messages listlengths 2 2 | instruction_seed stringlengths 44 3.07k | response_seed stringlengths 44 3.07k | _source stringclasses 1
value | gpt41_mini_response stringlengths 10.4k 39.5k | __original_row_idx int64 7 56.3k | length int64 10.4k 39.5k | 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 33 502 | _majority_responses sequencelengths 1 16 | verified_final_reasoning_trace stringlengths 7.65k 87.9k | conversations listlengths 2 2 |
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[{"content":"Positive integers $a$, $b$, and $c$ are chosen so that $a<b<c$, and the system of equat(...TRUNCATED) | "Positive integers $a$, $b$, and $c$ are chosen so that $a<b<c$, and the system of equations \\[\n2x(...TRUNCATED) | "Positive integers $a$, $b$, and $c$ are chosen so that $a<b<c$, and the system of equations \\[\n2x(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the original problem:\n\n---\n\n### Original Problem\n\nPositive integers \\(a, b, c\(...TRUNCATED) | 5,162 | 17,699 | 1,175 | ["Okay, so I need to find the minimum value of c where a, b, c are positive integers with a < b < c,(...TRUNCATED) | ["To solve the problem, we need to find the minimum value of \\( c \\) such that the system of equat(...TRUNCATED) | ["<think>\nOkay, so I need to find the minimum value of c where a, b, c are positive integers with a(...TRUNCATED) | [
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] | "The provided answer is entirely in English, containing mathematical notations and explanations with(...TRUNCATED) | ["<think>\nOkay, so I need to find the minimum value of c where a, b, c are positive integers with a(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. The problem says:\n\nPositive integers \\(a\(...TRUNCATED) | [{"from":"human","value":"Positive integers $a$, $b$, and $c$ are chosen so that $a<b<c$, and the sy(...TRUNCATED) |
[{"content":"Let $a$ and $b$ be complex numbers such that $\\frac{a+b}{a-b}$ is purely imaginary and(...TRUNCATED) | "Let $a$ and $b$ be complex numbers such that $\\frac{a+b}{a-b}$ is purely imaginary and $|a|^2 = |b(...TRUNCATED) | "Let $a$ and $b$ be complex numbers such that $\\frac{a+b}{a-b}$ is purely imaginary and $|a|^2 = |b(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n- \\(a, b \\in \\mathbb{C}\\),\n- \\(\\frac{a+b}{a-b}\\) is purely imaginary,\n- \\(|a|^2 =(...TRUNCATED) | 17,510 | 18,875 | 557 | ["Okay, so I need to find the value of |(conjugate(a)/b)| given that (a + b)/(a - b) is purely imagi(...TRUNCATED) | ["Given complex numbers \\(a\\) and \\(b\\) such that \\(\\frac{a+b}{a-b}\\) is purely imaginary and(...TRUNCATED) | ["<think>\nOkay, so I need to find the value of |(conjugate(a)/b)| given that (a + b)/(a - b) is pur(...TRUNCATED) | [
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] | The provided answer is entirely in English, which confirms that it contains only one language. | ["<think>\nOkay, so I need to find the value of |(conjugate(a)/b)| given that (a + b)/(a - b) is pur(...TRUNCATED) | "<think>\nOkay, so I need to compute |\\overline{a}/b| given two conditions: (a + b)/(a - b) is pure(...TRUNCATED) | [{"from":"human","value":"Let $a$ and $b$ be complex numbers such that $\\frac{a+b}{a-b}$ is purely (...TRUNCATED) |
[{"content":"Consider the function\n\\[f(x) = \\cot \\left( x + \\frac{\\pi}{12} \\right) + 2 \\sin (...TRUNCATED) | "Consider the function\n\\[f(x) = \\cot \\left( x + \\frac{\\pi}{12} \\right) + 2 \\sin \\left( 2x +(...TRUNCATED) | "Consider the function\n\\[f(x) = \\cot \\left( x + \\frac{\\pi}{12} \\right) + 2 \\sin \\left( 2x +(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the function:\n\\[\nf(x) = \\cot \\left( x + \\frac{\\pi}{12} \\right) + 2 \\sin \\left( 2x +(...TRUNCATED) | 8,889 | 17,627 | 2,687 | ["Okay, so I need to find the smallest x that maximizes the function f(x) in the interval from -5π/(...TRUNCATED) | ["To find the smallest \\( x \\) that maximizes the function \\( f(x) = \\cot \\left( x + \\frac{\\p(...TRUNCATED) | ["<think>\nOkay, so I need to find the smallest x that maximizes the function f(x) in the interval f(...TRUNCATED) | [
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] | "The response is written wholly in English, maintaining consistency within a single language. Theref(...TRUNCATED) | ["<think>\nOkay, so I need to find the smallest x that maximizes the function f(x) in the interval f(...TRUNCATED) | "<think>\nOkay, so I need to find the smallest x that maximizes the function f(x) in the interval fr(...TRUNCATED) | [{"from":"human","value":"Consider the function\n\\[f(x) = \\cot \\left( x + \\frac{\\pi}{12} \\righ(...TRUNCATED) |
