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": "The radius of a sphere that touches all the edges of a regular tetrahedron is 1. Find the edge length of the tetrahedron.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that the graph of the power function $y=f(x)$ passes through the point $(-2,-\\frac{1}{8})$, find the value of $x$ that satisfies $f(x)=27$.",
"role": "user"
}
] | math | {
"ground_truth": "x=\\frac{1}{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": "In triangle $\\triangle XYZ$, where $X < Y$, an altitude is drawn from $Z$ to side $XY$, splitting angle $Z$ into $Z_1$ adjacent to side $y$ (opposite $X$) and $Z_2$ adjacent to ... | math | {
"ground_truth": "B) \\( Z_1 - Z_2 = 10^\\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 circles with centers $A$, $B$, $C$, and $D$ and points $P$ and $Q$ lying on all four circles, with the radius of circle $A$ being $\\tfrac{5}{8}$ times the radius of circle... | math | {
"ground_truth": "78",
"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": "Consider a set of integers defined as 'spacy' if it includes no more than one out of any four consecutive integers. Determine how many subsets of $\\{1, 2, 3, \\dots, 15\\}$, inc... | math | {
"ground_truth": "181",
"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 the cases when the system will have two distinct solutions. The quadratic equation will have two distinct positive roots \\( x_{1,2} = a \\pm 4 \\sqrt{a-3} \\) if\n\n\\[... | math | {
"ground_truth": "a \\in (3, 4) \\cup (12, 19) \\cup (19, +\\infty); \\, x = y = a \\pm 4 \\sqrt{a-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 square \\(ABCD\\) with side length \\(2\\), circle \\(\\omega\\) is inscribed. \\(\\omega\\) intersects line \\(CD\\) at \\(M\\), and line \\(AM\\) intersects \\(\\omega\\) at... | math | {
"ground_truth": "**D)** \\(\\frac{\\sqrt{65}}{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": "Ati has $ 7$ pots of flower, ordered in $ P_1,P_2,P_3,P_4,P_5,P_6,P_7$ . She wants to rearrange the position of those pots to $ B_1,B_2,B_2,B_3,B_4,B_5,B_6,B_7$ such that fo... | math | {
"ground_truth": "3447",
"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": "Suppose that $\\triangle ABC$ is an equilateral triangle of side length $s$, with the property that there is a unique point $P$ inside the triangle such that $AP=\\sqrt{2}$, $BP=... | math | {
"ground_truth": "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": "Find all positive integers $n < 589$ for which $589$ divides $n^2 + n + 1$ .",
"role": "user"
}
] | math | {
"ground_truth": "49, 216, 315, 482",
"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": "Three compressor stations are not located on the same line but are connected by straight roads. The distance from the first station to the third station via the second station is... | math | {
"ground_truth": "0 < a < 100 ; \\, x = 42 \\, \\text{km}, \\, y = 24 \\, \\text{km}, \\, z = 33 \\, \\text{km}",
"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 the complex number $z=1-i$, determine the coordinates of the point corresponding to $z+z^{2}$ in the complex plane.",
"role": "user"
}
] | math | {
"ground_truth": "(1,-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": "\\(\\frac{b^{2}-3b-(b-1)\\sqrt{b^{2}-4}+2}{b^{2}+3b-(b+1)\\sqrt{b^{2}-4}+2} \\cdot \\sqrt{\\frac{b+2}{b-2}} \\quad ; \\quad b > 2\\)",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1-b}{1+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": "In the center of a rectangular billiard table with a length of 3 meters and a width of 1 meter, a billiard ball is placed. The ball is struck randomly, and after the strike, it s... | math | {
"ground_truth": "\\frac{2}{\\pi} \\left( 3 \\arccos \\left( \\frac{1}{4} \\right) - \\arcsin \\left( \\frac{3}{4} \\right) + \\arccos \\left( \\frac{3}{4} \\right) \\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": "Calculate $15 \\cdot \\left( \\frac{1}{3} + \\frac{1}{6} + \\frac{1}{4} \\right)^{-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{60}{3}",
"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 diagram, rectangle PQRS has PQ = 30 and rectangle WXYZ has ZY = 15. If S is on WX and X is on SR, such that SX = 10, calculate the value of WR.",
