conversations listlengths 2 2 | question stringlengths 40 3.04k ⌀ | source stringclasses 5
values | id int64 9.51k 49.6k ⌀ | prompt listlengths 2 2 | 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 |
|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To determine the fastest way to travel from village \\( A \\) to village \\( B \\), let's consider different scenarios.\n\n1. **Direct Path Through Swamp:**\n - Travel directly through the swamp from \\( A \\) to \\( B \\).\n - The distance traveled would be the direct line segment connecting \\( A \\) and \\(... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To find the area of the triangle with vertices at \\(\\mathbf{0}\\), \\(\\mathbf{a}\\), and \\(\\mathbf{2b}\\), we can use the formula involving the determinant of vectors.\n\nFirstly, let's express the coordinates:\n\\[\n\\mathbf{a} = \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}, \\quad \\mathbf{b} = \\begin{pmatrix}... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"from": "user",
"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: $- \\frac {24}{7}$"
},
{
"from": "assistant",
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"Given that $\\cos(\\pi - \\alpha) = \\frac{4}{5}$, we can use trigonometric identities to determine the values of other trigonometric functions related to $\\alpha$. \n\nFirstly, let's simplify the given expression:\n1. We know from the cosine identity that $\\cos(\\pi - \\alpha) = -\\cos(\\alpha)$.\n Therefore,... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"from": "user",
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To determine which description about the function \\( f(x) = (x^2 - 2x + 2)e^x - \\frac{e}{3}x^3 \\) is incorrect, we need to analyze its behavior, including finding critical points and understanding the nature of these points.\n\n**Step 1: Find the first derivative \\( f'(x) \\)**\n\n\\[ f(x) = (x^2 - 2x + 2)e^x ... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To solve the problem, we need to minimize \\(a + b + c + d + e + f\\) while satisfying the equation \\(a + 2b + 6c + 30d + 210e + 2310f = 2^{15}\\). Let's start by expressing \\(2^{15}\\):\n\n\\[2^{15} = 32768\\]\n\nWe will maximize the coefficients with the largest values first because they contribute more signif... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To find the general term \\(a_n\\) of the sequence \\(\\{a_n\\}\\), we start from the given information: the sum of the first \\(n\\) terms is \\(S_n = 2a_n - 1\\).\n\n**Step 1: Express \\(S_{n-1}\\)**\nFirstly, consider the sum of the first \\(n-1\\) terms:\n\\[ S_{n-1} = 2a_{n-1} - 1 \\]\n\n**Step 2: Relate \\(S... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[
{
"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?"
},
{
"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 like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | alternative | [
"To solve this problem, we need to determine how many natural numbers \\( n > 1 \\) satisfy the condition that there exist \\( n \\) consecutive natural numbers whose sum equals 2016.\n\nLet's denote these \\( n \\) consecutive natural numbers as:\n\\[ a, a+1, a+2, \\ldots, a+n-1 \\]\n\nThe sum of these \\( n \\) c... | [
false,
false
] | [
"",
""
] | {
"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",
"n_responses": 2
} |
[{"from":"user","value":"$ABCDEF$ is a hexagon inscribed in a circle such that the measure of $\\ang(...TRUNCATED) | "$ABCDEF$ is a hexagon inscribed in a circle such that the measure of $\\angle{ACE}$ is $90^{\\circ}(...TRUNCATED) | null | null | [{"content":"You like to find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | alternative | ["To solve the problem, we need to analyze the given information about the hexagon \\(ABCDEF\\) insc(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.225:9080/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":"Return your final response within \\boxed{}. If $c$ is a constant such that(...TRUNCATED) | "If $c$ is a constant such that $x^2+100x+c$ is equal to the square of a binomial, then what is $c$?(...TRUNCATED) | null | null | [{"content":"You like to find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | alternative | ["To solve this problem, we need to determine the value of \\( c \\) such that the quadratic express(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.225:9080/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":"Given an increasing sequence $\\{a_{n}\\}$ where all terms are positive int(...TRUNCATED) | "Given an increasing sequence $\\{a_{n}\\}$ where all terms are positive integers, the sum of the fi(...TRUNCATED) | null | null | [{"content":"You like to find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | alternative | ["To solve this problem, we need to determine the form of the sequence \\(\\{a_n\\}\\) given that \\(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.225:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 2