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": "Given a sequence $\\left\\{ a_n \\right\\}$ where each term is positive, and the sum of the first $n$ terms is $S_n$, it is known that $2$, $a_n$, and $S_n$ form an arithmetic se... | math | {
"ground_truth": "\\frac{n}{4(n+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": "There are $n$ mathematicians seated around a circular table with $n$ seats numbered $1,$ $2,$ $3,$ $...,$ $n$ in clockwise order. After a break they again sit around the table. T... | math | {
"ground_truth": "333",
"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 the function $f(x) = \\frac{x^2 - 4x + 3 + a}{x - 1}$, where $a$ is a constant;\n(1) When $a=2$, solve the inequality $f(x) \\geq 1$;\n(2) When $a < 0$, find the range of t... | math | {
"ground_truth": "(-\\infty, \\frac{a}{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": "A certain school has a total of 2000 students in the primary and high school levels. In order to understand their vision conditions, a sampling survey is now being conducted. If ... | math | {
"ground_truth": "200",
"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": "The product $N$ of three positive integers is $8$ times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of $N$.",
"role": ... | math | {
"ground_truth": "560",
"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 the even function $f(x)$ is increasing on $(-\\infty, -1]$, compare the values of $f(-1.5)$, $f(-1)$, and $f(2)$.",
"role": "user"
}
] | math | {
"ground_truth": "f(2) < f(-1.5) < f(-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": "In $\\triangle ABC$, $\\angle A = 120^\\circ$, $\\angle B = 30^\\circ$, $\\angle C = 30^\\circ$, $\\overline{AH}$ is a median, and $\\overline{BM}$ is also a median. Calculate $\... | math | {
"ground_truth": "30^\\circ",
"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 ellipse $C: \\frac{x^{2}}{3}+ \\frac{y^{2}}{2}=1$ with left and right foci $F_1$ and $F_2$, respectively, and the line $l: y=kx+1$ intersecting the ellipse at points $A... | math | {
"ground_truth": "2, 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point \\( P \\) is selected at random from the interior of the hexagon with vertices \\( A = (0, 0) \\), \\( B = (3, 0) \\), \\( C = (4.5, \\sqrt{3}) \\), \\( D = (3, 2\\sqrt{3})... | math | {
"ground_truth": "\\frac{6 \\sqrt{3} - \\pi}{6 \\sqrt{3}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many distinct solutions are there to the equation \\( |x-10| = |x-3| \\)?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 8 bus services, 3 train services, and 2 ferry services from location A to location B in one day. Find the total number of different ways a person can travel from A to B... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ 30$ students participated in the mathematical Olympiad. Each of them was given $ 8$ problems to solve. Jury estimated their work with the following rule:\r\n1) Each problem ... | math | {
"ground_truth": "60",
"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 sets \\( A = \\{ x \\mid -2 < x < -1, \\text{ or } x > 1 \\} \\) and \\( B = \\{ x \\mid x^2 + ax + b \\leq 0, a, b \\in \\mathbb{R} \\} \\), if \\( A \\cup B = \\{ x \... | math | {
"ground_truth": "a = -4, b = 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": "Calculate $(8^5 \\div 8^2) \\cdot 4^6$.",
"role": "user"
}
] | math | {
"ground_truth": "2^{21}",
"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": "We say that a positive integer N is *nice* if it satisfies the following conditions: $\\bullet$ All of its digits are $1$ or $2$ $\\bullet$ All numbers formed by $3$ cons... | math | {
"ground_truth": "2221211122",
"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 positive integers $N$ and $N^2$ both end in the same sequence of four digits $abcd$ when written in base 10, where digit $a$ is not zero. Find the three-digit number ... | math | {
"ground_truth": "937",
"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 graph of $(x-1)^2 + y^2 = m$ is tangent to the graph of $x + y = 1$, determine the value of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "Given that the complex numbers corresponding to points $A$ and $B$ on the complex plane are $z\\_1=\\sin^{2}\\theta+i$ and $z\\_2=-\\cos^{2}\\theta+i\\cos 2\\theta$, respectively... | math | {
