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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"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 | [
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"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | \text{Travel via village | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and going really deep into detail about how I should solve this.\n\n1. **Understand the Problem**: The three villages form a triangle with Village C being equidistant from Villages A and B. We need to find the optimal path for traveling from Vi... | [
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[
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"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 $\\mathbf{2b}.$"
},
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"value": "<think>\nOkay... | null | null | null | [
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"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 7 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n1. **Understand the Problem:**\n - We are given two vectors, \\(\\mathbf{a}\\) and \\(\\mathbf{b}\\).\n - The points involved are \\(\\mathbf{0}\\) (the origin), \\(\\mathbf{a... | [
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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 like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | C | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n1. **Understanding Given Information:** The given information is $\\cos(\\pi - \\alpha) = \\frac{4}{5}$. We know from trigonometric identities that $\\cos(\\pi - x) = -\\cos(x)$, ... | [
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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 like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | B | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n1. **Analyze the Function \\( f(x) = (x^2 - 2x + 2)e^x - \\frac{e}{3} x^3 \\):**\n - We need to find critical points by taking the derivative of \\( f(x) \\).\n - Determine if... | [
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[
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"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 solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 1 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step 1: Understanding the Equation\nThe equation given is:\n\\[ a + 2b + 6c + 30d + 210e + 2310f = 2^{15}. \\]\nWe need to find the values of \\(a\\), \\(b\\), \\(c\\), \\(d\\... | [
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[
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"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 $a_n$."
},
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"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 | [
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"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 2^{n-1 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\nStep 1: Understand the given information.\n- We are given a sequence \\(\\{a_n\\}\\) whose sum of the first \\(n\\) terms \\(S_n = 2a_n - 1\\).\n- This means \\(S_n\\) can be expr... | [
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[
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"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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"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 solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 5 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Understanding the Problem:\n- We need to find natural numbers \\( n > 1 \\) such that there exists a sequence of \\( n \\) consecutive natural numbers whose sum equals 2016.\n... | [
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