data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest positive integer $k{}$ satisfying the following condition: For any configuration of chess queens on a $100 \\times 100$ chequered board, the queens can... | math | {
"ground_truth": "k = 5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $x$ for which the following equation holds true:\n\\[1 \\cdot 2021 + 2 \\cdot 2020 + 3 \\cdot 2019 + \\dots + 2020 \\cdot 2 + 2021 \\cdot 1 = 2021 \\cdot 1... | math | {
"ground_truth": "674",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $[x]$ denote the greatest integer less than or equal to $x$. When $0 \\leqslant x \\leqslant 10$, find the number of distinct integers represented by the function $f(x) = [x]... | math | {
"ground_truth": "61",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the random variable $\\xi \\sim N(2, \\sigma ^{2})$, and $P(0 \\leqslant \\xi \\leqslant 2) + P(\\xi > m) = 0.5$, determine the value of $m$.",
"role": "user"
}
... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many 15-letter arrangements of 5 A's, 5 B's, and 5 C's have no B's in the first 5 letters, no C's in the next 5 letters, and no A's in the last 5 letters, with the types of l... | math | {
"ground_truth": "\\sum_{k=0}^{5}\\binom{5}{k}^2\\binom{5}{5-k}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A reservoir has two inlet pipes, Pipe A and Pipe C, and two outlet pipes, Pipe B and Pipe D. To fill the reservoir, it takes 3 hours using only Pipe A and 5 hours using only Pipe... | math | {
"ground_truth": "20 \\frac{3}{4} \\text{ hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many ways can 7 people be seated in a row of chairs if three of them, Wilma, Paul, and Natasha, each refuse to sit next to the other two?",
"role": "user"
}
] | math | {
"ground_truth": "1440",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area of $\\triangle APB$ is $\\frac{1}{2} \\times 2 \\times 2 \\sin\\left(\\frac{\\pi}{2}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It costs 3 cents to copy a page. How many pages can you copy for $25?",
"role": "user"
}
] | math | {
"ground_truth": "833",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An illusionist and his assistant are about to perform the following magic trick.\n\nLet $k$ be a positive integer. A spectator is given $n=k!+k-1$ balls numbered $1,2,…,n$ .... | math | {
"ground_truth": "\\text{The strategy works for } n = k! + k - 1.",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rose has a $5 \\times 7$ index card. If she shortens the length of one side of this card by $2$ inches and the other side by $1$ inch, what would the area of the card be in squar... | math | {
"ground_truth": "\\textbf{(D) } 18",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The angle bisector of the acute angle formed at the origin by the graphs of the lines $y = x$ and $y=3x$ has equation $y=kx.$ Find the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1 + \\sqrt{5}}{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\t\\prod_{n=1}^{1996}{(1+nx^{3^n})}= 1+ a_{1}x^{k_{1}}+ a_{2}x^{k_{2}}+...+ a_{m}x^{k_{m}}$ where $a_{1}, a_{1}, . . . , a_{m}$ are nonzero and $k_{1} < k_{2} <...< k_{m... | math | {
"ground_truth": "665280",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Masha, while bored during a math lesson, performed the following operation on a certain 2015-digit natural number: she removed the last digit from its decimal notation, multiplie... | math | {
"ground_truth": "09",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Once, the beautiful Queen Guinevere, while in her parents' castle, asked King Arthur to send her 20 pearls. The roads were unsafe, so Arthur decided to send 40 pearls via differe... | math | {
"ground_truth": "\\text{For } 0 < p < \\frac{1}{3}, \\text{send} \\textbf{four} \\text{ messengers. For } \\frac{1}{3} \\leq p < 1, \\text{send} \\textbf{ two} \\text{ messengers.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number \\(s\\) can be expressed as a four-place decimal \\(0.wxyz\\), where \\(w, x, y,\\) and \\(z\\) represent digits. It is desired to approximate \\(s\\) by a fraction wh... | math | {
"ground_truth": "418",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $x^2 + y^2 = 16x + 8y + 20,$ find the largest and smallest possible values of $4x + 3y$.",
"role": "user"
}
] | math | {
"ground_truth": "116",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a table $n \\times 9$ ( $n$ rows and $9$ columns), determine the maximum of $n$ that we can write one number in the set $\\left\\{ {1,2,...,9} \\right\\}$ in each ce... | math | {
"ground_truth": "8!",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive number $x$, $x\\%$ of $x$ plus 6 equals 10. Calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the \"24-point game,\" players draw 4 cards from a deck of 52 cards (excluding jokers) and use the numbers on these cards (A=1, J=11, Q=12, K=13) with the operations of additi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted as $S_n$, and it is known that $a_2=-5$, $S_5=-20$. \n(I) Find the general formula for the s... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sales of a certain brand of TV in a shopping mall were good. According to statistics, the monthly sales volume $y$ (units) in the first half of last year (January to June) ha... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\theta$ be the angle between the line\n\\[\\frac{x}{4} = \\frac{y - 2}{2} = \\frac{z + 1}{5}\\]\nand the plane $8x + 4y - z = 15.$ Find $\\cos \\theta.$",
"role": "user... | math | {