"ground_truth": "\\theta=\\frac{5\\pi}{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": "In Mrs. Lively's class, three-fourths of the boys and two-thirds of the girls passed the handwriting test. It is known that an equal number of boys and girls passed the test. Add... | math | {
"ground_truth": "21",
"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 vectors $\\overrightarrow{a}=(1,k)$ and $\\overrightarrow{b}=(2,2)$, and $\\overrightarrow{a}+\\overrightarrow{b}$ is colinear with $\\overrightarrow{a}$, find the value of... | math | {
"ground_truth": "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 number of integers $n$ that satisfy\n\\[20 < n^2 < 150.\\]",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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 right triangle \\(DEF\\), where \\(\\angle E\\) is the right angle, \\(\\cos D = \\frac{8\\sqrt{65}}{65}\\). Given that \\(EF = \\sqrt{65}\\), find the length of \\(DE\\).",
... | 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 real numbers \\( x \\) and \\( y \\) satisfy the equation\n\\[ 2^{x} + 3^{y} = 4^{x} + 9^{y} \\]\n\nFind the range of \\( U = 8^{x} + 27^{y} \\).",
"role": "user"
}
] | 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": "The graph shows the mass, in kilograms, of Jeff's pet Atlantic cod, given its age in years. Find the age of the cod when its mass is $15 \\mathrm{~kg}$.",
"role": "user"
}
... | math | {
"ground_truth": "7",
"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 an arithmetic sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted by $S_n$. Given $S_{m-1}=-2$, $S_{m}=0$, and $S_{m+1}=3$, find the common difference $d=$ ... | math | {
"ground_truth": "m = 5",
"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": "Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are ... | math | {
"ground_truth": "341",
"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 focus of the parabola $y^2=2px$ coincides with the right focus of the ellipse $\\frac{x^2}{6} + \\frac{y^2}{2} = 1$, find the value of $p$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that point $P(x,y)$ is a moving point on the circle $x^{2}+y^{2}=2y$,\n(1) Find the range of $z=2x+y$;\n(2) If $x+y+a\\geqslant 0$ always holds, find the range of real numb... | math | {
"ground_truth": "6-2\\sqrt{73}",
"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": "The third and fourth terms of a geometric sequence are 12 and 18, respectively. What is the second term?",
"role": "user"
}
] | math | {
"ground_truth": "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 quadruples \\(\\left(p_{1}, p_{2}, p_{3}, p_{4}\\right)\\), where \\(p_{1}, p_{2}, p_{3}, p_{4}\\) are all prime numbers, and satisfy:\n(1) \\(p_{1}<p_{2}<p_{3}<p_{... | math | {
"ground_truth": "(2, 5, 19, 37), (2, 11, 19, 31), (2, 13, 19, 29)",
"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 points A and B are 12 units apart, determine how many points C exist such that the perimeter of triangle ABC is 60 units and the area of triangle ABC is 144 square uni... | math | {
"ground_truth": "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": "Convert the point $\\left( 4, \\pi, 6 \\right)$ in cylindrical coordinates to rectangular coordinates.",
"role": "user"
}
] | math | {
"ground_truth": "(-4, 0, 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": "A few (at least $5$ ) integers are put on a circle, such that each of them is divisible by the sum of its neighbors. If the sum of all numbers is positive, what is its minimal v... | math | {
"ground_truth": "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": "Given that rose bushes are spaced about $1$ foot apart, find the number of bushes needed to surround a circular patio whose radius is $12$ feet.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"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": "What is the maximum number of pawns that can be placed on a chessboard (no more than one pawn per square), given:\n\n1) A pawn cannot be placed on square e4;\n2) No two pawns can... | math | {