[{"content":"Let $x, y, z, w$ be distinct positive integers such that $x + y = z - w$ and the produc(...TRUNCATED) | "Let $x, y, z, w$ be distinct positive integers such that $x + y = z - w$ and the product $xy$ and $(...TRUNCATED) | "Let $x, y, z, w$ be distinct positive integers such that $x + y = z - w$ and the product $xy$ and $(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given four distinct positive integers \\(x, y, z, w\\) such that:\n\\[\nx + y = z - w\n\\]\nand bot(...TRUNCATED) | 28,887 | 24,484 | 3,457 | ["Alright, let's try to tackle this problem. So, we need to find four distinct positive integers x, (...TRUNCATED) | ["Given four distinct positive integers \\(x, y, z, w\\) such that \\(x + y = z - w\\) and the produ(...TRUNCATED) | ["<think>\nAlright, let's try to tackle this problem. So, we need to find four distinct positive int(...TRUNCATED) | [
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] | "The provided answer contains only one language, which is English. The entire text is written and st(...TRUNCATED) | ["<think>\nAlright, let's try to tackle this problem. So, we need to find four distinct positive int(...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem. So we have four distinct positive integers x,(...TRUNCATED) | [{"from":"human","value":"Let $x, y, z, w$ be distinct positive integers such that $x + y = z - w$ a(...TRUNCATED) |
[{"content":"The integer solutions $(x,y)$ of the equation $xy^2-(y+2)x^2=2005$ are such that all th(...TRUNCATED) | "The integer solutions $(x,y)$ of the equation $xy^2-(y+2)x^2=2005$ are such that all the numbers $\(...TRUNCATED) | "The integer solutions $(x,y)$ of the equation $xy^2-(y+2)x^2=2005$ are such that all the numbers $\(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\nxy^2 - (y+2)x^2 = 2005,\n\\]\nwe are to consider all integer solutions \\(...TRUNCATED) | 5,975 | 26,618 | 2,075 | ["Okay, let's try to tackle this problem. The equation given is \\( xy^2 - (y + 2)x^2 = 2005 \\). We(...TRUNCATED) | ["The given equation is \\( xy^2 - (y + 2)x^2 = 2005 \\). We need to find the integer solutions \\(((...TRUNCATED) | ["<think>\nOkay, let's try to tackle this problem. The equation given is \\( xy^2 - (y + 2)x^2 = 200(...TRUNCATED) | [
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] | The provided answer is written entirely in English, with no use of another language. | ["<think>\nOkay, let's try to tackle this problem. The equation given is \\( xy^2 - (y + 2)x^2 = 200(...TRUNCATED) | "<think>\nOkay, let's see. I need to solve this equation: \\( xy^2 - (y + 2)x^2 = 2005 \\). And then(...TRUNCATED) | [{"from":"human","value":"The integer solutions $(x,y)$ of the equation $xy^2-(y+2)x^2=2005$ are suc(...TRUNCATED) |
[{"content":"In triangle $PQR,$ $PQ = 17,$ $QR = 20,$ $RP = 23,$ and point $H$ is the orthocenter. P(...TRUNCATED) | "In triangle $PQR,$ $PQ = 17,$ $QR = 20,$ $RP = 23,$ and point $H$ is the orthocenter. Points $P',$ (...TRUNCATED) | "In triangle $PQR,$ $PQ = 17,$ $QR = 20,$ $RP = 23,$ and point $H$ is the orthocenter. Points $P',$ (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n\n- Triangle \\(PQR\\) with sides \\(PQ = 17\\), \\(QR = 20\\), and \\(RP = 23\\).\n- \(...TRUNCATED) | 35,359 | 10,476 | 2,146 | ["Okay, so I have this problem here about triangle PQR with sides PQ=17, QR=20, RP=23. H is the orth(...TRUNCATED) | ["To solve the problem of finding the area of the union of the two regions enclosed by triangles \\((...TRUNCATED) | ["<think>\nOkay, so I have this problem here about triangle PQR with sides PQ=17, QR=20, RP=23. H is(...TRUNCATED) | [
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] | The answer provided contains text in English, which is the only language used. | ["<think>\nOkay, so I need to find the area of the union of the two regions enclosed by triangle PQR(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the union of the two regions enclosed by triangle PQR (...TRUNCATED) | [{"from":"human","value":"In triangle $PQR,$ $PQ = 17,$ $QR = 20,$ $RP = 23,$ and point $H$ is the o(...TRUNCATED) |
[{"content":"There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. (...TRUNCATED) | "There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. If no more t(...TRUNCATED) | "There are 5 circles on a plane, with each circle intersecting exactly 3 other circles. If no more t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem Restatement:** \nThere are 5 circles on a plane. Each circle intersects exactly 3 other (...TRUNCATED) | 13,491 | 10,925 | 605 | ["Okay, so I have this problem here: There are 5 circles on a plane, each intersecting exactly 3 oth(...TRUNCATED) | ["To determine the number of intersection points for 5 circles on a plane where each circle intersec(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: There are 5 circles on a plane, each intersecting exac(...TRUNCATED) | [
