messages listlengths 2 2 | instruction_seed stringlengths 51 1.26k | response_seed stringlengths 51 1.26k | _source stringclasses 1
value | gpt41_mini_response stringlengths 10.4k 35k | __original_row_idx int64 2 51.6k | length int64 10.4k 35k | ms_id int64 17 3.94k | reasoning sequencelengths 16 16 | deepseek_solution sequencelengths 16 16 | final_reasoning_trace sequencelengths 16 16 | correct sequencelengths 16 16 | classifier_reasoning stringlengths 127 1.39k | _majority_responses sequencelengths 1 16 | verified_final_reasoning_trace stringlengths 8.79k 91.4k | conversations listlengths 2 2 |
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[{"content":"A triangle with side lengths 3, 4, and 5 is inscribed in a rectangle. The vertices of t(...TRUNCATED) | "A triangle with side lengths 3, 4, and 5 is inscribed in a rectangle. The vertices of the triangle (...TRUNCATED) | "A triangle with side lengths 3, 4, and 5 is inscribed in a rectangle. The vertices of the triangle (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem:** \nA triangle with side lengths 3, 4, and 5 is inscribed in a rectangle such that the (...TRUNCATED) | 51,118 | 15,845 | 954 | ["Okay, so I need to find the area of a rectangle in which a 3-4-5 triangle is inscribed, with the t(...TRUNCATED) | ["Given a 3-4-5 triangle inscribed in a rectangle with its vertices at the midpoints of the rectangl(...TRUNCATED) | ["<think>\nOkay, so I need to find the area of a rectangle in which a 3-4-5 triangle is inscribed, w(...TRUNCATED) | [
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] | "The provided answer correctly analyzes the geometric arrangement of the triangle and rectangle, est(...TRUNCATED) | ["<think>\nOkay, so I need to find the area of a rectangle in which a 3-4-5 triangle is inscribed, w(...TRUNCATED) | "<think>\nOkay, so there's this problem where a 3-4-5 triangle is inscribed in a rectangle, and the (...TRUNCATED) | [{"from":"human","value":"A triangle with side lengths 3, 4, and 5 is inscribed in a rectangle. The (...TRUNCATED) |
[{"content":"Three cylindrical containers have radii 3 cm, 4 cm, and 5 cm, and all have the same hei(...TRUNCATED) | "Three cylindrical containers have radii 3 cm, 4 cm, and 5 cm, and all have the same height of 12 cm(...TRUNCATED) | "Three cylindrical containers have radii 3 cm, 4 cm, and 5 cm, and all have the same height of 12 cm(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n\n- Three cylindrical containers with radii \\( r_1 = 3 \\) cm, \\( r_2 = 4 \\) cm, \\((...TRUNCATED) | 21,847 | 10,701 | 1,627 | ["Okay, let's see. I need to figure out how many times the smallest container (radius 3 cm) will be (...TRUNCATED) | ["The problem involves three cylindrical containers with radii 3 cm, 4 cm, and 5 cm, all having the (...TRUNCATED) | ["<think>\nOkay, let's see. I need to figure out how many times the smallest container (radius 3 cm)(...TRUNCATED) | [
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] | "The provided response correctly analyzes the problem regarding the three cylindrical containers, ca(...TRUNCATED) | ["<think>\nOkay, let's see. I need to figure out how many times the smallest container (radius 3 cm)(...TRUNCATED) | "<think>\nOkay, so we have three cylindrical containers with radii 3 cm, 4 cm, and 5 cm. All of them(...TRUNCATED) | [{"from":"human","value":"Three cylindrical containers have radii 3 cm, 4 cm, and 5 cm, and all have(...TRUNCATED) |
[{"content":"There are five green balls and three red balls in a bag. When two balls are randomly ch(...TRUNCATED) | "There are five green balls and three red balls in a bag. When two balls are randomly chosen from th(...TRUNCATED) | "There are five green balls and three red balls in a bag. When two balls are randomly chosen from th(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's carefully analyze the problem and derive the expectation:\n\n---\n\n### Problem Restatement:\(...TRUNCATED) | 27,092 | 13,011 | 2,752 | ["Okay, let's see. There's a problem here with green and red balls in a bag. Five green and three re(...TRUNCATED) | ["The problem involves a bag with 5 green balls and 3 red balls. When two balls are drawn without re(...TRUNCATED) | ["<think>\nOkay, let's see. There's a problem here with green and red balls in a bag. Five green and(...TRUNCATED) | [
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] | "The provided answer correctly identifies the steps to compute the expected value of the difference (...TRUNCATED) | ["<think>\nOkay, let's see. There's a problem here with green and red balls in a bag. Five green and(...TRUNCATED) | "<think>\nOkay, so there's this problem with a bag containing five green balls and three red balls. (...TRUNCATED) | [{"from":"human","value":"There are five green balls and three red balls in a bag. When two balls ar(...TRUNCATED) |
