messages listlengths 2 2 | instruction_seed stringlengths 35 3.07k | response_seed stringlengths 35 3.07k | _source stringclasses 1
value | gpt41_mini_response stringlengths 10.4k 40.8k | __original_row_idx int64 2 54.8k | length int64 10.4k 40.8k | ms_id int64 0 3.95k | reasoning sequencelengths 16 16 | deepseek_solution sequencelengths 16 16 | final_reasoning_trace sequencelengths 16 16 | correct sequencelengths 16 16 | classifier_reasoning stringlengths 42 562 | _majority_responses sequencelengths 1 16 | verified_final_reasoning_trace stringlengths 4.48k 88k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[{"content":"Given that $\\triangle ABC$ is an equilateral triangle, how many circles can be inscrib(...TRUNCATED) | "Given that $\\triangle ABC$ is an equilateral triangle, how many circles can be inscribed into it i(...TRUNCATED) | "Given that $\\triangle ABC$ is an equilateral triangle, how many circles can be inscribed into it i(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nConsider an equilateral triangle \\(\\triangle ABC\\) with a certain si(...TRUNCATED) | 30,395 | 13,780 | 3,811 | ["Okay, so I have this problem here about an equilateral triangle, ABC. The question is asking how m(...TRUNCATED) | ["Given an equilateral triangle \\( \\triangle ABC \\), we need to determine how many circles can be(...TRUNCATED) | ["<think>\nOkay, so I have this problem here about an equilateral triangle, ABC. The question is ask(...TRUNCATED) | [
true,
true,
true,
true,
true,
true,
true,
false,
true,
true,
true,
true,
true,
false,
true,
true
] | "The provided answer does not contain any paragraphs exceeding 750 words, as it consists of many sho(...TRUNCATED) | ["<think>\nOkay, so I have this problem here about an equilateral triangle, ABC. The question is ask(...TRUNCATED) | "<think>\nAlright, so I need to figure out how many circles can be inscribed in an equilateral trian(...TRUNCATED) | [{"from":"human","value":"Given that $\\triangle ABC$ is an equilateral triangle, how many circles c(...TRUNCATED) |
[{"content":"Let $f(x)$ be a function defined by $f(x) = x^2 + ax + b$, where $a$ and $b$ are consta(...TRUNCATED) | "Let $f(x)$ be a function defined by $f(x) = x^2 + ax + b$, where $a$ and $b$ are constants. If $f(2(...TRUNCATED) | "Let $f(x)$ be a function defined by $f(x) = x^2 + ax + b$, where $a$ and $b$ are constants. If $f(2(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the function:\n\\[\nf(x) = x^2 + ax + b,\n\\]\nwhere \\(a\\) and \\(b\\) are constants.\n\nWe(...TRUNCATED) | 5,819 | 11,197 | 2,039 | ["Okay, so I need to find the value of 'a' in the quadratic function f(x) = x² + a x + b. The given(...TRUNCATED) | ["Given the function \\( f(x) = x^2 + ax + b \\) with constants \\( a \\) and \\( b \\), we need to (...TRUNCATED) | ["<think>\nOkay, so I need to find the value of 'a' in the quadratic function f(x) = x² + a x + b. (...TRUNCATED) | [
true,
true,
true,
false,
true,
true,
false,
true,
false,
true,
false,
true,
true,
true,
true,
true
] | "The answer provided does not contain any long paragraphs, as all sections of text are adequately se(...TRUNCATED) | ["<think>\nOkay, so I need to find the value of 'a' in the quadratic function f(x) = x² + a x + b. (...TRUNCATED) | "<think>\nOkay, so I have this problem here where I need to find the value of \\( a \\) for the quad(...TRUNCATED) | [{"from":"human","value":"Let $f(x)$ be a function defined by $f(x) = x^2 + ax + b$, where $a$ and $(...TRUNCATED) |
