conversations listlengths 2 2 | question stringlengths 40 3.04k ⌀ | source stringclasses 5
values | id int64 9.51k 49.6k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 57 | prompt_type stringclasses 1
value | 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": "Return your final response within \\boxed{}. Three villages are located in a swampy area. From village $C$, which is equidistant from village $A$ and village $B$, there are straight concrete roads leading to both $A$ and $B$. How can we travel from $A$ to $B$ in the shortest time... | Three villages are located in a swampy area. From village $C$, which is equidistant from village $A$ and village $B$, there are straight concrete roads leading to both $A$ and $B$. How can we travel from $A$ to $B$ in the shortest time if we can travel at speed $v$ on the concrete road and at speed $w$ in the swamp, wh... | 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{Travel via village | rephrase | [
"Rewritten Question: Three villages A, B, and C form an equilateral triangle. Traveling on the roads between any two villages is faster than traveling through the swamp. What is the optimal path to travel from A to B in the shortest time given that speed on the road is \\(v\\) and speed in the swamp is \\(w\\), whe... | [
false,
false
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"",
""
] | {
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"chat_template_applied": true,
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"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"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",
"n_responses": 2
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[
{
"from": "user",
"value": "Let $\\mathbf{a} = \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}$ and $\\mathbf{b} = \\begin{pmatrix} 1 \\\\ 3 \\end{pmatrix}.$ Find the area of the triangle with vertices $\\mathbf{0},$ $\\mathbf{a},$ and $\\mathbf{2b}.$"
},
{
"from": "assistant",
"value": "<think>\nOkay... | null | 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... | 7 | rephrase | [
"Rewritten Question: Find the area of the triangle with vertices $\\mathbf{0},$ $\\mathbf{a} = \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix},$ and $\\mathbf{2b} = \\begin{pmatrix} 2 \\\\ 6 \\end{pmatrix}.$\n\nStep 1: Identify the vectors representing two sides of the triangle.\nThe vectors are $\\mathbf{a} = \\begin{pma... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"model_name": "hosted_vll... | {
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[
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"value": "Given $\\cos (\\pi-\\alpha)= \\frac {4}{5}$, and $\\alpha$ is an angle in the third quadrant, the value of $\\tan 2\\alpha$ is ( ).\n\nA: $ \\frac {3}{4}$\n\nB: $- \\frac {3}{4}$\n\nC: $ \\frac {24}{7}$\n\nD: $- \\frac {24}{7}$"
},
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"value": "<th... | Given $\cos (\pi-\alpha)= \frac {4}{5}$, and $\alpha$ is an angle in the third quadrant, the value of $\tan 2\alpha$ is ( ).
A: $ \frac {3}{4}$
B: $- \frac {3}{4}$
C: $ \frac {24}{7}$
D: $- \frac {24}{7}$ | 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... | C | rephrase | [
"Rewritten Question: Given $\\cos(\\pi - \\alpha) = \\frac{4}{5}$ and $\\alpha$ is in the third quadrant, find $\\tan(2\\alpha)$.\n\nStep 1: Use the identity for cosine of a difference from pi.\n$\\cos(\\pi - \\alpha) = -\\cos(\\alpha)$. Therefore, $-\\cos(\\alpha) = \\frac{4}{5}$ which means $\\cos(\\alpha) = -\\f... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
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"value": "Given the descriptions about the function $f(x)=(x^{2}-2x+2)e^{x}- \\frac{e}{3}x^{3}$, the incorrect one is $(\\quad\\quad)$.\nA: No maximum value\nB: The maximum value is $2$\nC: The minimum value is $\\frac{2e}{3}$\nD: The graph of the function $g(x)=f(x)-2$ intersects the $x$-... | Given the descriptions about the function $f(x)=(x^{2}-2x+2)e^{x}- \frac{e}{3}x^{3}$, the incorrect one is $(\quad\quad)$.
A: No maximum value
B: The maximum value is $2$
C: The minimum value is $\frac{2e}{3}$
D: The graph of the function $g(x)=f(x)-2$ intersects the $x$-axis at two points | 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: Determine which statement about the function \\( f(x) = (x^2 - 2x + 2)e^x - \\frac{e}{3}x^3 \\) is incorrect among:\nA: No maximum value\nB: The maximum value is 2\nC: The minimum value is \\(\\frac{2e}{3}\\)\nD: The graph of the function \\( g(x) = f(x) - 2 \\) intersects the x-axis at two poi... | [
false,
false
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"",
""
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"api_url": "http://10.32.36.225:9080/v1",
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"chat_template_applied": true,
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"n": 1,
"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
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[
{
"from": "user",
"value": "Consider the set of all ordered $6$-tuples of nonnegative integers $(a,b,c,d,e,f)$ such that \\[a+2b+6c+30d+210e+2310f=2^{15}.\\] In the tuple with the property that $a+b+c+d+e+f$ is minimized, what is the value of $c$?\n\n\n[i]2021 CCA Math Bonanza Tiebreaker Round #1[/i]"
},
... | Consider the set of all ordered $6$-tuples of nonnegative integers $(a,b,c,d,e,f)$ such that \[a+2b+6c+30d+210e+2310f=2^{15}.\] In the tuple with the property that $a+b+c+d+e+f$ is minimized, what is the value of $c$?