"ground_truth": "39",
"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 set $A=\\{x|-1<x<2\\}$, and set $B=\\{x|1<x<3\\}$, then $A\\cap B=$ ?",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|1<x<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": "Consider the graph of $y = \\frac{r(x)}{s(x)}$, where $r(x)$ is linear and $s(x)$ is quadratic. The graph has vertical asymptotes at $x = -2$ and $x = 3$, and passes through the ... | 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": "Given the sequence $\\{v_n\\}$ defined by $v_1 = 7$ and $v_{n+1} - v_n = 5 + 6(n-1)$ for $n=1,2,3,\\dots$, express $v_n$ as a polynomial in $n$ and calculate the algebraic sum of... | 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": "Divide 2004 into the sum of n consecutive natural numbers, where n is a natural number greater than 1, and determine the number of ways to do this.",
"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": "Antal numbers 100 matchboxes from 1 to 100 and puts an arbitrary number of matches in each box. Bea randomly selects 15 boxes, and Antal counts the matches in those boxes (withou... | math | {
"ground_truth": "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": "Given $A$ can finish a task in $12$ days, $B$ is $20\\%$ more efficient than $A$, and $C$ works twice as efficiently as $A$, calculate how many days it will take for $B$ and $C$ ... | math | {
"ground_truth": "3.75",
"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 inverse of the matrix\n\\[\n\\begin{pmatrix} 4 & -2 \\\\ 8 & -4 \\end{pmatrix}.\n\\]\nIf the inverse does not exist, then enter the zero matrix.",
"role": "user"
}... | math | {
"ground_truth": "\\begin{pmatrix} 0 & 0 \\\\ 0 & 0 \\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": "Given a right triangle \\(ABC\\) with legs \\(AB = 42\\) and \\(BC = 56\\). A circle passing through point \\(B\\) intersects side \\(AB\\) at point \\(P\\), side \\(BC\\) at poi... | math | {
"ground_truth": "1250",
"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 all pairs of natural numbers such that the sum of each number in the pair with 1 is divisible by the other number.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 1), (1, 2), (2, 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 $\\triangle ABC$, points $G$ and $H$ are on $\\overline{AB}$ and $\\overline{BC}$, respectively. If $\\overline{AG}$ and $\\overline{CH}$ intersect at $P$ such that $AP/PG=5$ ... | math | {
"ground_truth": "\\frac{3}{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": "Let $n$ and $m$ be natural numbers such that $m+\u0006 i=a_ib_i^2$ for $i=1,2, \\cdots\u0002 n$ \u000e where $a_i$ and $b_i$ are natural numbers and $a_i$ is not div... | math | {
"ground_truth": "n = 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": "In \\( \\triangle ABC \\) with \\( AB = 15 \\), \\( BC = 14 \\), and \\( AC = 16 \\), let \\( N \\) be a point on \\( \\overline{AC} \\) such that the circumcircles of \\( \\tria... | math | {
"ground_truth": "\\frac{15}{14}",
"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 three numbers will be randomly chosen without replacement from $\\{2, 3, 4, 5, 6, 9\\}$, what is the probability that their product will be a multiple of 12? Express your answ... | 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": "Bill is buying cans of soup. Cans come in $2$ shapes. Can $A$ is a rectangular prism shaped can with dimensions $20\\times16\\times10$ , and can $B$ is a cylinder shaped c... | math | {
"ground_truth": "3200 - 1000\\pi \\approx 58.41",
"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 values of x for which the equation $5y^2 + 3y + 2 = 3(8x^2 + y + 1)$ holds true, given that $y = 3x$.",
"role": "user"
}
] | math | {
"ground_truth": "x = \\pm \\frac{1}{\\sqrt{21}}",
"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": "Positive real numbers $x \\neq 1$ and $y \\neq 1$ satisfy $\\log_2{x} = \\log_y{8}$ and $xy = 128$. What is $(\\log_2{\\tfrac{x}{y}})^2$?\nA) 32\nB) 35\nC) 37\nD) 40\nE) 45",
... | math | {
"ground_truth": "C) 37",