[{"content":"Find the value of k such that the equation (x-1)(x-2)(x-3) + k(x-4)(x-5)(x-6) = 0 has e(...TRUNCATED) | "Find the value of k such that the equation (x-1)(x-2)(x-3) + k(x-4)(x-5)(x-6) = 0 has exactly one r(...TRUNCATED) | "Find the value of k such that the equation (x-1)(x-2)(x-3) + k(x-4)(x-5)(x-6) = 0 has exactly one r(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\n(x-1)(x-2)(x-3) + k(x-4)(x-5)(x-6) = 0,\n\\]\nwe want to find the value(s(...TRUNCATED) | 28,251 | 25,198 | 3,232 | ["Okay, so I have this equation: (x - 1)(x - 2)(x - 3) + k(x - 4)(x - 5)(x - 6) = 0. I need to find (...TRUNCATED) | ["To find the value of \\( k \\) such that the equation \\((x-1)(x-2)(x-3) + k(x-4)(x-5)(x-6) = 0\\)(...TRUNCATED) | ["<think>\nOkay, so I have this equation: (x - 1)(x - 2)(x - 3) + k(x - 4)(x - 5)(x - 6) = 0. I need(...TRUNCATED) | [
false,
true,
true,
true,
false,
true,
false,
false,
true,
false,
true,
true,
false,
false,
true,
false
] | The provided answer contains long paragraphs that exceed the 750-word limit set by the guidelines. | ["<think>\nOkay, so I need to find the value of k such that the equation (x-1)(x-2)(x-3) + k(x-4)(x-(...TRUNCATED) | "<think>\nOkay, so I need to find the value of k such that the equation (x - 1)(x - 2)(x - 3) + k(x (...TRUNCATED) | [{"from":"human","value":"Find the value of k such that the equation (x-1)(x-2)(x-3) + k(x-4)(x-5)(x(...TRUNCATED) |
[{"content":"Consider the system of equations\n\\begin{align*}\nx&=y+z\\\\\ny&=z+w\\\\\nz&=w+x\\\\\n(...TRUNCATED) | "Consider the system of equations\n\\begin{align*}\nx&=y+z\\\\\ny&=z+w\\\\\nz&=w+x\\\\\nw&=x+y\n\\en(...TRUNCATED) | "Consider the system of equations\n\\begin{align*}\nx&=y+z\\\\\ny&=z+w\\\\\nz&=w+x\\\\\nw&=x+y\n\\en(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Consider the system of equations:\n\\[\n\\begin{cases}\nx = y + z \\\\\ny = z + w \\\\\nz = w + x \(...TRUNCATED) | 49,672 | 17,580 | 3,772 | ["Okay, so I need to solve this system of equations where each variable is defined in terms of the o(...TRUNCATED) | ["To determine all possible values of \\(x + y + z + w\\) for the given system of equations:\n\\[\n\(...TRUNCATED) | ["<think>\nOkay, so I need to solve this system of equations where each variable is defined in terms(...TRUNCATED) | [
true,
false,
true,
true,
false,
false,
true,
false,
false,
true,
false,
false,
true,
false,
false,
true
] | "The provided answer does not contain any long paragraphs that exceed 750 words. Each paragraph seem(...TRUNCATED) | ["<think>\nOkay, so I need to solve this system of equations where each variable is defined in terms(...TRUNCATED) | "<think>\nOkay, so I have this system of equations:\n\nx = y + z \ny = z + w \nz = w + x \nw = x (...TRUNCATED) | [{"from":"human","value":"Consider the system of equations\n\\begin{align*}\nx&=y+z\\\\\ny&=z+w\\\\\(...TRUNCATED) |
[{"content":"Consider a rational function of the form\n\\[r(x) = \\frac{2x^2 + kx + 1}{x^2 + kx + 2}(...TRUNCATED) | "Consider a rational function of the form\n\\[r(x) = \\frac{2x^2 + kx + 1}{x^2 + kx + 2}\\]\ndefined(...TRUNCATED) | "Consider a rational function of the form\n\\[r(x) = \\frac{2x^2 + kx + 1}{x^2 + kx + 2}\\]\ndefined(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the rational function:\n\\[\nr(x) = \\frac{2x^2 + kx + 1}{x^2 + kx + 2}\n\\]\ndefined for all(...TRUNCATED) | 36,370 | 19,790 | 2,797 | ["Okay, so I need to figure out the values of k such that the rational function r(x) = (2x² + kx + (...TRUNCATED) | ["To determine the values of \\( k \\) such that \\( r(x) \\geq 1 \\) for all real \\( x \\), we sta(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the values of k such that the rational function r(x) = (2x(...TRUNCATED) | [
true,
false,
true,
false,
true,
true,
false,
true,
false,
true,
true,
true,
true,
true,
false,
false
