messages listlengths 2 2 | instruction_seed stringlengths 43 1.39k | response_seed stringlengths 43 1.39k | _source stringclasses 1
value | gpt41_mini_response stringlengths 10.4k 32.3k | __original_row_idx int64 616 63.1k | length int64 10.4k 32.3k | ms_id int64 38 3.94k | reasoning sequencelengths 16 16 | deepseek_solution sequencelengths 16 16 | final_reasoning_trace sequencelengths 16 16 | _majority_responses sequencelengths 8 8 | verified_final_reasoning_trace stringlengths 12.1k 80k | conversations listlengths 2 2 |
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[{"content":"Find the function $f(x)$ such that\n\\[f(f(x)) = f(x) + \\sqrt{x}.\\]","role":"user"},{(...TRUNCATED) | Find the function $f(x)$ such that
\[f(f(x)) = f(x) + \sqrt{x}.\] | Find the function $f(x)$ such that
\[f(f(x)) = f(x) + \sqrt{x}.\] | ai2-adapt-dev/openmath-2-math | "Given the functional equation:\n\\[\nf(f(x)) = f(x) + \\sqrt{x}.\n\\]\n\nWe want to find all functi(...TRUNCATED) | 28,340 | 16,106 | 1,771 | ["Okay, so I need to find a function f(x) such that when I apply f to itself, I get f(x) plus the sq(...TRUNCATED) | ["To find the function \\( f(x) \\) such that \\( f(f(x)) = f(x) + \\sqrt{x} \\), we start by consid(...TRUNCATED) | ["<think>\nOkay, so I need to find a function f(x) such that when I apply f to itself, I get f(x) pl(...TRUNCATED) | ["<think>\nOkay, so I need to find a function f(x) such that when I apply it twice, I get f(x) plus (...TRUNCATED) | "<think>\nOkay, so I need to find a function f(x) such that when I apply f to itself, f(f(x)), it eq(...TRUNCATED) | [{"from":"human","value":"Find the function $f(x)$ such that\n\\[f(f(x)) = f(x) + \\sqrt{x}.\\]"},{"(...TRUNCATED) |
[{"content":"What is the largest positive integer $n$ such that $n^2+2n+2018$ is divisible by $37$?"(...TRUNCATED) | What is the largest positive integer $n$ such that $n^2+2n+2018$ is divisible by $37$? | What is the largest positive integer $n$ such that $n^2+2n+2018$ is divisible by $37$? | ai2-adapt-dev/openmath-2-math | "We want to find the largest positive integer \\( n \\) such that\n\n\\[\n37 \\mid n^2 + 2n + 2018.\(...TRUNCATED) | 62,734 | 13,471 | 3,920 | ["Alright, so I need to find the largest positive integer n such that n² + 2n + 2018 is divisible b(...TRUNCATED) | ["To find the largest positive integer \\( n \\) such that \\( n^2 + 2n + 2018 \\) is divisible by 3(...TRUNCATED) | ["<think>\nAlright, so I need to find the largest positive integer n such that n² + 2n + 2018 is di(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest positive integer n such that n² + 2n + 2018 is divis(...TRUNCATED) | "<think>\nOkay, so I need to find the largest positive integer n such that n² + 2n + 2018 is divisi(...TRUNCATED) | [{"from":"human","value":"What is the largest positive integer $n$ such that $n^2+2n+2018$ is divisi(...TRUNCATED) |
[{"content":"Let $a$ and $b$ be the two distinct solutions to the equation $x^2+5x-6=\\frac{1}{x}$. (...TRUNCATED) | "Let $a$ and $b$ be the two distinct solutions to the equation $x^2+5x-6=\\frac{1}{x}$. If $a>b$, wh(...TRUNCATED) | "Let $a$ and $b$ be the two distinct solutions to the equation $x^2+5x-6=\\frac{1}{x}$. If $a>b$, wh(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\nx^2 + 5x - 6 = \\frac{1}{x}\n\\]\nwith \\(a\\) and \\(b\\) as the two dis(...TRUNCATED) | 2,238 | 10,858 | 139 | ["Alright, so I have this equation to solve: \\(x^2 + 5x - 6 = \\frac{1}{x}\\). The problem states t(...TRUNCATED) | ["To solve the equation \\(x^2 + 5x - 6 = \\frac{1}{x}\\), we first eliminate the denominator by mul(...TRUNCATED) | ["<think>\nAlright, so I have this equation to solve: \\(x^2 + 5x - 6 = \\frac{1}{x}\\). The problem(...TRUNCATED) | ["<think>\nAlright, so I have this equation here: \\( x^2 + 5x - 6 = \\frac{1}{x} \\). The problem s(...TRUNCATED) | "<think>\nOkay, let's see. The problem is asking for the value of \\( a - b \\) where \\( a \\) and (...TRUNCATED) | [{"from":"human","value":"Let $a$ and $b$ be the two distinct solutions to the equation $x^2+5x-6=\\(...TRUNCATED) |