[{"content":"The cube of an integer is 155 less than the square of the integer. What is the product (...TRUNCATED) | "The cube of an integer is 155 less than the square of the integer. What is the product of all integ(...TRUNCATED) | "The cube of an integer is 155 less than the square of the integer. What is the product of all integ(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's translate the problem into an equation first.\n\nLet the integer be \\( x \\).\n\n- The cube (...TRUNCATED) | 31,104 | 12,847 | 520 | ["Okay, let's try to figure out this problem. So, we need to find integers where the cube of the int(...TRUNCATED) | ["Given the problem, we need to find integers \\( x \\) such that the cube of the integer is 155 les(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem. So, we need to find integers where the cube o(...TRUNCATED) | [
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] | "The answer provided concludes that there are no integer solutions to the equation, which is correct(...TRUNCATED) | ["<think>\nOkay, let's see. The problem says: \"The cube of an integer is 155 less than the square o(...TRUNCATED) | "<think>\nOkay, so the problem says: \"The cube of an integer is 155 less than the square of the int(...TRUNCATED) | [{"from":"human","value":"The cube of an integer is 155 less than the square of the integer. What is(...TRUNCATED) |
[{"content":"Let $f(x) = ax^2+bx+c$ be a quadratic function such that $$\\frac{f(-1)}{f(1)} = \\frac(...TRUNCATED) | "Let $f(x) = ax^2+bx+c$ be a quadratic function such that $$\\frac{f(-1)}{f(1)} = \\frac{f(2)}{f(-2)(...TRUNCATED) | "Let $f(x) = ax^2+bx+c$ be a quadratic function such that $$\\frac{f(-1)}{f(1)} = \\frac{f(2)}{f(-2)(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\\[\nf(x) = ax^2 + bx + c,\n\\]\nwith the condition\n\\[\n\\frac{f(-1)}{f(1)} = \\frac{f(2)(...TRUNCATED) | 12,997 | 11,180 | 504 | ["Okay, so I need to find the value of 'a' in the quadratic function f(x) = ax² + bx + c. The given(...TRUNCATED) | ["Given the quadratic function \\( f(x) = ax^2 + bx + c \\) with the conditions \\( \\frac{f(-1)}{f((...TRUNCATED) | ["<think>\nOkay, so I need to find the value of 'a' in the quadratic function f(x) = ax² + bx + c. (...TRUNCATED) | [
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] | "The provided answer correctly follows the steps required to solve for the value of a in the quadrat(...TRUNCATED) | ["<think>\nOkay, so I need to find the value of 'a' in the quadratic function f(x) = ax² + bx + c. (...TRUNCATED) | "<think>\nOkay, let me try to figure this problem out. So, we have a quadratic function f(x) = ax² (...TRUNCATED) | [{"from":"human","value":"Let $f(x) = ax^2+bx+c$ be a quadratic function such that $$\\frac{f(-1)}{f(...TRUNCATED) |
[{"content":"An infinite set of congruent spheres are packed into a cylinder with a circular base. T(...TRUNCATED) | "An infinite set of congruent spheres are packed into a cylinder with a circular base. The spheres f(...TRUNCATED) | "An infinite set of congruent spheres are packed into a cylinder with a circular base. The spheres f(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- A cylinder with a circular base, radius \\( R = 5 \\) units.\n- It contains an infini(...TRUNCATED) | 25,607 | 17,383 | 2,303 | ["Okay, let's see. So, there's this problem about spheres packed into a cylinder, and when the cylin(...TRUNCATED) | ["The problem involves an infinite set of congruent spheres packed into a cylinder with a circular b(...TRUNCATED) | ["<think>\nOkay, let's see. So, there's this problem about spheres packed into a cylinder, and when (...TRUNCATED) | [
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] | "The analysis of the problem correctly identifies that the cylinders' height must be proportional to(...TRUNCATED) | ["<think>\nOkay, let's see. So, there's this problem about spheres packed into a cylinder, and when (...TRUNCATED) | "<think>\nOkay, so I need to find the height of the cylinder. Let me start by understanding the prob(...TRUNCATED) | [{"from":"human","value":"An infinite set of congruent spheres are packed into a cylinder with a cir(...TRUNCATED) |
[{"content":"In an international soccer tournament, teams can have players from the same continent. (...TRUNCATED) | "In an international soccer tournament, teams can have players from the same continent. A coach is s(...TRUNCATED) | "In an international soccer tournament, teams can have players from the same continent. A coach is s(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's carefully unpack the problem and notations:\n\n---\n\n### What is given?\n\n- **Players and t(...TRUNCATED) | 43,515 | 16,987 | 3,219 | ["Okay, let's try to figure out this problem step by step. It's a bit complex with all these constra(...TRUNCATED) | ["Given the problem constraints and requirements, we need to determine the maximum number of pairs o(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem step by step. It's a bit complex with all thes(...TRUNCATED) | [
