data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs of positive integers \\((n, p)\\) such that \\(p\\) is a prime, \\(n \\leq 2p\\), and \\((p-1)^{n} + 1\\) is divisible by \\( (1, p) \\).",
"role": "user"... | math | {
"ground_truth": "(2,2), (3,3), (1,p) \\text{ for any prime } p",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three positive integers have an arithmetic mean of 30 and median of 29. If the median is 6 less than the largest number, what is the smallest number?",
"role": "user"
}
] | math | {
"ground_truth": "26",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real numbers $p$ such that the polynomial:\n\\[ x^4 - 2px^3 + x^2 - 2px + 1 = 0 \\]\nhas at least two distinct positive real roots.",
"role": "user"
}
] | math | {
"ground_truth": "\\left( \\frac{5}{4}, \\infty \\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given six different awards are to be given to four students, with each student receiving at least one award. Calculate the number of different ways the awards can be distributed.... | math | {
"ground_truth": "1560",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube has 3 blue faces, 2 red faces, and 1 green face. What is the probability that when it is rolled, a blue or a green face will be facing up?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a circle C with a radius of 3, the center C is below the x-axis and on the line $y=x$, and the chord cut by circle C on the x-axis is $2\\sqrt{5}$. \n(Ⅰ) Find the equation... | math | {
"ground_truth": "y=x+1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an isosceles triangle with sides of $5$ and $10$, the perimeter of the triangle is ______.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the \\( n \\)-th polynomial \\( p(x) \\) satisfies \\( p(k) = \\frac{1}{C_{n+1}^{k}} \\) for \\( k = 0, 1, 2, \\ldots, n \\), find \\( p(n+1) \\).",
"role": "user"... | math | {
"ground_truth": "\\begin{cases} \n1 & \\text{if } n \\text{ is even,} \\\\\n0 & \\text{if } n \\text{ is odd.}\n\\end{cases}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$, $b$, and $c$ be the roots of the equation $x^3 - 15x^2 + 22x - 8 = 0$. Find the value of $\\frac{a}{\\frac{1}{a}+bc} + \\frac{b}{\\frac{1}{b}+ca} + \\frac{c}{\\frac{1}{c... | math | {
"ground_truth": "\\frac{181}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Isabella traveled from the United States to Canada with $d$ U.S. dollars. Upon entering Canada, she exchanged all her money at a rate where $5$ U.S. dollars could be exchanged fo... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integer triples \\((x, y, z)\\) such that:\n\n\\[ x^{2} + y^{2} + 1 = 2^{z} \\]",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0), (1, 0, 1), (-1, 0, 1), (0, 1, 1), (0, -1, 1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define two sequences of vectors $(\\mathbf{u}_n)$ and $(\\mathbf{z}_n)$ as follows: Start with $\\mathbf{u}_0 = \\begin{pmatrix} 2 \\\\ 2 \\end{pmatrix}$ and $\\mathbf{z}_0 = \\b... | math | {
"ground_truth": "\\begin{pmatrix} 0 \\\\ 0 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which pair $(A,B)$,\n$x^2+xy+y=A$ and $\\frac{y}{y-x}=B$ has no real roots.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 2/3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of distinct intersection points for the graphs of the equations $(x - y + 2)(2x + 3y - 6) = 0$ and $(3x - 2y - 1)(x + 2y - 4) = 0$ in the $xy$-plane.\nA) 0\nB) 1\... | math | {
"ground_truth": "\\text{C) } 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain clothing factory produces jackets and $T$-shirts, with each jacket priced at $100$ yuan and each $T$-shirt priced at $60$ yuan. During a promotional period, the factory... | math | {
"ground_truth": "3480",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A block wall 120 feet long and 9 feet high will be constructed using blocks that are 1 foot high and either 3 feet long, 2 feet long, or 1 foot long (no blocks may be cut). The v... | math | {
"ground_truth": "B) 365 blocks",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Meena owns a bottle cap collection. While on a vacation, she finds a large number of bottle caps, increasing her collection size by $40\\%$ . Later on her same vacation, she dec... | math | {
"ground_truth": "175",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sandy plans to paint her daughter's playhouse including two trapezoidal sides of the roof and the front triangular face, all shaded in the diagram. The paint covers 100 square fe... | math | {
"ground_truth": "\\$15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find $n$ such that $n - 76$ and $n + 76$ are both cubes of positive integers.",
"role": "user"
}
] | math | {