[{"content":"For how many positive integral values of $b$ is it true that $y = 3$ is the only positi(...TRUNCATED) | "For how many positive integral values of $b$ is it true that $y = 3$ is the only positive integer s(...TRUNCATED) | "For how many positive integral values of $b$ is it true that $y = 3$ is the only positive integer s(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "We are given the system:\n\\[\n\\begin{cases}\nb y + 1 = 2^y \\\\\ny^2 - 2y - b = 0\n\\end{cases}\n(...TRUNCATED) | 17,960 | 11,214 | 1,122 | ["Alright, so I have this problem here where I need to find how many positive integer values of \\( (...TRUNCATED) | ["To determine how many positive integer values of \\( b \\) make \\( y = 3 \\) the only positive in(...TRUNCATED) | ["<think>\nAlright, so I have this problem here where I need to find how many positive integer value(...TRUNCATED) | ["<think>\nOkay, so I need to figure out for how many positive integer values of \\( b \\) the syste(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many positive integer values of \\( b \\) make it true t(...TRUNCATED) | [{"from":"human","value":"For how many positive integral values of $b$ is it true that $y = 3$ is th(...TRUNCATED) |
[{"content":"Given a right triangle $ABC$ in a three-dimensional space, where $A$ is on the positive(...TRUNCATED) | "Given a right triangle $ABC$ in a three-dimensional space, where $A$ is on the positive $x$-axis, $(...TRUNCATED) | "Given a right triangle $ABC$ in a three-dimensional space, where $A$ is on the positive $x$-axis, $(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the problem step by step.\n\n---\n\n### Given:\n\n- Triangle \\( ABC \\) is right ang(...TRUNCATED) | 21,957 | 10,825 | 1,372 | ["Okay, let's see. We have a right triangle ABC in 3D space. Point A is on the positive x-axis, poin(...TRUNCATED) | ["Given a right triangle \\(ABC\\) in three-dimensional space, where \\(A\\) is on the positive \\(x(...TRUNCATED) | ["<think>\nOkay, let's see. We have a right triangle ABC in 3D space. Point A is on the positive x-a(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this problem step by step. First, let me make sure I understand(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. First, let me make sure I understand (...TRUNCATED) | [{"from":"human","value":"Given a right triangle $ABC$ in a three-dimensional space, where $A$ is on(...TRUNCATED) |
[{"content":"Let $f$ be a real-valued function defined for all real numbers, and consider a parametr(...TRUNCATED) | "Let $f$ be a real-valued function defined for all real numbers, and consider a parametric graph\n$x(...TRUNCATED) | "Let $f$ be a real-valued function defined for all real numbers, and consider a parametric graph\n$x(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\n\\[\nx = g(t) = t^3 - 3t^2 + 5, \\quad y = h(t) = t^3 - 2t^2 - 1,\n\\]\nand the function (...TRUNCATED) | 53,041 | 13,170 | 3,315 | ["Okay, so I need to figure out the range of the function f(x), given that f(g(t)) = h(t), where g(t(...TRUNCATED) | ["Given the functions \\( g(t) = t^3 - 3t^2 + 5 \\) and \\( h(t) = t^3 - 2t^2 - 1 \\), we need to de(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the range of the function f(x), given that f(g(t)) = h(t), (...TRUNCATED) | ["<think>\nAlright, let's tackle this problem step by step. So, we have a function f defined for all(...TRUNCATED) | "<think>\nOkay, so I need to find the range of the function f(x) given that f(g(t)) = h(t), where g((...TRUNCATED) | [{"from":"human","value":"Let $f$ be a real-valued function defined for all real numbers, and consid(...TRUNCATED) |
[{"content":"Suppose that $a$ and $b$ are positive integers, and that the equation $x^3-ax+b=0$ has (...TRUNCATED) | "Suppose that $a$ and $b$ are positive integers, and that the equation $x^3-ax+b=0$ has solutions $a(...TRUNCATED) | "Suppose that $a$ and $b$ are positive integers, and that the equation $x^3-ax+b=0$ has solutions $a(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given that \\(a\\) and \\(b\\) are positive integers and the cubic equation \n\\[\nx^3 - a x + b = (...TRUNCATED) | 7,392 | 24,952 | 462 | ["Alright, let's see. The problem says that for positive integers a and b, the equation x³ - a x + (...TRUNCATED) | ["Given the equation \\(x^3 - ax + b = 0\\) with solutions \\(a\\), \\(b\\), and \\(\\sqrt{ab}\\), w(...TRUNCATED) | ["<think>\nAlright, let's see. The problem says that for positive integers a and b, the equation x³(...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem where we have positive integers a and b, and the eq(...TRUNCATED) | "<think>\nAlright, so I need to find positive integers a and b such that the equation x³ - a x + b (...TRUNCATED) | [{"from":"human","value":"Suppose that $a$ and $b$ are positive integers, and that the equation $x^3(...TRUNCATED) |