"role": "user"
}
] | math | {
"ground_truth": "35",
"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 quadrilateral $ABCD$ , we have $AB = 5$ , $BC = 6$ , $CD = 5$ , $DA = 4$ , and $\\angle ABC = 90^\\circ$ . Let $AC$ and $BD$ meet at $E$ . Compute $\\dfrac{BE}{ED}... | math | {
"ground_truth": "\\frac{5}{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": "**p1.** Calculate $A \\cdot B +M \\cdot C$ , where $A = 1$ , $B = 2$ , $C = 3$ , $M = 13$ .**p2.** What is the remainder of $\\frac{2022\\cdot2023}{10}$ ?**p3.** Daniel an... | math | {
"ground_truth": "13",
"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 $\\det \\mathbf{A} = -2$, find $\\det (\\mathbf{A}^4)$.",
"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": "A group of women working together at the same rate can build a wall in $45$ hours. When the work started, all the women did not start working together. They joined the worked o... | math | {
"ground_truth": "75",
"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": "Vivian needs to shovel snow off a rectangular section of a park pathway that is 30 feet long and 4 feet wide. Initially, the snow was 1 foot deep across the entire pathway, but d... | math | {
"ground_truth": "90",
"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 $\\{a_n\\}$, where $a_1=1$ and $a_{n+1}=2a_n+4$, find the general formula for $\\{a_n\\}$.",
"role": "user"
}
] | math | {
"ground_truth": "a_n=5\\cdot2^{n-1}-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 \\(\\triangle ABC\\) have side lengths \\(AB=30\\), \\(BC=32\\), and \\(AC=34\\). Point \\(X\\) lies in the interior of \\(\\overline{BC}\\), and points \\(I_1\\) and \\(I_2\... | math | {
"ground_truth": "126",
"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 $m$ and $n$ be positive integers and $p$ a prime number. Find all triples $(m, n, p)$ that satisfy $\\mathrm{C}_{m}^{3} - 4 = p^{n}$.",
"role": "user"
}
] | math | {
"ground_truth": "(7, 1, 31)",
"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 man walked a certain distance at a constant pace. If he increased his speed by $\\frac{1}{3}$ mile per hour, he would have completed the journey in five-sixths of the time; if ... | math | {
"ground_truth": "\\frac{35}{96}",
"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 positive value of $t$ that satisfies $ab = t-3i$ given $|a|=2$ and $|b|=5$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{91}",
"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 bag contains a certain number of candies, which can be evenly distributed among $4$, $5$, $6$, $7$, or $8$ friends with none left over. What is the smallest number of candies t... | math | {
"ground_truth": "840",
"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 every odd composite positive integer $n$, define $r(n)$ as the sum of the numbers in the prime factorization of $n$, each counted with their multiplicity. For example, $r(15)... | math | {
"ground_truth": "C) the set of integers greater than 5 except for 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": "A convex polyhedron $Q$ has $30$ vertices, $70$ edges, and $42$ faces, of which $26$ are triangular, $12$ are quadrilaterals, and $4$ are pentagons. Determine the number of space... | math | {
"ground_truth": "321",
"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 set of all positive real values of \\( x \\) such that \\( (x-1)(x-2)(x-3) < 0 \\)?\n\n(a) \\( (1,2) \\)\n\n(b) \\( (1,3) \\)\n\n(c) \\( (0,1) \\cup (2,3) \\)\n\n(d) ... | math | {
"ground_truth": "(0,1) \\cup (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": "The Pythagoras High School band has $120$ female and $110$ male members. The Pythagoras High School orchestra has $100$ female and $130$ male members. There are $90$ females and ... | math | {
"ground_truth": "B) 10",
"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 peculiar spinner has three outcomes: green, red, and blue. It lands on green with probability $\\frac{1}{4}$, on red with probability $\\frac{1}{2}$, and on blue with probabili... | math | {
"ground_truth": "\\$1.00",
"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": "Real numbers $a$, $b$, $c$ satisfy $2^{a}=5$, $2^{b}=10$, $2^{c}=80$. Evaluate the algebraic expression $2006a-3344b+1338c$.",
