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 40.8k | __original_row_idx int64 18 63.1k | length int64 10.4k 40.8k | ms_id int64 1 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 10.9k 96.2k | conversations listlengths 2 2 |
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[{"content":"A polynomial $P(x)$ has the property that $P(1), P(2), P(3), P(4)$ are four consecutive(...TRUNCATED) | "A polynomial $P(x)$ has the property that $P(1), P(2), P(3), P(4)$ are four consecutive terms in an(...TRUNCATED) | "A polynomial $P(x)$ has the property that $P(1), P(2), P(3), P(4)$ are four consecutive terms in an(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given a polynomial \\(P(x)\\) such that \\(P(1), P(2), P(3), P(4)\\) are four consecutive terms in (...TRUNCATED) | 52,704 | 14,779 | 3,294 | ["Okay, so I need to solve this problem about a polynomial P(x). Let me read it again:\n\n\"A polyno(...TRUNCATED) | ["Given a polynomial \\( P(x) \\) such that \\( P(1), P(2), P(3), P(4) \\) are four consecutive term(...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem about a polynomial P(x). Let me read it again:\n\n\(...TRUNCATED) | ["<think>\nOkay, let's see. The problem says that there's a polynomial P(x) such that P(1), P(2), P((...TRUNCATED) | "<think>\nOkay, let's see. The problem says that there's a polynomial P(x) such that P(1), P(2), P(3(...TRUNCATED) | [{"from":"human","value":"A polynomial $P(x)$ has the property that $P(1), P(2), P(3), P(4)$ are fou(...TRUNCATED) |
[{"content":"Consider the set of all triangles $ORQ$ where $O$ is the origin and $R$ and $Q$ are dis(...TRUNCATED) | "Consider the set of all triangles $ORQ$ where $O$ is the origin and $R$ and $Q$ are distinct points(...TRUNCATED) | "Consider the set of all triangles $ORQ$ where $O$ is the origin and $R$ and $Q$ are distinct points(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nGiven points \\( R, Q \\) with nonnegative integer coordinates \\((x, y(...TRUNCATED) | 35,112 | 19,731 | 2,194 | ["Okay, so I need to solve this problem about triangles ORQ where O is the origin, and R and Q are d(...TRUNCATED) | ["To solve the problem, we need to find the number of distinct triangles \\(ORQ\\) where \\(O\\) is (...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem about triangles ORQ where O is the origin, and R an(...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem. So, we need to find the number of distinct t(...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem. So, we need to find the number of distinct tr(...TRUNCATED) | [{"from":"human","value":"Consider the set of all triangles $ORQ$ where $O$ is the origin and $R$ an(...TRUNCATED) |
[{"content":"Suppose $p(x) = x^4 + ax^3 + bx^2 + ax + 1$ is a polynomial whose roots are all complex(...TRUNCATED) | "Suppose $p(x) = x^4 + ax^3 + bx^2 + ax + 1$ is a polynomial whose roots are all complex numbers lyi(...TRUNCATED) | "Suppose $p(x) = x^4 + ax^3 + bx^2 + ax + 1$ is a polynomial whose roots are all complex numbers lyi(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the polynomial:\n\\[\np(x) = x^4 + a x^3 + b x^2 + a x + 1,\n\\]\nwhere \\(a,b\\) are integer(...TRUNCATED) | 59,782 | 20,540 | 3,736 | ["Okay, so I have this problem here: I need to find the largest possible value of |a| where the poly(...TRUNCATED) | ["Given the polynomial \\( p(x) = x^4 + ax^3 + bx^2 + ax + 1 \\) with all roots on the circle \\( |z(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: I need to find the largest possible value of |a| where(...TRUNCATED) | ["<think>\nOkay, so I have this problem here about a polynomial \\( p(x) = x^4 + ax^3 + bx^2 + ax + (...TRUNCATED) | "<think>\nOkay, so I have this problem here about a quartic polynomial \\( p(x) = x^4 + ax^3 + bx^2 (...TRUNCATED) | [{"from":"human","value":"Suppose $p(x) = x^4 + ax^3 + bx^2 + ax + 1$ is a polynomial whose roots ar(...TRUNCATED) |