"ground_truth": "140",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Amy paid $X$ dollars and Zoe paid $Y$ dollars, with $X > Y$, determine the amount of money Zoe must give to Amy so that they share the costs equally.",
"role": "us... | math | {
"ground_truth": "\\frac{X-Y}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A box contains 8 white balls and 7 black balls. Five balls are drawn out of the box at random. What is the probability that they all are of the same color?",
"role": "user"
... | math | {
"ground_truth": "\\dfrac{77}{3003}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which values of the parameter \\( a \\), the equation\n\n\\[ \n\\log _{2}\\left(2 x^{2}-x-2 a-4 a^{2}\\right)+3 \\log _{1 / 8}\\left(x^{2}-a x-2 a^{2}\\right)=0 \n\\]\n\nhas ... | math | {
"ground_truth": "( \\frac{3}{5}, 1 )",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are eight individuals, including yourself, and a total fundraising goal of $2400, as well as a $20 fee per person for administration costs, calculate the amount ... | math | {
"ground_truth": "320",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the operation $a \\odot b$ is defined as $\\begin{cases}b, & \\text{if } a \\geqslant b, \\\\ a, & \\text{if } a < b,\\end{cases}$ then the explicit formula for the function $... | math | {
"ground_truth": "f(x) = \\begin{cases} 2-x, & \\text{if } x \\geqslant 1 \\\\ x, & \\text{if } x < 1 \\end{cases}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify: $\\dfrac{\\sqrt{1+2\\sin 610^{\\circ}\\cos 430^{\\circ}}}{\\sin 250^{\\circ}+\\cos 790^{\\circ}}=$\\_\\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation\n\\[(x - \\sqrt[3]{17})(x - \\sqrt[3]{67})(x - \\sqrt[3]{137}) = \\frac{2}{5}\\]has three distinct solutions \\( u, v, \\) and \\( w.\\) Calculate the value of \\( u... | math | {
"ground_truth": "221 + \\frac{6}{5} - 3 \\cdot 1549",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the arithmetic sequence $1$, $6$, $11$, $16$, $21$, $\\ldots$. Find the $20^{\\text{th}}$ term in the sequence.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle is circumscribed around a square with side length $a$, and a regular hexagon is circumscribed around the circle. Determine the area of the hexagon.",
"role": "user"
... | math | {
"ground_truth": "\\sqrt{3} a^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The areas of three squares are 64, 81, and 144. What is the geometric mean of their side lengths?",
"role": "user"
}
] | math | {
"ground_truth": "9.5244",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It takes a steamer $5$ days to go from Gorky to Astrakhan downstream the Volga river and $7$ days upstream from Astrakhan to Gorky. How long will it take for a raft to float ... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Danny wants to give his dog, Rex, the maximum space to roam on his circular playground. He plans to tether Rex to a circular fence that has a radius of 20 feet using a 30-foot ro... | math | {
"ground_truth": "540\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Express $\\frac{213_8}{12_3}+\\frac{234_5}{32_4}$ in base 10.",
"role": "user"
}
] | math | {
"ground_truth": "31\\frac{9}{14}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the expression \\(a \\cdot (b + (c \\cdot (d - e)))\\), and given that Larry correctly evaluated it by ignoring the parentheses, compute the value of \\(e\\) that would all... | math | {
"ground_truth": "\\frac{23}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f$ be a function for which $f\\left(\\dfrac{x}{2}\\right) = x^3 - x + 2$. Find the sum of all values of $z$ for which $f(4z) = 8$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $15 \\times 30 + 45 \\times 15 + 90$.",
"role": "user"
}
] | math | {
"ground_truth": "1215",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the simplified form of $(x + y)^{-2}(x^{-1} + z y^{-1})$ and express your answer using negative exponents.\n**A)** $x^{-1}y^{-1}(x+y)^{-2}$\n**B)** $y^{-1}(x+y)^{-2} + z x^{... | math | {
"ground_truth": "y^{-1}(x+y)^{-2} + z x^{-1} y^{-1}(x+y)^{-2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If circle $C_1: x^2 + y^2 = 16$ is tangent to circle $C_2: (x-a)^2 + y^2 = 1$, then the value of $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "a = \\pm5 \\text{ or } \\pm3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the arithmetic mean of $a$ and $b$ is triple their geometric mean, with $a>b>0$, calculate the ratio $a/b$.",
"role": "user"
}
] | math | {
"ground_truth": "38",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For the five types of phenomena in life: ① \"Very likely to happen\", ② \"Certain to happen\", ③ \"Possible to happen\", ④ \"Impossible to happen\", ⑤ \"Not very likely to happen... | math | {
