data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all integers $n\\geq 1$ for which the numbers $1,2,\\ldots,n$ may be (re)ordered as $a_1,a_2,\\ldots,a_n$ in such a way that the average $\\dfrac {a_1+a_2+\\cdot... | math | {
"ground_truth": "n \\in \\{1, 3\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $ \\triangle{ABC}$ , where $ A$ is at $ (0,0)$ , $ B$ is at $ (20,0)$ , and $ C$ is on the positive $ y$ -axis. Cone $ M$ is formed when $ \\triangle{ABC}$ is... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the function y = -x^3 + ax is monotonous on the interval [1, +∞), what is the maximum value of a?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $\\omega_1, \\omega_2, \\omega_3, \\ldots, \\omega_{2020!}$ be the distinct roots of $x^{2020!} - 1$ . Suppose that $n$ is the largest integer such that $2^n$ divides ... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $D(n)$ denote the number of ways of writing the positive integer $n$ as a product $n = f_1 \\cdot f_2 \\cdots f_k$, where $k\\ge 1$, the $f_i$ are integers strictly greater... | math | {
"ground_truth": "\\textbf{112}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 $3$ is a solution to the equation $x^4 + kx^2 - 26 = 0$, determine the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{55}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 the function $f(x)=x^{3}-6x-1$. \n$(1)$ Find the equation of the tangent line to the function $f(x)$ at $x=2$; \n$(2)$ Determine the intervals of monotonicity for the fun... | math | {
"ground_truth": "(- \\sqrt {2}, \\sqrt {2})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $\\triangle ABC$, the angles opposite sides $a$, $b$, and $c$ are $A$, $B$, and $C$ respectively. If $b(2-\\cos A) = a(\\cos B+1)$ and $a+c=4$, then the maximum value... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $\\mathbb{Q}$ be the set of rational numbers, $\\mathbb{Z}$ be the set of integers. On the coordinate plane, given positive integer $m$ , define $$ A_m = \\left\\{ (x,... | math | {
"ground_truth": "\\frac{2015}{6}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 real numbers $x$ and $y$ satisfying $x - \\sqrt{x+1} = \\sqrt{y+1} - y$, find the range of $x + y$.",
"role": "user"
}
] | math | {
"ground_truth": "[-\\sqrt{5} + 1, \\sqrt{5} + 1]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the number of subsets \\( B \\) of the set \\( \\{1, 2, \\ldots, 2005\\} \\) such that the sum of its elements leaves a remainder of 2006 when divided by 2048.",
"role":... | math | {
"ground_truth": "2^{1994}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the three sides of a triangle be $\\ell, m, n$ , respectively, satisfying $\\ell>m>n$ and $\\left\\{\\frac{3^\\ell}{10^4}\\right\\}=\\left\\{\\frac{3^m}{10^4}\\right\\}=\... | math | {
"ground_truth": "3003",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\[ (4x - 1) \\cdot \\left( \\frac{1}{8x} \\cdot \\left( (\\sqrt{8x - 1} + 4x)^{-1} - (\\sqrt{8x - 1} - 4x)^{-1} \\right) \\right)^{1/2} \\]",
"role": "user"
}
] | math | {
"ground_truth": "\\text{ -1 if } x \\in \\left[\\frac{1}{8}, \\frac{1}{4} \\right), \\; 1 \\text{ if } x \\in \\left(\\frac{1}{4}, \\infty \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If there are exactly two points on the circle $(x-3)^{2}+(y+5)^{2}=r^{2}$ that are at a distance of 1 from the line $4x-3y=2$, then find the range of the radius $r$.",
"role"... | math | {
"ground_truth": "(4,6)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 point $ P$ is chosen at random in the interior of equilateral triangle $ ABC$, determine the probability that $ \\triangle ABP$ has a greater area than each of $... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two ants, one starting at $(-1,1)$ and the other at $(1,1)$, walk to the right along the parabola $y=x^{2}$ such that their midpoint moves along the line $y=1$ with constant spee... | math | {
"ground_truth": "3 \\sqrt{3} - 3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a regular tetrahedron $S A B C$, the segment $D O$ connects the midpoint $D$ of edge $S A$ with the centroid $O$ of face $A B C$, and point $E$ is the midpoint of edge $S B$. ... | math | {
"ground_truth": "o+\\rfrac{5\\sqrt{3}}+{18}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of \\( \\text{rem}'\\left(\\frac{5}{9}, -\\frac{3}{7}\\right) \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{62}{63}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\\begin{cases} x=1+\\cos \\phi \\\\ y=\\sin \\phi \\end{cases}$, where $\\phi$ is the param... | math | {