[i]2021 CCA Math Bonanza Tiebreaker Round #1[/i] | 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... | 1 | rephrase | [
"Rewritten Question: Find the value of \\( c \\) in the 6-tuple \\((a, b, c, d, e, f)\\) of nonnegative integers that minimizes \\( a + b + c + d + e + f \\) given \\( a + 2b + 6c + 30d + 210e + 2310f = 32768 \\).\n\nStep-by-step solution:\n1. We need to minimize \\( a + b + c + d + e + f \\). To do this, we should... | [
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",
"n_responses": 2
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[
{
"from": "user",
"value": "Given a sequence $\\{a_n\\}$ where the sum of the first $n$ terms $S_n = 2a_n - 1$, find the general term formula for $a_n$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I have this sequence {a_n} where the sum of the first n terms, S_n, is given by ... | Given a sequence $\{a_n\}$ where the sum of the first $n$ terms $S_n = 2a_n - 1$, find the general term formula for $a_n$. | 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... | 2^{n-1 | rephrase | [
"Rewritten Question: Find the general term formula for $a_n$ given that the sum of the first $n$ terms $S_n = 2a_n - 1$.\n\nStep 1: Express $S_{n-1}$ using the given relation.\nSince $S_n = 2a_n - 1$, we can write $S_{n-1} = 2a_{n-1} - 1$ (for $n \\geq 2$).\n\nStep 2: Use the definition of $S_n$ and $S_{n-1}$ to ex... | [
false,
false
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"",
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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
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[
{
"from": "user",
"value": "Problem 3. How many natural numbers $n>1$ exist, for which there are $n$ consecutive natural numbers, the sum of which is equal to 2016?"
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how many natural numbers n > 1 exist such that there ar... | Problem 3. How many natural numbers $n>1$ exist, for which there are $n$ consecutive natural numbers, the sum of which is equal to 2016? | 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... | 5 | rephrase | [
"Rewritten Question: Find how many natural numbers \\( n > 1 \\) exist such that the sum of \\( n \\) consecutive natural numbers equals 2016.\n\nTo solve this problem, let's consider a sequence of \\( n \\) consecutive natural numbers starting from some number \\( k \\). The numbers can be written as \\( k, k+1, k... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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",
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[
{
"from": "user",
"value": "$ABCDEF$ is a hexagon inscribed in a circle such that the measure of $\\angle{ACE}$ is $90^{\\circ}$. What is the average of the measures, in degrees, of $\\angle{ABC}$ and $\\angle{CDE}$?\n\n[i]2018 CCA Math Bonanza Lightning Round #1.3[/i]"
},
{
"from": "assistant",
... | $ABCDEF$ is a hexagon inscribed in a circle such that the measure of $\angle{ACE}$ is $90^{\circ}$. What is the average of the measures, in degrees, of $\angle{ABC}$ and $\angle{CDE}$?
[i]2018 CCA Math Bonanza Lightning Round #1.3[/i] | 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... | 45 | rephrase | [
"Rewritten Question: In a hexagon $ABCDEF$ inscribed in a circle with $\\angle ACE = 90^\\circ$, find the average of $\\angle ABC$ and $\\angle CDE$.\n\nStep-by-Step Solution:\n1. Since $\\angle ACE = 90^\\circ$, triangle $ACE$ is a right triangle with hypotenuse being the diameter of the circumscribed circle.\n2. ... | [
false,
false
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"",
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"api_url": "http://10.32.36.225:9080/v1",
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"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
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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": "Return your final response within \\boxed{}. If $c$ is a constant such that $x^2+100x+c$ is equal to the square of a binomial, then what is $c$?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: If c is a constant such that x² + 100x + c... | If $c$ is a constant such that $x^2+100x+c$ is equal to the square of a binomial, then what is $c$? | 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... | 2500 | rephrase | [
"Rewritten Question: If \\( x^2 + 100x + c \\) is equal to the square of a binomial, find \\( c \\).\n\nTo solve this problem, we need to express \\( x^2 + 100x + c \\) as the square of a binomial.\n\nStep-by-step solution:\n1. A binomial squared can be written in the form \\( (x + a)^2 = x^2 + 2ax + a^2 \\).\n2. B... | [
false,
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"",
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"api_url": "http://10.32.36.225:9080/v1",
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"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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"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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