"role": "user"
}
] | math | {
"ground_truth": "2008",
"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": "Mad scientist Kyouma writes $N$ positive integers on a board. Each second, he chooses two numbers $x, y$ written on the board with $x > y$ , and writes the number $x^2-y^2$... | math | {
"ground_truth": "N = 252",
"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 square of perimeter 24 is inscribed in a square of perimeter 36. Find the longest distance between a vertex of the inner square and a vertex of the outer square.",
"role": ... | math | {
"ground_truth": "7.5\\sqrt{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 $\\sin 2\\theta =a$, $\\cos 2\\theta =b$, $0 \\lt \\theta\\ \\ \\lt \\frac{π}{4}$, provide the five possible answers for the value of $\\tan (\\theta +\\frac{π}{4}$): ① $\\... | math | {
"ground_truth": "①\\ ④\\ 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": "Find $ [\\sqrt{19992000}]$ where $ [x]$ is the greatest integer less than or equal to $ x$ .",
"role": "user"
}
] | math | {
"ground_truth": "4471",
"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 function $f(x)=2 \\sqrt{3}\\sin x-2\\cos x $.\n\n(1) Find the maximum and minimum values of $f(x)$ when $x\\in [0,\\pi]$.\n\n(2) If $f(x)=0$, find the value of $\\frac{... | math | {
"ground_truth": "2- \\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": "Given the vectors $\\overrightarrow {a} = (3, 2)$, $\\overrightarrow {b} = (-1, 2)$, and $\\overrightarrow {c} = (4, 1)$,\n1. Find the magnitude of $3\\overrightarrow {a} + \\ove... | math | {
"ground_truth": "\\left(4 - \\frac{\\sqrt{5}}{5}, 1 - \\frac{2\\sqrt{5}}{5}\\right)",
"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 equation of the directrix of the parabola $x = -\\frac{1}{4} y^2$.",
"role": "user"
}
] | math | {
"ground_truth": "x = 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": "Rationalize the denominator for the expression \\(\\sqrt{\\frac{5}{12}}\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{15}}{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": "Define a positive integer \\( n \\) as a \"factorial tail\" if there exists a positive integer \\( m \\) such that the decimal representation of \\( m! \\) ends in exactly \\( n ... | math | {
"ground_truth": "396",
"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": "How many sets of two or more consecutive positive integers have a sum of 21?\nA) 0\nB) 1\nC) 2\nD) 3\nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "B) 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": "An arithmetic sequence $\\{a_n\\}$ satisfies: $a_1 = -8$, $a_2 = -6$. If the same number is added to $a_1$, $a_4$, and $a_5$, and the resulting three numbers form a geometric seq... | 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": "Let $S=\\{1,2,\\ldots ,98\\}$ . Find the least natural number $n$ such that we can pick out $10$ numbers in any $n$ -element subset of $S$ satisfying the following condit... | math | {
"ground_truth": "n = 50",
"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": "Last year Ana was $5$ times as old as Bonita, and this year Ana's age is the square of Bonita's age. If Ana and Bonita were born on the same date in different years, $n$ years ap... | math | {
"ground_truth": "12",
"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": "Consider an alphabet of 2 letters. A word is any finite combination of letters. We will call a word unpronounceable if it contains more than two of the same letter in a row. How ... | math | {
"ground_truth": "86",
"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 the right-angle coordinate system, the points\n\n$$\nA(0,9), \\quad B(6,3), \\quad C\\left(-\\frac{1}{3},-1\\right) \\quad \\text { and } D\\left(3,-\\frac{7}{2}\\right)\n$$\n... | math | {
"ground_truth": "P_1(1,4) \\quad \\text{and} \\quad P_2(-6,-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": "A certain fee-based app (mobile application) has been loved by users since its launch due to its simple interface design, convenient operation, and powerful practical functions. ... | math | {
"ground_truth": "5.1\\ \\text{ten thousand people}",