"ground_truth": "8 \\sqrt {2} - 8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 positive integers \\( n \\) such that \\( 3^n + 1 \\) is divisible by \\( n^2 \\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "[help me] Let m and n denote the number of digits in $2^{2007}$ and $5^{2007}$ when expressed in base 10. What is the sum m + n?",
"role": "user"
}
] | math | {
"ground_truth": "2008",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to shuffle a deck of 32 cards?",
"role": "user"
}
] | math | {
"ground_truth": "32!",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An integer $N$ is selected at random in the range $1 \\leq N \\leq 2020$. What is the probability that the remainder when $N^8$ is divided by $5$ is $1$?\nA) $\\frac{1}{5}$\nB) $... | math | {
"ground_truth": "\\textbf{(D)} \\frac{4}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 that in the rectangular coordinate system $(xOy)$, the parametric equations of circle $C$ are $ \\begin{cases} x=3+2\\cos \\theta \\ y=-4+2\\sin \\theta \\end{cases} (\\the... | math | {
"ground_truth": "2 \\sqrt {d^{2}-4}= \\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $S$ be the sum of the base 10 logarithms of all the proper divisors of 1000000. What is the integer nearest to $S$ ?",
"role": "user"
}
] | math | {
"ground_truth": "141",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We are given a map divided into $13\\times 13$ fields. It is also known that at one of the fields a tank of the enemy is stationed, which we must destroy. To achieve this we ne... | math | {
"ground_truth": "254",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 the center of the hyperbola given by the equation \\(9x^2 - 54x - 36y^2 + 288y - 576 = 0.\\)",
"role": "user"
}
] | math | {
"ground_truth": "(3,4)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 the sequence $\\left\\{ a_n \\right\\}$, $a_1=2$, $a_{n+1}=2a_n$, and $S_n$ is the sum of the first $n$ terms of $\\left\\{ a_n \\right\\}$. If $S_n=126$, then $n=$ ?",
"r... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $p=2017$ be a prime. Find the remainder when \\[\\left\\lfloor\\dfrac{1^p}p\\right\\rfloor + \\left\\lfloor\\dfrac{2^p}p\\right\\rfloor+\\left\\lfloor\\dfrac{3^p}p\\right\... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 scores of five students, 71, 76, 80, 82, and 91, which are listed in ascending order, and the fact that the class average always remains an integer after each score is ... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using sticks of the same length, you can form the digits 0 to 9. Using 10 such sticks, how many digits can be formed?",
"role": "user"
}
] | math | {
"ground_truth": "59",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Twelve pencils are sharpened so that all of them have different lengths. Masha wants to arrange the pencils in a box in two rows of 6 pencils each, such that the lengths of the p... | math | {
"ground_truth": "132",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a rising number, such as $234689$, is a positive integer each digit of which is larger than each of the digits to its left, consider the six-digit rising numbers forme... | math | {
"ground_truth": "\\textbf{(D)} \\ 8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 the positive primes $p$ for which there exist integers $m,n$ satisfying :\r $p=m^2+n^2$ and $m^3+n^3-4$ is divisible by $p$ .",
"role": "user"
}
] | math | {
"ground_truth": "p = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integers $n$ are there such that $n$ is a multiple of $7$, and the least common multiple of $7!$ and $n$ equals $7$ times the greatest common divisor of $14!$ a... | math | {
"ground_truth": "192",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 largest positive number \\( c \\) such that for every natural number \\( n \\), the inequality \\( \\{n \\sqrt{2}\\} \\geqslant \\frac{c}{n} \\) holds, where \\( \\{n \\... | math | {
"ground_truth": "\\frac{1}{2\\sqrt{2}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the following 4 by 4 grid with one corner square removed:\nYou may start at any square in this grid and at each move, you may either stop or travel to an adjacent square... | math | {
"ground_truth": "14007",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $F$ is the right focus of the hyperbola $C: x^{2}- \\frac {y^{2}}{8}=1$, and $P$ is a point on the left branch of $C$, $A(0,6 \\sqrt {6})$, when the perimeter of $\\tr... | math | {
"ground_truth": "2 \\sqrt {6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the expression $(-\\frac{7}{8})^{0}+[(-2)^{3}]^{-\\frac{2}{3}}$, find the value.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the sum of all integers $0\\le a \\le124$ so that $a^3-2$ is a multiple of $125$ .",
"role": "user"
}
] | math | {
