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value | gpt41_mini_response stringlengths 10.4k 40.8k | __original_row_idx int64 21 52.8k | length int64 10.4k 40.8k | ms_id int64 15 3.94k | reasoning sequencelengths 16 16 | deepseek_solution sequencelengths 16 16 | final_reasoning_trace sequencelengths 16 16 | correct sequencelengths 16 16 | classifier_reasoning stringlengths 64 469 | _majority_responses sequencelengths 2 16 | verified_final_reasoning_trace stringlengths 6.34k 101k | conversations listlengths 2 2 |
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[{"content":"In the figure, arc $PQR$ of the circle with center $O$ has a measure of $60$ degrees an(...TRUNCATED) | "In the figure, arc $PQR$ of the circle with center $O$ has a measure of $60$ degrees and chord $PQ$(...TRUNCATED) | "In the figure, arc $PQR$ of the circle with center $O$ has a measure of $60$ degrees and chord $PQ$(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's carefully analyze the problem step by step.\n\n---\n\n### Problem Restatement:\n\n- We have a(...TRUNCATED) | 45,717 | 13,900 | 1,592 | ["Okay, so I need to figure out the area of this region bounded by arc PQR, segment RQ, and the two (...TRUNCATED) | ["Given a circle with center \\( O \\) and an arc \\( PQR \\) measuring \\( 60^\\circ \\), where cho(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the area of this region bounded by arc PQR, segment RQ, and(...TRUNCATED) | [
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[{"content":"Let's create a new problem inspired by the given one:\n\nConsider a circle $\\mathcal{C(...TRUNCATED) | "Let's create a new problem inspired by the given one:\n\nConsider a circle $\\mathcal{C}$ centered (...TRUNCATED) | "Let's create a new problem inspired by the given one:\n\nConsider a circle $\\mathcal{C}$ centered (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's restate and analyze the problem carefully:\n\n---\n\n**Problem:**\n\n- Circle \\(\\mathcal{C}(...TRUNCATED) | 38,079 | 11,315 | 3,048 | ["Okay, let's try to tackle this problem. So, we have a circle centered at the origin with radius 1.(...TRUNCATED) | ["Given a circle \\(\\mathcal{C}\\) centered at the origin with radius 1, we need to find the number(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this problem. So, we have a circle centered at the origin with (...TRUNCATED) | [
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] | "The provided answer contains multiple long paragraphs, as it consists of numerous sections that exc(...TRUNCATED) | ["<think>\nAlright, let's tackle this problem. So, we have a circle centered at the origin with radi(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem. So, we have a circle centered at the origin with r(...TRUNCATED) | [{"from":"human","value":"Let's create a new problem inspired by the given one:\n\nConsider a circle(...TRUNCATED) |
[{"content":"The city's three subway lines have different schedules: Line A runs every 12 minutes, L(...TRUNCATED) | "The city's three subway lines have different schedules: Line A runs every 12 minutes, Line B runs e(...TRUNCATED) | "The city's three subway lines have different schedules: Line A runs every 12 minutes, Line B runs e(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's carefully analyze the problem step-by-step.\n\n---\n\n### Problem recap:\n\n- There are three(...TRUNCATED) | 10,351 | 13,371 | 2,947 | ["Okay, so there's this problem about subway lines and waiting times. Let me try to understand it. T(...TRUNCATED) | ["The problem involves determining the maximum amount of time a commuter will have to wait before be(...TRUNCATED) | ["<think>\nOkay, so there's this problem about subway lines and waiting times. Let me try to underst(...TRUNCATED) | [
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] | "The provided answer is structured with short sections and does not contain any paragraphs longer th(...TRUNCATED) | ["<think>\nOkay, so there's this problem about subway lines and waiting times. Let me try to underst(...TRUNCATED) | "<think>\nOkay, so there's this problem about subway lines and figuring out the maximum wait time a (...TRUNCATED) | [{"from":"human","value":"The city's three subway lines have different schedules: Line A runs every (...TRUNCATED) |
