conversations listlengths 2 2 | problem stringlengths 16 14k ⌀ | deepseek_reasoning stringlengths 832 115k ⌀ | deepseek_solution stringlengths 0 13.3k ⌀ | ground_truth_solution stringlengths 1 7.96k ⌀ | domain stringclasses 6
values | source stringclasses 9
values | test_cases stringlengths 33 44.2M ⌀ | starter_code stringlengths 0 956 ⌀ | response stringlengths 1.25k 120k ⌀ |
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"value": "10. If $z_{1}, z_{2}, z_{3}$ satisfy $\\left|z_{1}\\right|=\\left|z_{2}\\right|=\\left|z_{3}\\right|=1, z_{1}+z_{2}+z_{3}=1, z_{1} z_{2} z_{3}=1$, then $\\left(z_{1}, z_{2}, z_{3}\\right)$ $=$ . $\\qquad$"
},
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"value": "<think>\nOkay, let's see. ... | null | null | null | null | null | null | null | null | null |
[
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"value": "In triangle \\(ABC\\), the sides opposite to angles \\(A, B,\\) and \\(C\\) are denoted by \\(a, b,\\) and \\(c\\) respectively. Given that \\(c = 10\\) and \\(\\frac{\\cos A}{\\cos B} = \\frac{b}{a} = \\frac{4}{3}\\). Point \\(P\\) is a moving point on the incircle of triangle \... | null | null | null | null | null | null | null | null | null |
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"value": "9. Given that $M N$ is a moving chord of the circumcircle of equilateral $\\triangle A B C$ with side length $2 \\sqrt{6}$, $M N=4$, and $P$ is a moving point on the sides of $\\triangle A B C$. Then the maximum value of $\\overrightarrow{M P} \\cdot \\overrightarrow{P N}$ is"
... | null | null | null | null | null | null | null | null | null |
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"value": "Let \\( X \\) be a set of \\( n \\) elements and \\( Y \\) be a subset of \\( X \\) with \\( k \\) elements. Prove that the largest family \\( S \\) of subsets of \\( X \\) that contain exactly \\( r \\) elements of \\( Y \\) consists of \\( C_{k} C_{n}^{[\\frac{n-k}{2}]} \\) sub... | null | null | null | null | null | null | null | null | null |
[{"from":"human","value":"Determine all functions $ f: \\mathbb{R} \\mapsto \\mathbb{R}$ with $ x(...TRUNCATED) | "Determine all functions $ f: \\mathbb{R} \\mapsto \\mathbb{R}$ with $ x,y \\in \\mathbb{R}$ suc(...TRUNCATED) | "Okay, so I need to find all real functions f such that for every real numbers x and y, the equation(...TRUNCATED) | "To determine all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(x - f(y)) = f(x (...TRUNCATED) | "**\n Assume \\( f \\) is not identically zero. From the periodicity and additivity, we can infer (...TRUNCATED) | math | numina_math | null | null | "<think>\nOkay, so I need to find all real functions f such that for every real numbers x and y, the(...TRUNCATED) |
[{"from":"human","value":"Given a circle and a point \\( M \\) inside it, the legs of a right angle (...TRUNCATED) | "Given a circle and a point \\( M \\) inside it, the legs of a right angle with vertex \\( M \\) int(...TRUNCATED) | "Alright, so I need to find the locus of the midpoint of segment AB, where A and B are points where (...TRUNCATED) | "The locus of the midpoint of segment \\( AB \\) as the right angle rotates around point \\( M \\) i(...TRUNCATED) | "\n1. **Introduce Notations:**\n - Let $H$ be the locus of the midpoint of segment $AB$.\n - Let(...TRUNCATED) | math | numina_math | null | null | "<think>\nAlright, so I need to find the locus of the midpoint of segment AB, where A and B are poin(...TRUNCATED) |
[{"from":"human","value":"In a certain country, the total salary of the top $10\\%$ highest-paid wor(...TRUNCATED) | "In a certain country, the total salary of the top $10\\%$ highest-paid workers accounts for $90\\%$(...TRUNCATED) | "Okay, let me try to figure this out. So the problem is about income distribution in a country. The (...TRUNCATED) | "**Step-by-Step Explanation and Answer:**\n\nThe problem asks whether a country where the top 10% of(...TRUNCATED) | "\nTo determine if it is possible that in a country where the top 10% of earners receive 90% of the (...TRUNCATED) | math | numina_math | null | null | "<think>\nOkay, let me try to figure this out. So the problem is about income distribution in a coun(...TRUNCATED) |
[{"from":"human","value":"Determine all real-coefficient polynomials \\( P(x) \\) that satisfy the e(...TRUNCATED) | "Determine all real-coefficient polynomials \\( P(x) \\) that satisfy the equation\n\n\\[ \nP(a-b) +(...TRUNCATED) | "Okay, so I need to find all real-coefficient polynomials \\( P(x) \\) that satisfy the equation \\((...TRUNCATED) | "To determine all real-coefficient polynomials \\( P(x) \\) that satisfy the equation \\( P(a-b) + P(...TRUNCATED) | "\n1. Substitute $a = b = c = 0$ in the given condition to see if it holds:\n \\[\n P(a-b) + P(b(...TRUNCATED) | math | numina_math | null | null | "<think>\nOkay, so I need to find all real-coefficient polynomials \\( P(x) \\) that satisfy the equ(...TRUNCATED) |
[{"from":"human","value":"The admission fee for an exhibition is $ \\$25$ per adult and $ \\$12$ per(...TRUNCATED) | "The admission fee for an exhibition is $ \\$25$ per adult and $ \\$12$ per child. Last Tuesday, th(...TRUNCATED) | "Okay, let me try to figure this problem out. So, the admission fee is $25 per adult and $12 per chi(...TRUNCATED) | "Given the admission fee of $25 per adult and $12 per child, and the total collection of $1950 last (...TRUNCATED) | "To solve the problem, we start by defining variables for the number of adults and children attendin(...TRUNCATED) | math | numina_math | null | null | "<think>\nOkay, let me try to figure this problem out. So, the admission fee is $25 per adult and $1(...TRUNCATED) |
[{"from":"human","value":"A famous story about the mathematicians G.H. Hardy and Srinivasa Ramanujan(...TRUNCATED) | "A famous story about the mathematicians G.H. Hardy and Srinivasa Ramanujan goes as follows (as told(...TRUNCATED) | "Okay, I need to solve this problem where I have to find the largest bus number up to a given m. A b(...TRUNCATED) | "To solve this problem, we need to find the largest number (up to a given limit \\( m \\)) that can (...TRUNCATED) | null | code | taco | {"inputs": ["1730\n", "100\n"], "outputs": ["1729\n", "none\n"]} | "<think>\nOkay, I need to solve this problem where I have to find the largest bus number up to a giv(...TRUNCATED) |
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