"ground_truth": "265",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 area of a triangle with angles $\\frac{1}{7} \\pi$ , $\\frac{2}{7} \\pi$ , and $\\frac{4}{7} \\pi $ , and radius of its circumscribed circle $R=1$ .",
"role": "u... | math | {
"ground_truth": "\\frac{\\sqrt{7}}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four positive integers $a, b, c, d$ satisfy the condition: $a < b < c < d$ . For what smallest possible value of $d$ could the following condition be true: the arithmetic me... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 can is in the shape of a right circular cylinder. The circumference of the base of the can is 18 inches, and the height of the can is 8 inches. A spiral stripe is painted on th... | math | {
"ground_truth": "\\sqrt{1360}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 least positive integer $k$ such that, in every convex 1001-gon, the sum of any k diagonals is greater than or equal to the sum of the remaining diagonals?",
"ro... | math | {
"ground_truth": "249750",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Farmer Yang has a \\(2015 \\times 2015\\) square grid of corn plants. One day, the plant in the very center of the grid becomes diseased. Every day, every plant adjacent to a dis... | math | {
"ground_truth": "2014",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A dart board is fashioned into a regular hexagon divided into regions, including a smaller central regular hexagon and six surrounding equilateral triangles. If a dart thrown at ... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "During the process of choosing trial points using the 0.618 method, if the trial interval is $[3, 6]$ and the first trial point is better than the second, then the third trial po... | math | {
"ground_truth": "5.292",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ant starts at a vertex of a cube, walking only along the edges, until it returns to the initial vertex, without passing through any vertex more than once. What is the longest ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ and $b$ be positive real numbers such that $3a + 2b = 2.$ Find the minimum value of\n\\[\\frac{1}{a} + \\frac{1}{b}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5 + 2\\sqrt{6}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 integer values of $p$ and $q$ will the equation $x^{2} + p x + q = 0$ have one root that is 4 times the other? How many solutions do we get if we consider $p$ and $q$ t... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathbb{Z}_{>0}$ denote the set of positive integers. For any positive integer $k$ , a function $f: \\mathbb{Z}_{>0} \\to \\mathbb{Z}_{>0}$ is called *$k$ -good* if $... | math | {
"ground_truth": "k \\ge 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 prime numbers are added in sequence starting with $2$. The first sum is $2$, the next sum is $2 + 3$, and this pattern continues. How many of the first 15 sums of this sequen... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 sum of the squares of the distances from the points of tangency of the incircle of a given triangle with its sides to the circumcenter, if the radius of the incircle is ... | math | {
"ground_truth": "R^2 + r^2 - 2Rr",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) Evaluate $ \\int_0^1 xe^{x^2}dx$ .\r\n\r\n(2) Let $ I_n\\equal{}\\int_0^1 x^{2n\\minus{}1}e^{x^2}dx$ . Express $ I_{n\\plus{}1}$ in terms of $ I_n$ .",
"role": "user... | math | {
"ground_truth": "I_{n+1} = \\frac{e}{2} - n I_n",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "I have two 20-sided dice. The first die has 5 maroon sides, 6 teal sides, 7 cyan sides, and 2 sparkly sides. The second die has 4 maroon sides, 7 teal sides, 8 cyan sides, and 1 ... | math | {
"ground_truth": "\\frac{3}{10}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 \\(\\mathbf{v} = \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}\\) and \\(\\mathbf{w} = \\begin{pmatrix} -4 \\\\ 1 \\end{pmatrix}\\), compute \\(\\text{proj}_{\\mathbf{w}} \\mathbf... | math | {
"ground_truth": "\\begin{pmatrix} \\frac{20}{17} \\\\ \\frac{-5}{17} \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 positive integers $n,$ let $\\nu_3 (n)$ denote the largest integer $k$ such that $3^k$ divides $n.$ Find the number of subsets $S$ (possibly containing 0 or 1 ele... | math | {
"ground_truth": "2^{81}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the polynomial $x^3 - 6x^2 + 11x - 6 = 0$ which has three real roots, $a$, $b$, and $c$. Calculate $\\frac{1}{a^2} + \\frac{1}{b^2} + \\frac{1}{c^2}$.",
"role": "use... | math | {