[{"content":"Consider the system of congruences:\n\n$$x\\equiv y\\pmod{12}, x\\equiv y\\pmod{19},$$\(...TRUNCATED) | "Consider the system of congruences:\n\n$$x\\equiv y\\pmod{12}, x\\equiv y\\pmod{19},$$\n\nand $$x^2(...TRUNCATED) | "Consider the system of congruences:\n\n$$x\\equiv y\\pmod{12}, x\\equiv y\\pmod{19},$$\n\nand $$x^2(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the system of congruences:\n\n\\[\n\\begin{cases}\nx \\equiv y \\pmod{12}, \\\\\nx \\equiv y (...TRUNCATED) | 26,243 | 18,500 | 2,493 | ["Okay, let's tackle this problem step by step. So, we have a system of congruences:\n\n1. \\( x \\e(...TRUNCATED) | ["Given the system of congruences:\n\n1. \\( x \\equiv y \\pmod{12} \\)\n2. \\( x \\equiv y \\pmod{1(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. So, we have a system of congruences:\n\n1. (...TRUNCATED) | [
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] | "The provided answer doesn't contain any paragraphs exceeding 750 words. It is structured in shorter(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. So, we have a system of congruences:\n\n1. (...TRUNCATED) | "<think>\nOkay, so I have this problem here with a system of congruences:\n\n1. \\( x \\equiv y \\pm(...TRUNCATED) | [{"from":"human","value":"Consider the system of congruences:\n\n$$x\\equiv y\\pmod{12}, x\\equiv y\(...TRUNCATED) |
[{"content":"Let $f(n)$ be the sum of the digits of a positive integer $n$. For how many values of $(...TRUNCATED) | "Let $f(n)$ be the sum of the digits of a positive integer $n$. For how many values of $n$ less than(...TRUNCATED) | "Let $f(n)$ be the sum of the digits of a positive integer $n$. For how many values of $n$ less than(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nDefine \\( f(n) \\) as the sum of the digits of a positive integer \\( (...TRUNCATED) | 27,963 | 10,833 | 3,063 | ["Okay, so I need to figure out how many numbers n ≤ 1000 have the property that for any positive (...TRUNCATED) | ["To determine how many values of \\( n \\) less than or equal to 1000 satisfy the equation \\( f(m (...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many numbers n ≤ 1000 have the property that for any (...TRUNCATED) | [
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] | "Yes, the provided answer is free of any long paragraphs. It conforms to the definition of paragraph(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many numbers n ≤ 1000 have the property that for any (...TRUNCATED) | "<think>\nOkay, so I need to figure out how many numbers n ≤ 1000 such that for any positive integ(...TRUNCATED) | [{"from":"human","value":"Let $f(n)$ be the sum of the digits of a positive integer $n$. For how man(...TRUNCATED) |
[{"content":"The foci of an ellipse are located at points $(1,2)$ and $(7,2).$ The ellipse is tangen(...TRUNCATED) | "The foci of an ellipse are located at points $(1,2)$ and $(7,2).$ The ellipse is tangent to the lin(...TRUNCATED) | "The foci of an ellipse are located at points $(1,2)$ and $(7,2).$ The ellipse is tangent to the lin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- The foci of the ellipse are at \\(F_1 = (1,2)\\) and \\(F_2 = (7,2)\\).\n- The ellips(...TRUNCATED) | 33,664 | 10,703 | 1,527 | ["Okay, so I need to find the length of the major axis of an ellipse. The foci are given at (1,2) an(...TRUNCATED) | ["The foci of the ellipse are located at points \\((1, 2)\\) and \\((7, 2)\\). The distance between (...TRUNCATED) | ["<think>\nOkay, so I need to find the length of the major axis of an ellipse. The foci are given at(...TRUNCATED) | [
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] | "The provided answer contains multiple long paragraphs that exceed 750 words, as demonstrated in the(...TRUNCATED) | ["<think>\nOkay, so I need to find the length of the major axis of an ellipse with foci at (1,2) and(...TRUNCATED) | "<think>\nOkay, so I need to find the length of the major axis of an ellipse. The foci are given at (...TRUNCATED) | [{"from":"human","value":"The foci of an ellipse are located at points $(1,2)$ and $(7,2).$ The elli(...TRUNCATED) |
[{"content":"Let $ a$, $ b$, $ c$ be nonzero real numbers such that $ a+b+c=0$ and $ a^3+b^3+c^3=a^5(...TRUNCATED) | "Let $ a$, $ b$, $ c$ be nonzero real numbers such that $ a+b+c=0$ and $ a^3+b^3+c^3=a^5+b^5+c^5$. F(...TRUNCATED) | "Let $ a$, $ b$, $ c$ be nonzero real numbers such that $ a+b+c=0$ and $ a^3+b^3+c^3=a^5+b^5+c^5$. F(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the new problem:\n\n---\n\n**Problem:**\n\nFind all triples of real numbers \\((a,b,c(...TRUNCATED) | 25,878 | 13,714 | 2,438 | ["Okay, let's see. We have this problem where we need to find all triples of real numbers a, b, c su(...TRUNCATED) | ["Given the conditions \\(abc = 1\\) and \\((a^2 - 1)(b^2 - 1)(c^2 - 1) = (ab - 1)(bc - 1)(ca - 1)\\(...TRUNCATED) | ["<think>\nOkay, let's see. We have this problem where we need to find all triples of real numbers a(...TRUNCATED) | [