"ground_truth": "②①③⑤④",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $m$ be the smallest positive integer such that $m^2+(m+1)^2+\\cdots+(m+10)^2$ is the square of a positive integer $n$ . Find $m+n$",
"role": "user"
}
] | math | {
"ground_truth": "95",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many numbers in the list $47$, $4747$, $474747$, $\\dots$, are prime?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the total length of the set of real numbers satisfying \\[\\frac{x^2 - 80x + 1500}{x^2 - 55x + 700} < 0.\\]",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the quadratic equation $x^2 - 5x + k = 0$ with roots $r_1$ and $r_2$, and given that $r_1^2$ and $r_2^2$ are the roots of another quadratic equation $x^2 + px + q = 0$, fin... | math | {
"ground_truth": "-13, 36",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find \\(453_{8} - 326_{8}\\). Express your answer in base \\(8\\).",
"role": "user"
}
] | math | {
"ground_truth": "125_8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The squares of two positive integers differ by 2016. Find the maximum possible sum of the two integers.\n\n[i]Proposed by Clive Chan",
"role": "user"
}
] | math | {
"ground_truth": "1008",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $2006$ students and $14$ teachers in a school. Each student knows at least one teacher (knowing is a symmetric relation). Suppose that, for each pair of a student a... | math | {
"ground_truth": "143",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation $y = -20t^2 + 32t + 60$ describes the height (in feet) of a ball thrown upwards at $32$ feet per second from $60$ feet above the ground. Find the time (in seconds) w... | math | {
"ground_truth": "\\frac{4 + \\sqrt{91}}{5} \\text{ seconds}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Inside a regular tetrahedron \\( ABCD \\) with edge length 1, there are two tangent spheres. One sphere is tangent to the three faces passing through point \\( A \\), and the oth... | math | {
"ground_truth": "\\frac{\\sqrt{6}-1}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many sets of two or more consecutive positive integers have a sum of $30$?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\left(625\\right)^{0.12}\\left(625\\right)^{0.08}$, calculate the numerical value of this expression.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\[\n\\begin{cases}\nx + y = 12 \\\\\n\\frac{x}{z} = \\frac{3}{2} \\\\\nz + u = 10 \\\\\ny \\cdot u = 36\n\\end{cases}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "x = 6, \\quad y = 6, \\quad z = 4, \\quad u = 6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**p4** Define the sequence ${a_n}$ as follows:\n1) $a_1 = -1$ , and\n2) for all $n \\ge 2$ , $a_n = 1 + 2 + . . . + n - (n + 1)$ .\nFor example, $a_3 = 1+2+3-4 = 2$ . Find ... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a batch of products from which three items are selected, let A be the event that all three products are not defective, B be the event that all three products are defective,... | math | {
"ground_truth": "1, 2, 5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all four-digit numbers $\\overline{abcd}$ which are perfect squares and for which the equality holds: $\\overline{ab}=3 \\cdot \\overline{cd} + 1$ .",
"role": "us... | math | {
"ground_truth": "2809",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Divide the set \\( M = \\{1, 2, \\ldots, 12\\} \\) of the first 12 positive integers into four subsets each containing three elements, such that in each subset, one number is the... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=4\\cos x\\sin (x+ \\frac{π}{6})$,\n\n(1) Find the smallest positive period of $f(x)$;\n\n(2) Find the symmetry axis and symmetry center of the graph of $... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integer $n$ when divided with number $3$ gives remainder $a$ , when divided with $5$ has remainder $b$ and when divided with $7$ gives remainder $c$ . Find r... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triathlete competes in a triathlon where the swimming, biking, and running segments are of lengths 1 km, 2 km, and 3 km respectively. The triathlete swims at a rate of 2 kilome... | math | {
"ground_truth": "\\mathrm{(B)}\\ 7.2\\text{ km/h}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the derivative.\n\n\\[ \ny = \\frac{8}{3} \\cdot \\operatorname{cth} 2x - \\frac{1}{3 \\operatorname{ch} x \\cdot \\operatorname{sh}^{3} x}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1 - 4 \\operatorname{sh}^2(x)}{\\operatorname{ch}^2(x) \\operatorname{sh}^4(x)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A large cube $n$ units on each side is fully painted blue on all six faces and then cut into $n^3$ smaller cubes. Exactly one-third of the total number of faces of these smaller ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From the digits set $\\{1,2,3,4,5,6,7,8,9\\}$, eight different digits are placed in an arrangement where five digits form a vertical column and four form a horizontal row, overla... | math | {