"ground_truth": "\\frac{49}{36}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 $i$ denotes the imaginary unit, find the value of the complex number $\\frac{i}{(1-i)^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $x$, $y$, and $2x + \\frac{y}{2}$ are not zero, simplify the expression $\\left( 2x + \\frac{y}{2} \\right)^{-1} \\left[(2x)^{-1} + \\left( \\frac{y}{2} \\right)^{-1} ... | math | {
"ground_truth": "(xy)^{-1}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Without using a calculator, find the largest prime factor of $16^4 + 4 \\times 16^2 + 4 - 15^4$.",
"role": "user"
}
] | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 $x - y = 10$ and $xy = 9$, what is the value of $x^2 + y^2$?",
"role": "user"
}
] | math | {
"ground_truth": "118",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 circular table has a radius of $5$ units. Eight rectangular place mats are placed on the table. Each place mat has a width of $2$ units and a length $y$. They are positioned su... | math | {
"ground_truth": "\\sqrt{24 - 5\\sqrt{2 - \\sqrt{2}} - \\frac{5\\sqrt{2 - \\sqrt{2}}}{2} + 1}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to choose 4 cards from a standard deck of 52 cards, if exactly two of them must be of the same suit and the other two each of different suits?",
"role... | math | {
"ground_truth": "158004",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 city has rich tourism resources. According to a survey conducted over the past month (consisting of 30 days), the number of tourists on the t-th day, denoted as $f(t)$ (in ten ... | math | {
"ground_truth": "441",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $ABC$ be a triangle with area $92$ square centimeters. Calculate the area of another triangle whose sides have the same lengths as the medians of triangle $ABC$ .",
... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 John made three purchases for $\\textdollar 2.45$, $\\textdollar 3.58$, and $\\textdollar 7.96$, calculate his total, rounded to the nearest dollar.",
"role": "use... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $PQR$, which is equilateral, lines $WX$, $YZ$, and $ST$ are parallel to $QR$, with $PW = WY = YS = ST$. Determine the ratio of the area of trapezoid $STQR$ to the are... | math | {
"ground_truth": "\\frac{9}{25}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are nine cards with the numbers from 1 to 9 (each used exactly once). These cards are arranged in a row such that there are no three consecutive cards forming an increasing... | math | {
"ground_truth": "\\text{on card } A: 5, \\text{ on card } B: 2, \\text{ on card } C: 9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The parabolas \\( y = a x^2 - 2 \\) and \\( y = 4 - b x^2 \\) intersect the coordinate axes at exactly four points, forming a kite with an area of 12. Find the value of \\( a + b... | math | {
"ground_truth": "1.5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given real numbers $x$, $y$, and $z$ are chosen independently and at random from the interval $[0, m]$ for some positive integer $m$. The probability that no two of $x$, $y$, and... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 beach resort is located \\(400\\) yards from a straight highway. Along this highway, a shopping mall is \\(700\\) yards away from a point on the highway directly opposite to th... | math | {
"ground_truth": "The correct answer is \\textbf{(B)} \\(464\\) yards.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 diagonal of a square is \\( \\sqrt{a^2 + 4b^2} \\), calculate the area of this square.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a^2 + 4b^2}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a coordinate plane, a square \\( K \\) is marked with vertices at points \\((0,0)\\) and \\((10,10)\\). Inside this square, depict the set \\( M \\) of points \\((x, y)\\) who... | math | {
"ground_truth": "10\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For natural numbers \\( a > b > 1 \\), define the sequence \\( x_{1}, x_{2}, \\ldots \\) by the formula \\( x_{n}=\\frac{a^{n}-1}{b^{n}-1} \\). Find the smallest \\( d \\) such t... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive real number $a$ and an integer $b$ between $3$ and $300$ inclusive, determine how many ordered pairs $(a,b)$ satisfy the equation $(\\log_b a)^{2018}=\\log_b(a^{... | math | {
"ground_truth": "894",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 net change in the population over these four years is a 20% increase, then a 30% decrease, then a 20% increase, and finally a 30% decrease. Calculate the net change in the po... | math | {
"ground_truth": "-29",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 degree of the polynomial $(x^2+y)^5 (x^3+y)^4$ in terms of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sheila has been invited to a picnic tomorrow. The picnic will occur regardless of the weather conditions. If it rains, there is a 30% chance that Sheila will decide to go. If it ... | math | {