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] | "The answer provided has multiple short paragraphs due to the character and formatting of the text. (...TRUNCATED) | ["<think>\nOkay, let's see. We have this problem where we need to find all triples of real numbers a(...TRUNCATED) | "<think>\nOkay, so I have this problem here where I need to find all triples of real numbers a, b, c(...TRUNCATED) | [{"from":"human","value":"Let $ a$, $ b$, $ c$ be nonzero real numbers such that $ a+b+c=0$ and $ a^(...TRUNCATED) |
[{"content":"Determine the number of positive integers $m \\le 500$ such that the product of the num(...TRUNCATED) | "Determine the number of positive integers $m \\le 500$ such that the product of the number $m$ and (...TRUNCATED) | "Determine the number of positive integers $m \\le 500$ such that the product of the number $m$ and (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given a positive integer \\( m \\leq 500 \\), we want to find how many such \\( m \\) satisfy:\n\n\(...TRUNCATED) | 20,573 | 12,025 | 1,364 | ["Okay, let's tackle this problem: Determine the number of positive integers \\( m \\le 500 \\) such(...TRUNCATED) | ["To determine the number of positive integers \\( m \\le 500 \\) such that the product of \\( m \\)(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem: Determine the number of positive integers \\( m \\le 500(...TRUNCATED) | [
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] | "The provided answer does not contain any paragraphs longer than 750 words. It is structured in a br(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem: Determine the number of positive integers \\( m \\le 500(...TRUNCATED) | "<think>\nOkay, so I need to find the number of positive integers m ≤ 500 where the product of m a(...TRUNCATED) | [{"from":"human","value":"Determine the number of positive integers $m \\le 500$ such that the produ(...TRUNCATED) |
[{"content":"All sides of the convex hexagon $ABCDEF$ are of equal length, and $\\angle A = \\angle (...TRUNCATED) | "All sides of the convex hexagon $ABCDEF$ are of equal length, and $\\angle A = \\angle B = 120^\\ci(...TRUNCATED) | "All sides of the convex hexagon $ABCDEF$ are of equal length, and $\\angle A = \\angle B = 120^\\ci(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given that \\(ABCDEF\\) is a convex hexagon with all sides equal and \\(\\angle A = \\angle B = 120(...TRUNCATED) | 35,341 | 12,979 | 2,129 | ["Okay, so I need to find the measure of angle F in this convex hexagon ABCDEF. All the sides are eq(...TRUNCATED) | ["Given a convex hexagon \\(ABCDEF\\) with all sides of equal length and \\(\\angle A = \\angle B = (...TRUNCATED) | ["<think>\nOkay, so I need to find the measure of angle F in this convex hexagon ABCDEF. All the sid(...TRUNCATED) | [
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[{"content":"Find the distance between the vertices of the curve given by the equation $xy = 2(x + 2(...TRUNCATED) | Find the distance between the vertices of the curve given by the equation $xy = 2(x + 2y)^2$. | Find the distance between the vertices of the curve given by the equation $xy = 2(x + 2y)^2$. | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\nxy = 2(x + 2y)^2,\n\\]\nwe want to find the distance between its vertices(...TRUNCATED) | 19,886 | 12,165 | 1,241 | ["Okay, so I need to find the distance between the vertices of the curve defined by the equation \\((...TRUNCATED) | ["To find the distance between the vertices of the curve given by the equation \\( xy = 2(x + 2y)^2 (...TRUNCATED) | ["<think>\nOkay, so I need to find the distance between the vertices of the curve defined by the equ(...TRUNCATED) | [
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] | "The response contains a long block of text where the explanation and calculations are provided, and(...TRUNCATED) | ["<think>\nOkay, so I need to find the distance between the vertices of the curve defined by the equ(...TRUNCATED) | "<think>\nOkay, so I need to find the distance between the vertices of the curve defined by the equa(...TRUNCATED) | [{"from":"human","value":"Find the distance between the vertices of the curve given by the equation (...TRUNCATED) |
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