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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"from": "user",
"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 336 | rephrase | [
"Rewritten Question: \n3 individuals (A, B, C) stand on 7 steps where each step can have at most 2 people, and positions on the same step are indistinguishable. Find the number of different ways they can stand.\n\nStep 1: Consider all possible distributions of the 3 individuals across the 7 steps.\n- All 3 on one s... | [
false,
false
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"",
""
] | {
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"n": 2,
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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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | B | rephrase | [
"Rewritten Question: Each exterior angle of a regular $n$-sided polygon measures $45^{\\circ}$. Find $n$.\n\nStep 1: Recall that the sum of all exterior angles of any polygon is $360^{\\circ}$.\nStep 2: Since the polygon is regular, all exterior angles are equal. Let each exterior angle be $x$ degrees. Therefore, f... | [
false,
false
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"",
""
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"model_name": "hosted_vll... | {
"backend": "litellm",
"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | E | rephrase | [
"Rewritten Question: \nGiven points $(x, y)$ where two out of the three values $3$, $x+2$, and $y-4$ are equal, and the remaining value is no greater than these two, describe the geometric figure formed by all such points.\n\nStep 1: Identify the conditions.\nThere are three possible cases:\n1. $3 = x + 2$ and $y -... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
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"chat_template_applied": true,
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"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \left( \dfrac{2}{3}, \dfrac{3}{4} \right] | rephrase | [
"Rewritten Question: Find the range of \\( k \\) such that the inequality \\( |x - 1| < kx \\) has exactly three integer solutions for \\( x \\).\n\nTo solve this problem, we need to consider the two cases of the absolute value expression:\n\n**Case 1:** When \\( x \\geq 1 \\), the inequality becomes:\n\\[ x - 1 < ... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"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 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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | A | rephrase | [
"Rewritten Question: Find $\\sin\\theta$ if the terminal side of angle $\\theta$ passes through the point $\\left(-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)$.\n\nStep 1: Identify the coordinates given for the point on the terminal side of the angle.\nThe coordinates are $\\left(-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"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": "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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \text{No such positive integers exist} | rephrase | [
"Rewritten Question: Find all positive integers \\( n > 1 \\) such that for any divisor \\( d \\) of \\( n \\), both \\( d^2 - d + 1 \\) and \\( d^2 + d + 1 \\) are prime.\n\nStep-by-step solution:\n\n1. **Consider small values of \\( n \\):**\n - If \\( n = 2 \\), the divisors are \\( 1 \\) and \\( 2 \\).\n ... | [
false,
false
] | [
"",
""
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"top_p": 0.8
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"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 16 | rephrase | [
"Rewritten Question: Find the value of \\(a^{m}a^{n}\\) given \\(a^{m}=2\\) and \\(a^{n}=8\\).\n\nStep 1: Recognize that \\(a^m \\cdot a^n = a^{m+n}\\).\nStep 2: Substitute the given values into the expression.\nStep 3: Calculate the product of \\(a^m\\) and \\(a^n\\).\n\n<answer>\n\\(2 \\cdot 8 = 16\\)\n</answer>"... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
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"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
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"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
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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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... |
\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}
| rephrase | [
"Rewritten Question: On an \\( mn \\)-grid chessboard, alternate coloring starts with a red square at the bottom-left corner such that no two adjacent squares share the same color. The main diagonal is colored alternately between red and blue. Calculate the total length of the red segments on this diagonal.\n\nTo s... | [
false,
false
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"",
""
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"backend": "litellm",
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"n": 2,
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"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":"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | Yes | rephrase | ["Rewritten Question: Given \\( f: \\mathbb{Q} \\rightarrow \\mathbb{Q} \\) such that \\( f(x+y) - f(...TRUNCATED) | [
false,
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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
} |
[{"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | rephrase | ["Rewritten Question: \n- Total students = 10000\n- Percentage liking science = 60%\n- Percentage of(...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) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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