"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 there are two-legged birds, three-legged fantasy creatures, and four-legged mammals in an exotic animal park, with a total of 200 heads and 558 legs, determine the num... | math | {
"ground_truth": "94",
"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) Alex is climbing a staircase with 10 steps. Each time, he jumps either one step up or two steps up. How many different ways are there for Alex to climb the staircase?\n\nb) Du... | math | {
"ground_truth": "512",
"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": "Tom's age is $T$ years, which is also the sum of the ages of his three children. His age $N$ years ago was twice the sum of their ages then. Calculate $T/N$.",
"role": "user"... | math | {
"ground_truth": "5",
"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 a geometric sequence $\\left\\{a_{n}\\right\\}$ with a common ratio $q \\in (1,2)$, and that $a_{n}$ is a positive integer for $1 \\leq n \\leq 6$, find the minimum value o... | math | {
"ground_truth": "243",
"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 mass of the new alloy be 1, and let the relative masses of the 1st, 2nd, and 3rd alloys in it be denoted by \\( x \\), \\( y \\), and \\( z \\) respectively. The chromium... | math | {
"ground_truth": "\\text{Answer}: \\text{the smallest percentage of chromium in the new alloy is $25\\%$, and the largest is $40\\%$.}",
"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 probability that event $A$ occurs be $\\frac{4}{5}$, the probability that event $B$ occurs be $\\frac{3}{4}$, and the probability that event $C$ occurs be $\\frac{2}{3}$.... | math | {
"ground_truth": "\\Big[0, \\frac{2}{3}\\Big]",
"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": "Points $A$, $B$, and $C$ are positioned sequentially such that the distance $AB$ is $a$ km, and the distance $BC$ is $b$ km. A cyclist starts from point $A$ and heads towards poi... | math | {
"ground_truth": "\\frac{a(a+b)}{2a+b}",
"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 $|\\overrightarrow{a}| = 1$, $|\\overrightarrow{b}| = \\sqrt{2}$, and $\\overrightarrow{a} \\perp \\overrightarrow{b}$, find $|\\overrightarrow{a} + \\overrightarrow{b... | 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": "A cyclic trapezoid has two parallel sides \\( a \\) and \\( b \\) where \\( a < b \\). From one endpoint of the longer base, the shorter base is seen at an angle of \\( 45^\\circ... | math | {
"ground_truth": "t_1 = \\frac{(a+b)(a - \\sqrt{2a^2 - b^2})}{4}, \\quad t_2 = \\frac{(a+b)(a + \\sqrt{2a^2 - b^2})}{4}",
"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": "Ninth-grader Gavrila decided to weigh a basketball, but he only had weights with a mass of 400 g, a light ruler with worn-off markings at the ends, a pencil, and many weightless ... | math | {
"ground_truth": "\\text{600g}",
"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": "Sally has six red cards numbered 1 through 6 and seven blue cards numbered 2 through 8. She attempts to create a stack where the colors alternate, and the number on each red card... | math | {
"ground_truth": "17",
"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 world-renowned Marxist theorist *Joric* is obsessed with both mathematics and social egalitarianism. Therefore, for any decimal representation of a positive integer $n$ , he... | math | {
"ground_truth": "\\frac{1}{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": "Find \\( x \\) if \\( \\log_8(3x - 5) = 2 \\).",
"role": "user"
}
] | math | {
"ground_truth": "x = 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": "Given the inequality $|x| \\leq 1$, find the solution set.",
"role": "user"
}
] | math | {
"ground_truth": "[-1, 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": "Write the canonical equations of the line.\n\n$$\n\\begin{aligned}\n& x+y+z-2=0 \\\\\n& x-y-2z+2=0\n\\end{aligned}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x}{-1} = \\frac{y - 2}{3} = \\frac{z}{-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": "(1) If $b < a < 0$, then among the following results: $① a+b < ab$; $② |a| > |b|$; $③ \\dfrac{1}{b} > \\dfrac{1}{a} > 0$; $④$ the minimum value of the expression $\\dfrac{b}{a} >... | 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": "The power function $f(x)=(m^{2}-m-1)x^{-2m-1}$ is monotonically increasing on $(0,+\\infty)$. Find the real number $m=$____.",
