nWe will break this down into cases based on how many people are on each... | [
false,
false
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"",
""
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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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"from": "assistant",
"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.",
"role": "system"
},
{
"content": "In a regular $n$-sided polygon,... | B | original | [
"To find the number of sides \\( n \\) of a regular polygon where each exterior angle measures \\( 45^\\circ \\), we can use the property that the sum of all exterior angles of any polygon is \\( 360^\\circ \\). For a regular polygon, all exterior angles are equal, so if each exterior angle is \\( 45^\\circ \\), th... | [
false,
false
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"",
""
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
{
"from": "user",
"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.",
"role": "system"
},
{
"content": "Let $S$ be a set of points $(x,... | E | original | [
"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 will consider all possible cases where two of these quan... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
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"n": 2,
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"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"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 $k$."
},
{
"from": "assistant",
"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.",
"role": "system"
},
{
"content": "If the solution set of the ineq... | \left( \dfrac{2}{3}, \dfrac{3}{4} \right] | original | [
"To determine the range of \\( k \\) such that the inequality \\( |x - 1| < kx \\) has exactly three integer solutions, we need to analyze this inequality for different values of \\( x \\).\n\n### Case 1: \\( x \\geq 1 \\)\n\nFor \\( x \\geq 1 \\), the absolute value can be removed as follows:\n\\[ |x - 1| = x - 1 ... | [
false,
false
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"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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} |
[
{
"from": "user",
"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.",
"role": "system"
},
{
"content": "If the terminal side of angle $... | A | original | [
"To determine \\(\\sin\\theta\\) given that the terminal side of angle \\(\\theta\\) passes through the point \\(\\left(-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)\\), we need to use the definition of sine in terms of coordinates on the unit circle.\n\nThe sine of an angle is defined as the y-coordinate of the poin... | [
false,
false
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"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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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*"
},
{
"from": "assistant",
"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.",
"role": "system"
},
{
"content": "Return your final response with... | \text{No such positive integers exist} | original | [
"To 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, we will analyze the conditions step by step.\n\nFirst, let's consider the smallest possible values for \\( n \\).\n\n### Case 1: \\( n = p \\) where ... | [
false,
false
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"",
""
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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} |
[
{
"from": "user",
"value": "Given $a^{m}=2$ and $a^{n}=8$, find the value of $a^{m}a^{n}$."
},
{
"from": "assistant",
"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.",
"role": "system"
},
{
"content": "Given $a^{m}=2$ and $a^{n}=8$, ... | 16 | original | [
"To find the value of \\( a^m a^n \\), we can use the properties of exponents. Specifically, we know that when multiplying powers with the same base, we add their exponents.\n\nWe are given:\n\\[ a^m = 2 \\]\n\\[ a^n = 8 \\]\n\nWe need to calculate \\( a^m a^n \\). Using the property of exponents:\n\n\\[\na^m a^n =... | [
false,
false
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"",
""
] | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given positive integers $m$ and $n$ so there is a chessboard with $mn$ $1 \\times 1$ grids. Colour the grids into red and blue (Grids that have a common side are not the same colour and the grid in the left corner at the bottom... | Given positive integers $m$ and $n$ so there is a chessboard with $mn$ $1 \times 1$ grids. Colour the grids into red and blue (Grids that have a common side are not the same colour and the grid in the left corner at the bottom is red). Now the diagnol that goes from the left corner at the bottom to the top righ... | 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.",
"role": "system"
},
{
"content": "Return your final response with... |
\begin{cases}
\sqrt{(m-1)^2 + (n-1)^2} & \text{if } m \text{ and } n \text{ are both even or both odd}, \\
\frac{\sqrt{(m-1)^2 + (n-1)^2}}{2} & \text{otherwise}.
\end{cases}
| original | [
"To solve this problem, we need to understand the coloring pattern on the chessboard and how it affects the diagonal.\n\nFirst, let's consider the coloring pattern:\n- The bottom-left grid is colored red.\n- Adjacent grids cannot be the same color, so if a grid is red, its adjacent grid must be blue, and vice versa... | [
false,
false
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"",
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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) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
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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 | ["To solve this problem, we need to follow a few steps:\n\n1. Calculate the total number of students(...TRUNCATED) | [
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""
] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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