"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 function $f(x)=\\frac{mx}{\\ln x}$, the tangent line to the curve $y=f(x)$ at the point $\\left( {{e}^{2}},f({{e}^{2}}) \\right)$ is perpendicular to the line $2x+y=0$ ... | math | {
"ground_truth": "k=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 complex numbers $z_1=2+i$ and $z_2=a-i$, where $z_1 \\cdot z_2$ is a real number, find the real number $a$.",
"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": "Determine the set of x-values that satisfy the inequality 3x^2 + 2x - 9 ≤ 0 and the inequality x ≥ -1.",
"role": "user"
}
] | math | {
"ground_truth": "[-1, 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": "Work base 3. (so each digit is 0,1,2)\r\n\r\nA good number of size $n$ is a number in which there are no consecutive $1$ 's and no consecutive $2$ 's. How many good 10-digit ... | math | {
"ground_truth": "4756",
"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 all natural numbers not exceeding 200 that leave a remainder of 7 when divided by 11 and a remainder of 5 when divided by 7 is $\\qquad$",
"role": "user"
}
] | math | {
"ground_truth": "351",
"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 least positive integer $n$ so that both $n$ and $n+1$ have prime factorizations with exactly four (not necessarily distinct) prime factors.",
"role": "user"
... | math | {
"ground_truth": "1155",
"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": "$ABC$ is a triangle. Reflect each vertex in the opposite side to get the triangle $A'B'C'$ . Find a necessary and sufficient condition on $ABC$ for $A'B'C'$ to be equilater... | math | {
"ground_truth": "\\triangle A'B'C' \\text{ is equilateral} \\iff \\triangle ABC \\text{ is isosceles with the angle between equal sides } 30^\\circ, 60^\\circ, \\text{ or } 150^\\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": "The decimal representation of a fraction ends in $0.\\overline{27}$. When this decimal is converted to a common fraction and reduced to its lowest terms, what is the denominator ... | math | {
"ground_truth": "11",
"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": "Vasya needs to write one digit on each face of several cubes in such a way that any ordered combination of three digits from 000 to 999 inclusive can be obtained by selecting som... | 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": "A home appliance has an in-store price of $\\$129.99$. An online advertisement offers the same product for four payments of $\\$29.99$ and a one-time shipping and handling fee of... | math | {
"ground_truth": "A) 0 cents",
"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": "Starting with the number 0, Casey performs an infinite sequence of moves as follows: he chooses a number from \\(\\{1, 2\\}\\) at random (each with probability \\(\\frac{1}{2}\\)... | math | {
"ground_truth": "\\frac{11}{2^{20}}",
"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 cells of a $2021\\times 2021$ table are filled with numbers using the following rule. The bottom left cell, which we label with coordinate $(1, 1)$ , contains the number ... | math | {
"ground_truth": "5",
"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 line $ax + 2y + 1 = 0$ is perpendicular to the line $x + y - 2 = 0$, find the value of $a$.",
"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": "Given an arithmetic sequence $\\{a_n\\}$, the sum of the first $n$ terms is denoted as $S_n$. Let $A(a_{1009},1)$, $B(2,-1)$, and $C(2,2)$ be three points on the coordinate plane... | math | {
"ground_truth": "0",
"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 \\( x_{0} - y_{0} \\), if \\( x_{0} \\) and \\( y_{0} \\) are the solutions to the system of equations:\n\n$$\n\\left\\{\\begin{array}{l}\nx^{3} - 2023x = y^{3} - 2023y + 20... | math | {
"ground_truth": "-2020",
"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$, medians $\\overline{AM}$ and $\\overline{BN}$ are perpendicular. If $AM = 15$ and $BN = 20$, find the length of side $AB$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{50}{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": "Vanya thought of a number and added the sum of its digits. The result was 2021. What number could Vanya have thought of?",
"role": "user"
}
] | math | {
"ground_truth": "2014 \\text{ or } 1996",