"role": "user"
}
] | math | {
"ground_truth": "m=-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 the line $l: kx - y + 1 - 2k = 0$ ($k \\in \\mathbb{R}$) passes through a fixed point $P$, the coordinates of point $P$ are \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 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": "Let's consider six numbers: 2, 3, 8, 9, 14, and 15. These numbers should be placed in a similar setup consisting of vertical and horizontal alignments such that the sum of the nu... | math | {
"ground_truth": "38",
"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": "15 balls numbered 1 through 15 are placed in a bin. In how many ways can 4 balls be drawn, in order, from the bin, if each ball remains outside the bin after it is drawn and at l... | math | {
"ground_truth": "31080",
"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 gumball machine contains $10$ red, $6$ white, $8$ blue, and $9$ green gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same c... | math | {
"ground_truth": "C) 13",
"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 area of a regular $n$-sided polygon inscribed in a unit circle is denoted as $f(n)$, where $n \\geqslant 3$. Then, $f(3)=$ ______; The following statements describe $f(n)$:\n... | math | {
"ground_truth": "1, 3, 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": "Given a parabola $y^2 = 2px$, where a straight line $l$ passes through its focus and is perpendicular to the x-axis, intersecting the parabola at points A and B. If $|AB| = 10$ a... | math | {
"ground_truth": "25",
"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": "The equation \\(64x^3 - 144x^2 + 92x - 15 = 0\\) has roots that form an arithmetic sequence. Calculate the difference between the largest and smallest root.",
"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": "Let $F$ be the focus of the parabola $y=- \\dfrac {1}{4}x^{2}$, and let line $l$, which is tangent to the parabola at point $P(-4,-4)$, intersect the $x$-axis at point $Q$. Find ... | math | {
"ground_truth": "\\dfrac {\\pi}{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": "A circle with center $O$ is divided into 16 equal arcs, marked with consecutive letters from $A$ to $P$. What is the total number of degrees in the sum of angles $x$ and $y$ if $... | math | {
"ground_truth": "90^\\circ",
"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": "For a positive constant $p$ , let $f(x)=\\int_{-1}^x \\{p-\\ln (1+|t|)\\}\\ dt.$ (1) Find the extreme value of $f(x)$ .\n\n(2) Find the range of $p$ such that the curve $y=... | math | {
"ground_truth": "\\ln(2\\ln(2)) < p < 2\\ln(2) - 1",
"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 polynomial $a x^{2} + b x + c$ has integer coefficients and two distinct roots that are greater than 0 but less than 1. How small can $|a|$ be?",
"role": "user"
}
] | math | {
"ground_truth": "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 that the numbers $1, 4, 7, 10, 13$ are placed in five squares such that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertic... | math | {
"ground_truth": "24",
"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": "$(-\\frac{1}{2})^{-1}+\\left(\\pi -3\\right)^{0}+|1-\\sqrt{2}|+\\sin 45^{\\circ}\\sin 30^{\\circ}=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5\\sqrt{2}}{4}-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": "Factorize: $\\frac{2}{9}a^{2}-\\frac{4}{3}a+2=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{9}(a-3)^{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": "The sum of the first \\( n \\) terms of a geometric sequence \\(\\{a_n\\}\\) with all real number terms is denoted by \\( S_n \\). Given \\( S_{10} = 10 \\) and \\( S_{30} = 70 \... | math | {
"ground_truth": "150",
"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 \\(5^4 = 25^m\\), what is \\(m\\)?",
"role": "user"
}
] | math | {