] | "The provided answer contains multiple short paragraphs rather than one single long paragraph, with (...TRUNCATED) | ["<think>\nOkay, so I need to figure out the values of k such that the rational function r(x) = (2x(...TRUNCATED) | "<think>\nOkay, so I need to figure out the values of k for which the rational function r(x) = (2x²(...TRUNCATED) | [{"from":"human","value":"Consider a rational function of the form\n\\[r(x) = \\frac{2x^2 + kx + 1}{(...TRUNCATED) |
[{"content":"Determine the number of functions $f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+$ such that\n\\(...TRUNCATED) | "Determine the number of functions $f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+$ such that\n\\[f(\\text{lc(...TRUNCATED) | "Determine the number of functions $f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+$ such that\n\\[f(\\text{lc(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the problem:\n\n> Determine the number of functions \\( f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+ (...TRUNCATED) | 50,868 | 14,378 | 2,784 | ["Okay, so I have this problem here where I need to determine the number of functions \\( f : \\math(...TRUNCATED) | ["To determine the number of functions \\( f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+ \\) such that for al(...TRUNCATED) | ["<think>\nOkay, so I have this problem here where I need to determine the number of functions \\( f(...TRUNCATED) | [
true,
true,
false,
true,
false,
false,
false,
true,
false,
false,
true,
true,
false,
false,
true,
false
] | "The provided answer contains many long paragraphs but does not have any paragraphs exceeding 750 wo(...TRUNCATED) | ["<think>\nOkay, so I have this problem here where I need to determine the number of functions \\( f(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many functions f from the positive integers to the posit(...TRUNCATED) | [{"from":"human","value":"Determine the number of functions $f : \\mathbb{Z}^+ \\to \\mathbb{Z}^+$ (...TRUNCATED) |
[{"content":"Let's consider a cubic polynomial with integer coefficients of the form $p(x) = x^3 + b(...TRUNCATED) | "Let's consider a cubic polynomial with integer coefficients of the form $p(x) = x^3 + bx^2 + cx + d(...TRUNCATED) | "Let's consider a cubic polynomial with integer coefficients of the form $p(x) = x^3 + bx^2 + cx + d(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nWe have a cubic polynomial with integer coefficients:\n\\[\np(x) = x^3 (...TRUNCATED) | 13,192 | 12,443 | 329 | ["Okay, so I need to find the sum of all possible integer values of \\( b \\) for the cubic polynomi(...TRUNCATED) | ["Given a cubic polynomial \\( p(x) = x^3 + bx^2 + cx + d \\) with integer coefficients, where \\( b(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of all possible integer values of \\( b \\) for the cubic(...TRUNCATED) | [
true,
true,
true,
false,
true,
true,
true,
true,
true,
false,
true,
true,
false,
true,
false,
true
] | "The response provided does not contain any long paragraphs exceeding 750 words, and is well-structu(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of all possible integer values of \\( b \\) for the cubic(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. So, we have a cubic polynomial with integer (...TRUNCATED) | [{"from":"human","value":"Let's consider a cubic polynomial with integer coefficients of the form $p(...TRUNCATED) |
[{"content":"Let $n$ be a positive integer that can be expressed as a product of powers of $p$ disti(...TRUNCATED) | "Let $n$ be a positive integer that can be expressed as a product of powers of $p$ distinct prime nu(...TRUNCATED) | "Let $n$ be a positive integer that can be expressed as a product of powers of $p$ distinct prime nu(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem Recap:**\n\nGiven a positive integer\n\\[\nn = q_1^{r_1} q_2^{r_2} \\cdots q_p^{r_p},\n\\(...TRUNCATED) | 29,583 | 21,370 | 3,508 | ["Okay, so I need to find the sum of the exponents in the prime factorization of a positive integer (...TRUNCATED) | ["Given a positive integer \\( n \\) expressed as a product of powers of \\( p \\) distinct prime nu(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of the exponents in the prime factorization of a positive(...TRUNCATED) | [