[{"content":"What is the largest positive integer n such that the number 2008^n can be expressed as (...TRUNCATED) | "What is the largest positive integer n such that the number 2008^n can be expressed as a product of(...TRUNCATED) | "What is the largest positive integer n such that the number 2008^n can be expressed as a product of(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem:**\n\nFind the largest positive integer \\( n \\) such that \\( 2008^n \\) can be express(...TRUNCATED) | 26,145 | 11,833 | 1,634 | ["Okay, let's try to figure out the largest positive integer n such that 2008^n can be expressed as (...TRUNCATED) | ["To determine the largest positive integer \\( n \\) such that \\( 2008^n \\) can be expressed as a(...TRUNCATED) | ["<think>\nOkay, let's try to figure out the largest positive integer n such that 2008^n can be expr(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest positive integer n such that 2008^n can be expressed (...TRUNCATED) | "<think>\nOkay, so I have this problem here: What is the largest positive integer n such that the nu(...TRUNCATED) | [{"from":"human","value":"What is the largest positive integer n such that the number 2008^n can be (...TRUNCATED) |
[{"content":"In triangle $ABC$, $AB = 3$, $AC = 4$, and $BC = 5$. The medians of the triangle are dr(...TRUNCATED) | "In triangle $ABC$, $AB = 3$, $AC = 4$, and $BC = 5$. The medians of the triangle are drawn, and the(...TRUNCATED) | "In triangle $ABC$, $AB = 3$, $AC = 4$, and $BC = 5$. The medians of the triangle are drawn, and the(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Triangle \\( ABC \\) with sides \\( AB = 3 \\), \\( AC = 4 \\), \\( BC = 5 \\).\n- Me(...TRUNCATED) | 51,372 | 12,331 | 3,210 | ["Okay, so I need to find the length of the median from vertex A to side BC in triangle ABC where AB(...TRUNCATED) | ["In triangle \\(ABC\\), \\(AB = 3\\), \\(AC = 4\\), and \\(BC = 5\\). We need to find the length of(...TRUNCATED) | ["<think>\nOkay, so I need to find the length of the median from vertex A to side BC in triangle ABC(...TRUNCATED) | ["<think>\nOkay, so I have this geometry problem here. Let me try to understand it step by step. The(...TRUNCATED) | "<think>\nOkay, so I need to find the length of the median from vertex A to side BC in triangle ABC (...TRUNCATED) | [{"from":"human","value":"In triangle $ABC$, $AB = 3$, $AC = 4$, and $BC = 5$. The medians of the tr(...TRUNCATED) |
[{"content":"Tom's team won a math competition with a total score of 240 points. Tom's score was 40 (...TRUNCATED) | "Tom's team won a math competition with a total score of 240 points. Tom's score was 40 points highe(...TRUNCATED) | "Tom's team won a math competition with a total score of 240 points. Tom's score was 40 points highe(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's define the variables:\n\n- Let \\( T \\) be Tom's score.\n- Let the other four team members' (...TRUNCATED) | 20,602 | 11,649 | 1,287 | ["Okay, let's try to solve this problem step by step. First, let me read it again to make sure I und(...TRUNCATED) | ["Tom's team won a math competition with a total score of 240 points. Tom's score was 40 points high(...TRUNCATED) | ["<think>\nOkay, let's try to solve this problem step by step. First, let me read it again to make s(...TRUNCATED) | ["<think>\nOkay, let's try to solve this problem step by step. First, let me read it again to make s(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. Hmm, so Tom's team won a math competit(...TRUNCATED) | [{"from":"human","value":"Tom's team won a math competition with a total score of 240 points. Tom's (...TRUNCATED) |
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