"ground_truth": "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": "A flower bouquet contains pink roses, red roses, pink carnations, red carnations, and yellow tulips. Two fifths of the pink flowers are roses, six sevenths of the red flowers are... | math | {
"ground_truth": "B) 55%",
"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 a card flipping game during a math class, the teacher numbered 54 playing cards in the order of 1, 2, 3, …, 54 and placed them face down in a row. There were exactly 54 studen... | math | {
"ground_truth": "1, 4, 9, 16, 25, 36, 49",
"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": "The Garfield Super Winners play $100$ games of foosball, in which teams score a non-negative integer number of points and the team with more points after ten minutes wins (if b... | math | {
"ground_truth": "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": "Given a right prism $ABC-A_{1}B_{1}C_{1}$ with height $3$, whose base is an equilateral triangle with side length $1$, find the volume of the conical frustum $B-AB_{1}C$.",
"... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{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": "Let $n$ be a positive integer and $a_1, a_2, \\dots, a_n$ non-zero real numbers. What is the least number of non-zero coefficients that the polynomial $P(x) = (x - a_1)(x - ... | math | {
"ground_truth": "(n+1) - \\left\\lceil \\frac{n-1}{2} \\right\\rceil",
"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 all functions $f: R \\to R ,g: R \\to R$ satisfying the following equality $f(f(x+y))=xf(y)+g(x)$ for all real $x$ and $y$ .\n\nI. Gorodnin",
"role": "user"
}
] | math | {
"ground_truth": "(f(x), g(x)) = (k, k(1 - x)) \\quad \\forall x",
"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": "Define a \"standard 01 sequence\" $\\{a_n\\}$ as follows: $\\{a_n\\}$ consists of $2m$ terms, among which $m$ terms are $0$ and $m$ terms are $1$. Moreover, for any $k \\leq 2m$,... | math | {
"ground_truth": "14",
"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 ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal, calculate the square of the ratio of the short s... | math | {
"ground_truth": "\\frac{\\sqrt{5}-1}{2}",
"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: $\\angle \\alpha =60^{\\circ}18'$, then the complement of $\\angle \\alpha$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "29^{\\circ}42'",
"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": "With inspiration drawn from the rectilinear network of streets in *New York* , the *Manhattan distance* between two points $(a,b)$ and $(c,d)$ in the plane is defined to be \... | math | {
"ground_truth": "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": "The sequence of integers \\( u_{0}, u_{1}, u_{2}, u_{3}, \\cdots \\) satisfies \\( u_{0}=1 \\), and for each positive integer \\( n \\), \\( u_{n+1} u_{n-1}=k u_{n} \\), where \\... | math | {
"ground_truth": "2000, 1000, 500, 400, 200, 100",
"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 centre of the circle passing through the midpoints of the sides of am isosceles triangle $ABC$ lies on the circumcircle of triangle $ABC$ . If the larger angle of triangle... | math | {
"ground_truth": "0^\\circ",
"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 universal set U={1,2,3,4,5,6,7,8}, set A={1,2,3}, and set B={2,3,4,5}, find the complement of the intersection of sets A and B with respect to the universal set U.",
... | math | {
"ground_truth": "\\{1,4,5,6,7,8\\}",
"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": "Calculate the following:\n1. 156-135÷9\n2. (124-56)÷4\n3. 55×6+45×6",
"role": "user"
}
] | math | {
"ground_truth": "600",
"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": "When the number \\(3^{800}\\) is divided by 17, find the remainder in the division.",
"role": "user"
}
] | math | {
"ground_truth": "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": "A circle with diameter $20$ has points $A, B, C, D, E,$ and $F$ equally spaced along its circumference. A second circle is tangent to the lines $AB$ and $AF$ and intern... | math | {
"ground_truth": "1240",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.