"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 \\( C=\\frac{5}{9}(F-32) \\), what is \\( F \\) when \\( C=40 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "104",
"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 that Teams A and B play a basketball championship series where the first team to win four games wins the championship, each team is equally likely to win each game, there a... | 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": "On a table there are $100$ red and $k$ white buckets for which all of them are initially empty. In each move, a red and a white bucket is selected and an equal amount of wate... | math | {
"ground_truth": "100",
"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 mathematics competition, there are 30 problems. Each correctly solved problem is worth 4 points, an incorrect solution results in a loss of 1 point, and no points are awarde... | math | {
"ground_truth": "145",
"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 quadratic function $f(x) = ax^2 + x$ has a minimum value, the solution set of the inequality $f(x) < 0$ is set $A$.\n(1) Find the set $A$;\n(2) Let set $B = \\{x \\,|\\, ... | math | {
"ground_truth": "\\sqrt{5} - 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 two numbers is $S$. If $5$ is added to each number and then each resulting number is tripled, calculate the sum of the final two numbers.",
"role": "user"
}
] | math | {
"ground_truth": "3S + 30",
"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 germination rate of seeds is $90\\%$. What is the probability that 5 out of 7 sown seeds will germinate?",
"role": "user"
}
] | math | {
"ground_truth": "0.124",
"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 positive real numbers $x$ and $y$ satisfy the relation $x + y = 3 \\sqrt{xy}$ . Find the value of the numerical expression $$ E=\\left| \\frac{x-y}{x+y}+\\frac{x^2-y^2... | 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 route from point A to point B consists only of uphill and downhill segments, with a total distance of 21 kilometers. If the uphill speed is 4 km/h and the downhill speed is 6... | math | {
"ground_truth": "4.5 \\, \\text{hours}",
"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 acute triangle $\\triangle ABC$ , point $R$ lies on the perpendicular bisector of $AC$ such that $\\overline{CA}$ bisects $\\angle BAR$ . Let $Q$ be the intersection... | 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": "Given that $θ$ is the angle of inclination of the line $2x-2y-1=0$, find the value of $θ$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{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": "Determine the exact value of the series\n\\[\n\\frac{1}{3 + 1} + \\frac{2}{3^3 + 1} + \\frac{4}{3^9 + 1} + \\frac{8}{3^{27} + 1} + \\frac{16}{3^{81} + 1} + \\dotsb.\n\\]",
"r... | math | {
"ground_truth": "\\frac{1}{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 \\[f(x) =\n\\begin{cases}\n6x + 8 & \\text{if } x < 3, \\\\\n3x - 9 & \\text{if } x \\ge 3.\n\\end{cases}\n\\]\nIf $f(x) = 3$, find the sum of all possible values of $x$.",
... | math | {
"ground_truth": "\\frac{19}{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": "Natural numbers starting from 1 are written in sequence. This forms the sequence of digits: 1234567891011121314... What is the digit in the 2021st position?",
"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": "A truck with a width of $2.7$ meters needs to pass through a semi-circular tunnel with a radius of $4.5$ meters. The maximum height of the truck's flat-top canopy from the ground... | math | {
"ground_truth": "3.6",
"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 complex numbers \\( z \\) and \\( w \\) satisfy \\( |z| = 3 \\) and \\( (z + \\bar{w})(\\bar{z} - w) = 7 + 4i \\), where \\( i \\) is the imaginary unit, and \\( \\bar{z} \\)... | math | {
"ground_truth": "\\sqrt{65}",
"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": "Solve the equation with respect to $x$: $kx^{2}-\\left(3k+3\\right)x+2k+6=0$.",
"role": "user"
}
] | math | {
"ground_truth": "{x}_{1}=2, {x}_{2}=1+\\frac{3}{k}",
"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": "For all real numbers $x$, simplify the expression $x[x\\{x(2-x)-4\\}+10]+1$.",