"ground_truth": "The correct answer is C) 39.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence $\\{y_{n}\\}_{n \\ge 1}$ is defined by \\[y_{1}=y_{2}=1,\\;\\; y_{n+2}= (4k-5)y_{n+1}-y_{n}+4-2k.\\] Determine all integers $k$ such that each term of this seque... | math | {
"ground_truth": "k = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:<br/>$(1)8+(-\\frac{1}{4})-5-\\left(-0.25\\right)$;<br/>$(2)-36\\times (-\\frac{2}{3}+\\frac{5}{6}-\\frac{7}{12}-\\frac{8}{9})$;<br/>$(3)-2+2\\div (-\\frac{1}{2})\\time... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ such that the following statement holds: Suppose real numbers $a_1$ , $a_2$ , $\\dots$ , $a_n$ , $b_1$ , $b_2$ , $\\dots$ , $b_n$ satisf... | math | {
"ground_truth": "n \\ge 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a segment $AB$ of length $26$, and points $C$ and $D$ located on $AB$ such that $AC=1$ and $AD=8$, let points $E$ and $F$ be on one of the semicircles with diameter $AB$ fo... | math | {
"ground_truth": "7\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many (not necessarily positive) integer values of $n$ is the value of $32000\\cdot \\left(\\tfrac{2}{5}\\right)^n$ an integer?",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the coordinates of the center of the hyperbola \\[\\frac{(3y-6)^2}{8^2} - \\frac{(4x-5)^2}{3^2} = 1.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac54, 2\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a group of 150 people, 120 indicated they liked Beethoven, and 95 indicated they liked Chopin. What is the minimum number of people who could have said they liked both Beethov... | math | {
"ground_truth": "65",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest positive integer $n$ such that $\\sqrt{n} - \\sqrt{n-1} < 0.005$?\nA) 9999\nB) 10000\nC) 10001\nD) 10002",
"role": "user"
}
] | math | {
"ground_truth": "C) 10001",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Diagrams $X$, $Y$, and $Z$ consist of two equilateral triangles and a square, respectively. Equilateral triangle $X$ has an area of $75\\sqrt{3}$ square inches, and equilateral t... | math | {
"ground_truth": "B) 25%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\{a_n\\}$ is an arithmetic sequence, with the first term $a_1 > 0$, $a_{2012} + a_{2013} > 0$, and $a_{2012} \\cdot a_{2013} < 0$, then the largest natural number $n$ for wh... | math | {
"ground_truth": "2012",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose \\(x^2\\) varies inversely with \\(y^4\\). If \\(x = 5\\) when \\(y = 2\\), find the value of \\(x^2\\) when \\(y = 4\\).",
"role": "user"
}
] | math | {
"ground_truth": "x^2 = \\frac{25}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive two-digit integers are factors of $2^{24}-1$?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Tom paid $95, Dorothy paid $140, and Sammy paid $165, calculate Tom gave Sammy $t$ dollars, and Dorothy gave Sammy $d$ dollars to share the costs equally, and then fin... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "a) What is the probability that the square of a randomly chosen integer ends in the digit 1? What is the probability that the cube of a randomly chosen integer ends in the digits... | math | {
"ground_truth": "0.4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the interval(s) where the function $y=\\log_{2}(3x^{2}-7x+2)$ is decreasing.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, \\frac{1}{3}) \\cup (2, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose two distinct integers are chosen from between 4 and 20, inclusive. What is the probability that their product is divisible by 4?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{68}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a^{m}=a^{n}$ ($a \\gt 0$ and $a\\neq 1$, $m$ and $n$ are positive integers), then $m=n$. Use the above conclusion to solve the following problems:<br/>\n$(1)$ If $2\\times 4^... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( f(x) = x^3 + ax + b \\), with \\( a \\neq b \\), and suppose the tangent lines to the graph of \\( f \\) at \\( x = a \\) and \\( x = b \\) are parallel. Find \\( f(1) \\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Among all pairs of real numbers $(a, b)$ such that $\\cos \\cos a = \\cos \\cos b$ with $-\\frac{5\\pi}{2} \\leq a, b \\leq \\frac{5\\pi}{2}$, Emily randomly selects a pair $(A, ... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of the quadratic polynomial\n\n$$\ny=\\frac{2}{\\sqrt{3}} x^{2}+b x+c\n$$\n\nintersects the positive half-axis of the $Oy$ axis at the point $M$, and the positive half-... | math | {