"ground_truth": "0.46 = 46\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 11 step paths are there from point $A$ to point $C$ which pass through point $B$ in a grid diagram? Assume $A$ is at the top left, $B$ is 4 steps right and 2 steps down ... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 triangle $XYZ$, $XY=15$ and $XZ=22$. The angle bisector of $\\angle X$ intersects $YZ$ at point $E$, and point $N$ is the midpoint of $XE$. Let $Q$ be the point of intersectio... | math | {
"ground_truth": "\\dfrac{22}{15}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$n$ balls are placed independently uniformly at random into $n$ boxes. One box is selected at random, and is found to contain $b$ balls. Let $e_n$ be the expected value of... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 sum of the real values of $x$ satisfying the equation $|x-1| = 3|x+3|$.",
"role": "user"
}
] | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 $f(x^3) = \\log_2{x}$, calculate $f(8)$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 a rhombus $ABCD$ with side length $2$ and $\\angle BAC=60^{\\circ}$, then $\\overrightarrow{BC} \\cdot \\overrightarrow{AC}=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 2019 students in a school, and some of these students are members of different student clubs. Each student club has an advisory board consisting of 12 students who are ... | math | {
"ground_truth": "\\binom{2003}{11}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $3\\times 6$ grid is filled with the numbers in the list $\\{1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9\\}$ according to the following rules: (1) Both the first three columns an... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 \\( y \\) be a positive integer such that \\( 7y \\equiv 1 \\pmod{29} \\).\n\nWhat is the remainder when \\( 8 + y \\) is divided by 29?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John needs to buy at least 60 fluid ounces of apple juice. The store sells juice in 150 milliliter bottles. Given that there are 34 fluid ounces in 1 liter, determine the smalles... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 ratio of the length to the width of a rectangle is $4$ : $3$. If the rectangle has diagonal of length $d$, then find the constant $k$ such that the area may be expressed as $... | math | {
"ground_truth": "\\frac{12}{25}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. Calculate the cost of purchasing 5 sandwiches and 8 sodas.",
"role": "user"
}
] | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Increasing the radius of a cylinder by $ 6$ units increased the volume by $ y$ cubic units. Increasing the altitude of the cylinder by $ 6$ units also increases the volume ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two circles centered at $O$ and $P$ have radii of length $5$ and $6$ respectively. Circle $O$ passes through point $P$ . Let the intersection points of circles $O$ a... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a library, there are 1485 boxes, each containing 42 books. When these are repacked into boxes containing 45 books each, how many books are left unpacked?",
"role": "user"
... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 a rectangle $ABCD$ with $AB = 8$ units and $BC = 6$ units. A line segment starts moving from vertex $A$ towards vertex $C$ along the diagonal $AC$. The line segment main... | math | {
"ground_truth": "B) 4 units",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "3000 people each go into one of three rooms randomly. What is the most likely value for the maximum number of people in any of the rooms?",
"role": "user"
}
] | math | {
"ground_truth": "1019",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $1234 \\times 2 + 2341 \\times 2 + 3412 \\times 2 + 4123 \\times 2$.",
"role": "user"
}
] | math | {
"ground_truth": "22220",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a plane, several points are marked such that no three points are collinear. A line is drawn through every pair of points. How many points are marked on the plane, given that a... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest common factor of 48, 160, and 120?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 positive geometric sequence $\\{a_n\\}$ with a common ratio $q > 1$, and it satisfies $a_2=6$, $a_1a_3+2a_2a_4+a_3a_5=900$. Let the sum of the first $n$ terms of the sequ... | math | {
"ground_truth": "\\dfrac{4}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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