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] | "The provided answer contains an excessive amount of dialogue and reasoning, which includes both a m(...TRUNCATED) | ["<think>\nOkay, so there's this problem about circles on a plane. Let me read it again: \"There are(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, we have 5 circles on a plane, each interse(...TRUNCATED) | [{"from":"human","value":"There are 5 circles on a plane, with each circle intersecting exactly 3 ot(...TRUNCATED) |
[{"content":"Let $f$ be a binary operation on the real numbers that satisfies the following properti(...TRUNCATED) | "Let $f$ be a binary operation on the real numbers that satisfies the following properties:\n\n1. $f(...TRUNCATED) | "Let $f$ be a binary operation on the real numbers that satisfies the following properties:\n\n1. $f(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given a binary operation \\( f:\\mathbb{R} \\times \\mathbb{R} \\to \\mathbb{R} \\) satisfying:\n\n(...TRUNCATED) | 32,336 | 21,038 | 794 | ["Okay, let's see. I need to find the value of f(3,2) where f is a binary operation on real numbers (...TRUNCATED) | ["Given a binary operation \\( f \\) on the real numbers satisfying the properties:\n\n1. \\( f(a, 0(...TRUNCATED) | ["<think>\nOkay, let's see. I need to find the value of f(3,2) where f is a binary operation on real(...TRUNCATED) | [
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] | "The provided answer only contains one language, which is English. There are no indications or trans(...TRUNCATED) | ["<think>\nOkay, let's see. I need to find the value of f(3,2) where f is a binary operation on real(...TRUNCATED) | "<think>\nOkay, let's see. I need to find the value of f(3,2) where f is a binary operation on real (...TRUNCATED) | [{"from":"human","value":"Let $f$ be a binary operation on the real numbers that satisfies the follo(...TRUNCATED) |
[{"content":"In a circle with center $O$, a point $P$ is chosen at random. What is the probability t(...TRUNCATED) | "In a circle with center $O$, a point $P$ is chosen at random. What is the probability that the tria(...TRUNCATED) | "In a circle with center $O$, a point $P$ is chosen at random. What is the probability that the tria(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem Restatement:** \nGiven a circle with center \\( O \\), a fixed tangent line touches the (...TRUNCATED) | 41,292 | 13,377 | 2,208 | ["Okay, so there's this problem about a circle with center O, and we randomly pick a point P on the (...TRUNCATED) | ["To determine the probability that the triangle formed by points \\(O\\), \\(P\\), and the point of(...TRUNCATED) | ["<think>\nOkay, so there's this problem about a circle with center O, and we randomly pick a point (...TRUNCATED) | [
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] | "The response is entirely in English, without any incorporated phrases or words from other languages(...TRUNCATED) | ["<think>\nOkay, so there's this problem about a circle with center O, and we randomly pick a point (...TRUNCATED) | "<think>\nOkay, so there's this geometry problem here about a circle with center O. We need to find (...TRUNCATED) | [{"from":"human","value":"In a circle with center $O$, a point $P$ is chosen at random. What is the (...TRUNCATED) |
[{"content":"A circular arc has a radius of $\\sqrt{72}$ cm, and the points $D$ and $E$ on the arc a(...TRUNCATED) | "A circular arc has a radius of $\\sqrt{72}$ cm, and the points $D$ and $E$ on the arc are connected(...TRUNCATED) | "A circular arc has a radius of $\\sqrt{72}$ cm, and the points $D$ and $E$ on the arc are connected(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- The radius of the circle is \\( R = \\sqrt{72} \\) cm.\n- Chord \\( DE \\) has length(...TRUNCATED) | 49,314 | 17,803 | 3,165 | ["Okay, let's try to tackle this geometry problem. Hmm, so there's a circular arc with radius sqrt(7(...TRUNCATED) | ["Given a circular arc with radius \\(\\sqrt{72}\\) cm, points \\(D\\) and \\(E\\) on the arc are co(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this geometry problem. Hmm, so there's a circular arc with radi(...TRUNCATED) | [
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] | The provided answer is entirely in English. | ["<think>\nOkay, let's try to tackle this geometry problem. Hmm, so there's a circular arc with radi(...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me first try to visualize it. There's (...TRUNCATED) | [{"from":"human","value":"A circular arc has a radius of $\\sqrt{72}$ cm, and the points $D$ and $E$(...TRUNCATED) |
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