"ground_truth": "\\frac{1}{2} \\text{ and } \\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integer pairs $(a, b)$ such that $\\frac{2^{a+b}+1}{2^a+2^b+1}$ is an integer.**General**\nFind all positive integer triples $(t, a, b)$ such that $\\fra... | math | {
"ground_truth": "(2, 1, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five monkeys share a pile of peanuts. The first monkey divides the peanuts into five piles, leaving one peanut which it eats, and takes away one pile. The second monkey then divi... | math | {
"ground_truth": "3121",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation \\(\\frac{\\sin 3x}{\\sin x} - \\frac{2 \\cos 3x}{\\cos x} = 5|\\sin x|\\).",
"role": "user"
}
] | math | {
"ground_truth": "x = \\pm \\arcsin \\frac{1}{4} + k\\pi, \\quad k \\in \\mathbb{Z}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many numbers are in the list $-48, -42, -36, \\ldots, 72, 78?$",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x+y=\\frac{11}{17} \\) and \\( x-y=\\frac{1}{119} \\), what is the value of \\( x^2-y^2 \\)? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{11}{2003}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the polynomial $$ P(x) = 1+3x + 5x^2 + 7x^3 + ...+ 1001x^{500}. $$ Express the numerical value of its derivative of order $325$ for $x = 0$ .",
"role": "user"
}... | math | {
"ground_truth": "651 \\cdot 325!",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sides of triangle are $x$ , $2x+1$ and $x+2$ for some positive rational $x$ . Angle of triangle is $60$ degree. Find perimeter",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nonnegative reals $x_1$ , $x_2$ , $\\dots$ , $x_n$ satisfies $x_1+x_2+\\dots+x_n=n$ . Let $||x||$ be the distance from $x$ to the nearest integer of $x$ (e.g. $||3.8... | math | {
"ground_truth": "\\frac{n^2 - n + 0.5}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola $y=-(x-5)^{2}+3$, find the coordinates of its vertex.",
"role": "user"
}
] | math | {
"ground_truth": "(5,3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( f(g(x)) = \\sin 2x \\) and \\( g(x) = \\tan \\frac{x}{2} \\) for \\( 0 < x < \\pi \\), then find \\( f\\left( \\frac{\\sqrt{2}}{2} \\right) = \\) ______.",
"role": "us... | math | {
"ground_truth": "\\frac{4 \\sqrt{2}}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Call a positive integer *prime-simple* if it can be expressed as the sum of the squares of two distinct prime numbers. How many positive integers less than or equal to $100$ ar... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given: \\(\\operatorname{ctg} \\alpha = \\frac{3}{4}\\), \\(\\operatorname{ctg} \\beta = \\frac{1}{7}\\), \\(0 < \\alpha < \\frac{\\pi}{2}\\), \\(0 < \\beta < \\frac{\\pi}{2}\\).... | math | {
"ground_truth": "\\frac{3\\pi}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular piece of paper $ABCD$ has sides of lengths $AB = 1$ , $BC = 2$ . The rectangle is folded in half such that $AD$ coincides with $BC$ and $EF$ is the foldin... | math | {
"ground_truth": "30^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $F_n$ be the $n$th Fibonacci number, defined by $F_1 = F_2 = 1$ and $F_{n + 1} = F_n + F_{n - 1}$. Calculate the product:\n\\[\\prod_{k = 3}^{101} \\left( \\frac{F_k}{F_{k - ... | math | {
"ground_truth": "(101, 102)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "I have a bag containing only red, blue, and green marbles. The ratio of red marbles to blue marbles to green marbles is $2:4:6$. If there are 42 green marbles in the bag, how man... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the price of a stamp is 25 cents, what is the maximum number of stamps that could be purchased with $50$?",
"role": "user"
}
] | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cashier mistakenly counted 15 nickels as dimes and 10 quarters as half-dollars. By how much, in cents, did the cashier overestimate or underestimate the total cash value?\nA) 2... | math | {
"ground_truth": "B) 325 cents",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "See all the problems from 5-th Kyiv math festival [here](http://www.mathlinks.ro/Forum/viewtopic.php?p=506789#p506789)\r\n\r\n\r\nTriangle $ABC$ and straight line $l$ are giv... | math | {
"ground_truth": "l_1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence $\\{a_{n}\\}_{n\\geq 0}$ is defined by $a_{0}=20,a_{1}=100,a_{n+2}=4a_{n+1}+5a_{n}+20(n=0,1,2,...)$ . Find the smallest positive integer $h$ satisfying $1998|a... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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