"role": "user"
}
] | math | {
"ground_truth": "-x^4+2x^3-4x^2+10x+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": "In a spelling bee, $60\\%$ of the students were eliminated after the first round. Only $\\frac{1}{4}$ of the remaining students were still in the contest after the second round. ... | math | {
"ground_truth": "300",
"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 large equilateral triangle is assembled using toothpicks to create rows of small equilateral triangles. If the base row of the triangle consists of 2500 small equilateral trian... | math | {
"ground_truth": "The correct answer is B) 4694375.",
"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": "What is the sum of the tens digit and the ones digit of the integer form of $(4+2)^{13}$?",
"role": "user"
}
] | math | {
"ground_truth": "13",
"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": "<u>Set 1</u>**p1.** Arnold is currently stationed at $(0, 0)$ . He wants to buy some milk at $(3, 0)$ , and also some cookies at $(0, 4)$ , and then return back home at $(0, ... | 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": "**p1.** An $18$ oz glass of apple juice is $6\\%$ sugar and a $6$ oz glass of orange juice is $12\\%$ sugar. The two glasses are poured together to create a cocktail. What ... | math | {
"ground_truth": "2014",
"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": "Julio is packing candies for a carnival giveaway. He packs them in groups of 5, and always has 4 candies left over. When packed in groups of 6, there are 3 left over. If the cand... | math | {
"ground_truth": "69",
"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 pairs of integers $a$ and $b$ are there such that $a$ and $b$ are between $1$ and $42$ and $a^9 = b^7 \\mod 43$ ?",
"role": "user"
}
] | math | {
"ground_truth": "42",
"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 consecutive positive integers have all powers of their prime factors as odd numbers?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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": "Cory has $4$ apples, $3$ oranges, $2$ bananas, and $1$ pear. He decides to eat one piece of fruit per day for ten days, with all pieces of fruit within each category being indist... | math | {
"ground_truth": "12600",
"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 integer \\( n \\geq 2 \\). An \\( n \\times n \\times n \\) cube is divided into \\( n^{3} \\) unit cubes. Each unit cube is colored with one color. For each \\(... | math | {
"ground_truth": "\\frac{n(n+1)(2n+1)}{6}",
"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": "On a $999\\times 999$ board a *limp rook* can move in the following way: From any square it can move to any of its adjacent squares, i.e. a square having a common side with it,... | math | {
"ground_truth": "996000",
"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 function $y = (x-a)^2 + (x-b)^2 + kx$, determine the value of $x$ at which $y$ is minimized.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a+b-k/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": "In a scenario on the Cartesian plane, for every 4 unit increase in the $x$-value, the $y$-value increases by 9 units. Determine how much the $y$-value increases when the $x$-valu... | math | {
"ground_truth": "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": "A company decides to have a Fun Friday every month that contains five Fridays. The company's fiscal year begins on Wednesday, March 1. What is the date of the first Fun Friday af... | math | {
"ground_truth": "\\text{April 28}",
"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": "Coach Grunt is preparing the 5-person starting lineup for his basketball team, the Grunters. There are 15 players on the team. Three of them, Ace, Zeppo, and Yasmine, are league ... | math | {
"ground_truth": "66",
"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 $a$ and $b$ be the two possible values of $\\tan\\theta$ given that \\[\\sin\\theta + \\cos\\theta = \\dfrac{193}{137}.\\] If $a+b=m/n$ , where $m$ and $n$ are rel... | math | {
"ground_truth": "28009",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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