true,
false,
false,
false,
false,
false,
false,
false,
false,
false,
true,
false,
true,
false,
false,
false
] | "The response does not contain any long paragraphs exceeding 750 words. All provided explanations ar(...TRUNCATED) | ["<think>\nOkay, so I need to find the sum of the exponents in the prime factorization of a positive(...TRUNCATED) | "<think>\nOkay, so I need to find the sum of the exponents in the prime factorization of a positive (...TRUNCATED) | [{"from":"human","value":"Let $n$ be a positive integer that can be expressed as a product of powers(...TRUNCATED) |
[{"content":"Compute the product of the roots of the equation \\[x^2\\ln x - 5x\\ln x + 2x^2 - 3x = (...TRUNCATED) | "Compute the product of the roots of the equation \\[x^2\\ln x - 5x\\ln x + 2x^2 - 3x = 0,\\]given t(...TRUNCATED) | "Compute the product of the roots of the equation \\[x^2\\ln x - 5x\\ln x + 2x^2 - 3x = 0,\\]given t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\nx^2 \\ln x - 5x \\ln x + 2x^2 - 3x = 0,\n\\]\nwith all roots real and pos(...TRUNCATED) | 24,653 | 14,632 | 2,018 | ["Okay, so I need to compute the product of the roots of the equation \\(x^2\\ln x - 5x\\ln x + 2x^2(...TRUNCATED) | ["To compute the product of the roots of the equation \\(x^2\\ln x - 5x\\ln x + 2x^2 - 3x = 0\\), we(...TRUNCATED) | ["<think>\nOkay, so I need to compute the product of the roots of the equation \\(x^2\\ln x - 5x\\ln(...TRUNCATED) | [
false,
true,
false,
false,
true,
true,
false,
true,
false,
true,
true,
true,
false,
true,
true,
false
] | "The provided answer contains several long paragraphs, each exceeding 750 words, particularly the de(...TRUNCATED) | ["<think>\nOkay, so I need to find the product of the roots of the equation \\(x^2\\ln x - 5x\\ln x (...TRUNCATED) | "<think>\nAlright, so I have this equation to solve: \\(x^2 \\ln x - 5x \\ln x + 2x^2 - 3x = 0\\). T(...TRUNCATED) | [{"from":"human","value":"Compute the product of the roots of the equation \\[x^2\\ln x - 5x\\ln x +(...TRUNCATED) |
[{"content":"In quadrilateral $ABCD$, $AB = 10$, $BC = 8$, $CD = 7$, and $DA = 9$. Points $E$ and $F(...TRUNCATED) | "In quadrilateral $ABCD$, $AB = 10$, $BC = 8$, $CD = 7$, and $DA = 9$. Points $E$ and $F$ are on $\\(...TRUNCATED) | "In quadrilateral $ABCD$, $AB = 10$, $BC = 8$, $CD = 7$, and $DA = 9$. Points $E$ and $F$ are on $\\(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Quadrilateral \\(ABCD\\) with sides:\n \\[\n AB = 10, \\quad BC = 8, \\quad CD = 7,(...TRUNCATED) | 32,411 | 12,751 | 934 | ["Okay, so I have this geometry problem here about quadrilateral ABCD. The sides are given: AB is 10(...TRUNCATED) | ["In quadrilateral \\(ABCD\\), we are given \\(AB = 10\\), \\(BC = 8\\), \\(CD = 7\\), and \\(DA = 9(...TRUNCATED) | ["<think>\nOkay, so I have this geometry problem here about quadrilateral ABCD. The sides are given:(...TRUNCATED) | [
false,
true,
false,
false,
true,
true,
false,
true,
false,
true,
true,
false,
true,
true,
true,
true
] | "The provided answer contains several long paragraphs and many steps exceeding 750 words. Although t(...TRUNCATED) | ["<think>\nAlright, let's try to solve this geometry problem step by step. It's about quadrilateral (...TRUNCATED) | "<think>\nAlright, let's try to solve this geometry problem step by step. It's about quadrilateral A(...TRUNCATED) | [{"from":"human","value":"In quadrilateral $ABCD$, $AB = 10$, $BC = 8$, $CD = 7$, and $DA = 9$. Poin(...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4