[{"content":"The curves $y^2 = x^3$ and $y^2 + x^2 = 1$ intersect at two points. Find the distance b(...TRUNCATED) | "The curves $y^2 = x^3$ and $y^2 + x^2 = 1$ intersect at two points. Find the distance between these(...TRUNCATED) | "The curves $y^2 = x^3$ and $y^2 + x^2 = 1$ intersect at two points. Find the distance between these(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the curves:\n\\[\ny^2 = x^3 \\quad \\text{and} \\quad y^2 + x^2 = 1.\n\\]\n\n**Step 1: Find t(...TRUNCATED) | 38,939 | 13,849 | 2,433 | ["Okay, so I need to find the distance between the two points where the curves y² = x³ and y² + x(...TRUNCATED) | ["To find the distance between the intersection points of the curves \\( y^2 = x^3 \\) and \\( y^2 +(...TRUNCATED) | ["<think>\nOkay, so I need to find the distance between the two points where the curves y² = x³ an(...TRUNCATED) | ["<think>\nAlright, so I need to find the distance between the two intersection points of the curves(...TRUNCATED) | "<think>\nOkay, so I need to find the distance between the two intersection points of the curves y²(...TRUNCATED) | [{"from":"human","value":"The curves $y^2 = x^3$ and $y^2 + x^2 = 1$ intersect at two points. Find t(...TRUNCATED) |
[{"content":"Find the pure imaginary solutions of the equation:\n\n\\[x^4 + 2x^3 - 7x^2 - 18x - 81 =(...TRUNCATED) | "Find the pure imaginary solutions of the equation:\n\n\\[x^4 + 2x^3 - 7x^2 - 18x - 81 = 0\\]\n\nEnt(...TRUNCATED) | "Find the pure imaginary solutions of the equation:\n\n\\[x^4 + 2x^3 - 7x^2 - 18x - 81 = 0\\]\n\nEnt(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the equation:\n\\[\nx^4 + 2x^3 - 7x^2 - 18x - 81 = 0\n\\]\n\nWe want to find **pure imaginary(...TRUNCATED) | 23,622 | 12,641 | 1,476 | ["Okay, so I need to find the pure imaginary solutions of the equation \\(x^4 + 2x^3 - 7x^2 - 18x - (...TRUNCATED) | ["To find the pure imaginary solutions of the equation \\(x^4 + 2x^3 - 7x^2 - 18x - 81 = 0\\), we su(...TRUNCATED) | ["<think>\nOkay, so I need to find the pure imaginary solutions of the equation \\(x^4 + 2x^3 - 7x^2(...TRUNCATED) | ["<think>\nOkay, so I need to find the pure imaginary solutions to the equation \\(x^4 + 2x^3 - 7x^2(...TRUNCATED) | "<think>\nOkay, so I need to find the pure imaginary solutions to the equation \\(x^4 + 2x^3 - 7x^2 (...TRUNCATED) | [{"from":"human","value":"Find the pure imaginary solutions of the equation:\n\n\\[x^4 + 2x^3 - 7x^2(...TRUNCATED) |
[{"content":"Let's say $a$ and $b$ are two positive integers that are relatively prime, and let $M$ (...TRUNCATED) | "Let's say $a$ and $b$ are two positive integers that are relatively prime, and let $M$ be the sum o(...TRUNCATED) | "Let's say $a$ and $b$ are two positive integers that are relatively prime, and let $M$ be the sum o(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nGiven two positive integers \\(a\\) and \\(b\\) that are relatively pri(...TRUNCATED) | 6,990 | 26,379 | 436 | ["Okay, let's try to figure out this problem. So, we have two positive integers, a and b, which are (...TRUNCATED) | ["Given two positive integers \\(a\\) and \\(b\\) that are relatively prime, we need to find the lar(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem. So, we have two positive integers, a and b, w(...TRUNCATED) | ["<think>\nAlright, so I need to find two positive integers, a and b, that are relatively prime. The(...TRUNCATED) | "<think>\nOkay, so I need to find two positive integers, a and b, that are relatively prime. Their g(...TRUNCATED) | [{"from":"human","value":"Let's say $a$ and $b$ are two positive integers that are relatively prime,(...TRUNCATED) |
[{"content":"Let $f(x) = x^5 - 4x^3 + 2x^2 + x + 1$. Determine the remainder when $f(x^{12})$ is div(...TRUNCATED) | "Let $f(x) = x^5 - 4x^3 + 2x^2 + x + 1$. Determine the remainder when $f(x^{12})$ is divided by $f(x(...TRUNCATED) | "Let $f(x) = x^5 - 4x^3 + 2x^2 + x + 1$. Determine the remainder when $f(x^{12})$ is divided by $f(x(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given \\( f(x) = x^5 - 4x^3 + 2x^2 + x + 1 \\), find the remainder when \\( f(x^{12}) \\) is divide(...TRUNCATED) | 16,715 | 12,579 | 1,044 | ["Okay, so I need to find the remainder when \\( f(x^{12}) \\) is divided by \\( f(x) \\), where \\((...TRUNCATED) | ["To determine the remainder when \\( f(x^{12}) \\) is divided by \\( f(x) \\), where \\( f(x) = x^5(...TRUNCATED) | ["<think>\nOkay, so I need to find the remainder when \\( f(x^{12}) \\) is divided by \\( f(x) \\), (...TRUNCATED) | ["<think>\nOkay, so I need to find the remainder when \\( f(x^{12}) \\) is divided by \\( f(x) \\), (...TRUNCATED) | "<think>\nOkay, so I need to find the remainder when f(x¹²) is divided by f(x), where f(x) is the (...TRUNCATED) | [{"from":"human","value":"Let $f(x) = x^5 - 4x^3 + 2x^2 + x + 1$. Determine the remainder when $f(x^(...TRUNCATED) |