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] | "The provided answer correctly concludes that due to the constraints of the problem, specifically th(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem step by step. It's a bit complex with all thes(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem step by step. It's a bit complex with all the c(...TRUNCATED) | [{"from":"human","value":"In an international soccer tournament, teams can have players from the sam(...TRUNCATED) |
[{"content":"A hyperbola is drawn with transverse and conjugate axes of lengths 12 and 10 respective(...TRUNCATED) | "A hyperbola is drawn with transverse and conjugate axes of lengths 12 and 10 respectively. Using on(...TRUNCATED) | "A hyperbola is drawn with transverse and conjugate axes of lengths 12 and 10 respectively. Using on(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Hyperbola with transverse axis length \\(2a = 12 \\implies a = 6\\)\n- Conjugate axis(...TRUNCATED) | 16,736 | 13,600 | 445 | ["Okay, so I need to find the radius of a circle that's tangent to a hyperbola. The hyperbola has a (...TRUNCATED) | ["Given a hyperbola with a transverse axis of length 12 and a conjugate axis of length 10, we need t(...TRUNCATED) | ["<think>\nOkay, so I need to find the radius of a circle that's tangent to a hyperbola. The hyperbo(...TRUNCATED) | [
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] | "The provided answer correctly follows the problem's requirements and steps logically through the ca(...TRUNCATED) | ["<think>\nOkay, so I need to find the radius of a circle that's tangent to a hyperbola. The hyperbo(...TRUNCATED) | "<think>\nOkay, so I need to find the radius of a circle that's tangent to a hyperbola, where the ci(...TRUNCATED) | [{"from":"human","value":"A hyperbola is drawn with transverse and conjugate axes of lengths 12 and (...TRUNCATED) |
[{"content":"Points $E,$ $F,$ $G,$ and $H$ are equally spaced on the circumferences of four concentr(...TRUNCATED) | "Points $E,$ $F,$ $G,$ and $H$ are equally spaced on the circumferences of four concentric circles c(...TRUNCATED) | "Points $E,$ $F,$ $G,$ and $H$ are equally spaced on the circumferences of four concentric circles c(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Given:**\n- Four concentric circles with center \\( O \\).\n- Radii of the circles: \n \\[\n r,(...TRUNCATED) | 39,479 | 12,643 | 3,578 | ["Okay, so we have this geometry problem here. Let me try to visualize it first. There are four conc(...TRUNCATED) | ["Given four concentric circles centered at \\( O \\) with radii \\( r \\), \\( r + d \\), \\( r + 2(...TRUNCATED) | ["<think>\nOkay, so we have this geometry problem here. Let me try to visualize it first. There are (...TRUNCATED) | [
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] | "The provided response meticulously analyzes the geometric relationships between various components (...TRUNCATED) | ["<think>\nOkay, so we have this geometry problem here. Let me try to visualize it first. There are (...TRUNCATED) | "<think>\nOkay, let's try to tackle this geometry problem. Hmm, points E, F, G, H are equally spaced(...TRUNCATED) | [{"from":"human","value":"Points $E,$ $F,$ $G,$ and $H$ are equally spaced on the circumferences of (...TRUNCATED) |
[{"content":"Mary and Jane are two secret agents who have agreed to meet at a certain location betwe(...TRUNCATED) | "Mary and Jane are two secret agents who have agreed to meet at a certain location between 8 PM and (...TRUNCATED) | "Mary and Jane are two secret agents who have agreed to meet at a certain location between 8 PM and (...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let's analyze the problem carefully.\n\n---\n\n### Problem restatement:\n- Mary and Jane each arriv(...TRUNCATED) | 5,954 | 11,096 | 2,063 | ["Okay, so Mary and Jane are supposed to meet between 8 PM and 9 PM. But there's an enemy agent who (...TRUNCATED) | ["Mary and Jane are secret agents who agree to meet between 8 PM and 9 PM. They arrive independently(...TRUNCATED) | ["<think>\nOkay, so Mary and Jane are supposed to meet between 8 PM and 9 PM. But there's an enemy a(...TRUNCATED) | [
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] | "The provided answer appropriately breaks down the complex problem into manageable parts, correctly (...TRUNCATED) | ["<think>\nOkay, so Mary and Jane are supposed to meet between 8 PM and 9 PM. But there's an enemy a(...TRUNCATED) | "<think>\nOkay, let's see. I need to find the probability that Mary and Jane meet without the enemy (...TRUNCATED) | [{"from":"human","value":"Mary and Jane are two secret agents who have agreed to meet at a certain l(...TRUNCATED) |
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