[{"content":"A bakery sells a total of 250 loaves of bread per day. They come in two types: whole wh(...TRUNCATED) | "A bakery sells a total of 250 loaves of bread per day. They come in two types: whole wheat and whit(...TRUNCATED) | "A bakery sells a total of 250 loaves of bread per day. They come in two types: whole wheat and whit(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's denote the intended number of whole wheat loaves as \\( W \\) and the intended number of whit(...TRUNCATED) | 49,205 | 16,850 | 3,075 | ["Okay, let me try to figure out this problem step by step. So, the bakery sells a total of 250 loav(...TRUNCATED) | ["The bakery sells a total of 250 loaves of bread per day, with an intended ratio of whole wheat to (...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem step by step. So, the bakery sells a total of(...TRUNCATED) | ["<think>\nOkay, let's see. The problem is about a bakery that sells a total of 250 loaves of bread (...TRUNCATED) | "<think>\nOkay, let's see. The problem is about a bakery that sells a total of 250 loaves of bread p(...TRUNCATED) | [{"from":"human","value":"A bakery sells a total of 250 loaves of bread per day. They come in two ty(...TRUNCATED) |
[{"content":"Given the complex function $f(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta$, where $z$ i(...TRUNCATED) | "Given the complex function $f(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta$, where $z$ is a complex (...TRUNCATED) | "Given the complex function $f(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta$, where $z$ is a complex (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\\[\nf(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta,\n\\]\nwhere \\(z, \\beta, \\delta \\in (...TRUNCATED) | 40,056 | 25,175 | 2,503 | ["Okay, let's see. I have this complex function f(z) = z³ + (2 - 3i)z² + βz + δ. The problem sta(...TRUNCATED) | ["Given the complex function \\( f(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta \\), where \\( z \\) (...TRUNCATED) | ["<think>\nOkay, let's see. I have this complex function f(z) = z³ + (2 - 3i)z² + βz + δ. The pr(...TRUNCATED) | ["<think>\nOkay, let's see. I have this complex function f(z) = z³ + (2 - 3i)z² + βz + δ. The pr(...TRUNCATED) | "<think>\nOkay, so I have this complex function f(z) = z³ + (2 - 3i)z² + βz + δ, where z is a co(...TRUNCATED) | [{"from":"human","value":"Given the complex function $f(z) = z^3 + (2 - 3i)z^2 + \\beta z + \\delta$(...TRUNCATED) |
[{"content":"Find all complex roots of\n\n$$x^5 + ix^4 + 3x^3 - 2ix^2 + 5x + 1 = 0$$\n\nEnter all th(...TRUNCATED) | "Find all complex roots of\n\n$$x^5 + ix^4 + 3x^3 - 2ix^2 + 5x + 1 = 0$$\n\nEnter all the complex ro(...TRUNCATED) | "Find all complex roots of\n\n$$x^5 + ix^4 + 3x^3 - 2ix^2 + 5x + 1 = 0$$\n\nEnter all the complex ro(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the polynomial:\n\\[\nx^5 + i x^4 + 3 x^3 - 2 i x^2 + 5 x + 1 = 0,\n\\]\nwe want to find all (...TRUNCATED) | 20,994 | 14,485 | 1,312 | ["Okay, so I need to find all the complex roots of this polynomial equation:\n\n$$x^5 + ix^4 + 3x^3 (...TRUNCATED) | ["To find all complex roots of the polynomial equation:\n\n$$x^5 + ix^4 + 3x^3 - 2ix^2 + 5x + 1 = 0$(...TRUNCATED) | ["<think>\nOkay, so I need to find all the complex roots of this polynomial equation:\n\n$$x^5 + ix^(...TRUNCATED) | ["<think>\nOkay, so I need to find all the complex roots of this polynomial equation: \n\n\\( x^5 + (...TRUNCATED) | "<think>\nOkay, so I need to find all the complex roots of the polynomial equation:\n\n$$x^5 + ix^4 (...TRUNCATED) | [{"from":"human","value":"Find all complex roots of\n\n$$x^5 + ix^4 + 3x^3 - 2ix^2 + 5x + 1 = 0$$\n\(...TRUNCATED) |
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