"ground_truth": "\\cos \\theta = \\frac{7\\sqrt{5}}{45}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let points $A = (0,0)$, $B = (2,3)$, $C = (4,4)$, and $D = (5,1)$. A line passing through $A$ cuts quadrilateral $ABCD$ into two pieces of equal area. If this line intersects $\\... | math | {
"ground_truth": "\\text{1. Calculate the area of quadrilateral } ABCD. \\text{ The area is given by: } Area = \\frac{1}{2} \\left| (0 \\cdot 3 - 2 \\cdot 0) + (2 \\cdot 4 - 3 \\cdot 4) + (4 \\cdot 1 - 4 \\cdot 5) + (5 \\cdot 0 - 1 \\cdot 0) \\right| = \\frac{1}{2} \\left| 0 - 2 + (-16) + 0 \\right| = \\frac{1}{2} \... | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An uncrossed belt, without any slack, is fitted around two circular pulleys, with one having a radius of $10$ inches and the other $6$ inches. The distance between the points whe... | math | {
"ground_truth": "2\\sqrt{173}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each of area 25. $H$ is the midpoint of both $BC$ and $EF$. Another square $IJKL$ intersects $ABCD$ and $EFGD$ such that $D$ is the ... | math | {
"ground_truth": "62.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest $a$ such that $\\frac{8\\sqrt{(3a)^2+(2)^2}-5a^2-2}{\\sqrt{2+5a^2}+4}=3$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\sqrt{\\frac{62}{5}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each positive integer, define a function \\[ f(n)=\\begin{cases}0, &\\text{if n is the square of an integer} \\left\\lfloor\\frac{1}{\\{\\sqrt{n}\\}}\\right\\rfloor, &\\text... | math | {
"ground_truth": "629",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the set $A={2,4,5,6,8,11,12,17}$, a fraction is formed using any two elements from the set as the numerator and denominator, respectively. If one of the chosen numbers is $... | math | {
"ground_truth": "\\frac{4}{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $f(x) = x^2 - 2x + 5$ and $g(x) = x + 3$, and introducing a new function $h(x) = 2x - 1$, what is the value of $f(g(h(5))) - g(f(h(5)))$?",
"role": "user"
}
] | math | {
"ground_truth": "54",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest possible sum of the digits in the base-seven representation of a positive integer less than $3000$?\nA) 22\nB) 23\nC) 24\nD) 25\nE) 27",
"role": "user"
... | math | {
"ground_truth": "\\textbf{(C) } 24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathbf{B} = \\frac{1}{7} \\begin{pmatrix} -5 & p \\\\ q & r \\end{pmatrix}$ be a matrix with integer entries where $\\mathbf{B}^2 = \\mathbf{I}$. Find the largest possible... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $16^x = 256$, calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ A = \\{ 1, 2, 3, \\cdots , 12 \\} $ . Find the number of one-to-one function $ f :A \\to A $ satisfying following condition: for all $ i \\in A $ , $ f(i)-i $ is not ... | math | {
"ground_truth": "55392",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\overline{AB}$ be a diameter in a circle of radius $5\\sqrt2.$ Let $\\overline{CD}$ be a chord in the circle that intersects $\\overline{AB}$ at a point $E$ such that $BE=2... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A teacher wants to arrange 5 copies of Introduction to Geometry and 3 copies of Calculus Made Easy on a bookshelf. In how many ways can he do this?",
"role": "user"
}
] | math | {
"ground_truth": "56",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parameterized curve $ C: x\\equal{}e^t\\minus{}e^{\\minus{}t},\\ y\\equal{}e^{3t}\\plus{}e^{\\minus{}3t}$ .\r\n\r\nFind the area bounded by the curve $ C$ , the $ x$ ... | math | {
"ground_truth": "\\frac{5\\sqrt{5}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the spring of 2000, a school fitness event commenced with 500 participants. The organizers anticipate that the number of participants will increase each year such that in 2001... | math | {
"ground_truth": "B) 1365",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that all three vertices of $\\bigtriangleup ABC$ lie on the parabola defined by $y=x^2$, with $A$ at the origin and $\\overline{BC}$ parallel to the $x$-axis, and the area ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $T = (1+i)^n + (1+i)^{-n}$, where $i = \\sqrt{-1}$ and $n$ is an integer, determine the total number of possible distinct values for $T$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $d$ be the greatest common divisor of $2^{30^{10}}-2$ and $2^{30^{45}}-2$ . Find the remainder when $d$ is divided by $2013$ .",
"role": "user"
}
] | math | {
"ground_truth": "2012",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the least possible value of (x+1)(x+3)(x+5)(x+7) + 2050, where x is a real number?",
"role": "user"
}
] | math | {
"ground_truth": "2034",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a certain meeting, there are 30 participants. Each person knows at most 5 other people among the remaining participants; for any group of five people, at least two people are ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Factor the expression $3x^2(x-5) + 5(x-5)$.",
"role": "user"
}
] | math | {
"ground_truth": "(3x^2+5)(x-5)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given sets $A=\\{x|x-2 \\gt 0\\}$ and $B=\\{x|x^{2}-3x+2\\leqslant 0\\}$, find the set $A\\cup B$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[1,+\\infty \\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define $f(x)$ as $\\frac{x^2-x-2}{x^2+x-6}$ . $f(f(f(f(1))))$ can be expressed as $\\frac{p}{q}$ for relatively prime positive integers $p,q$ . Find $10p+q$ .",
"ro... | math | {
"ground_truth": "211",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The coefficient of $x^2y^7$ in the expansion of $(x-y)(x+y)^8$ is _________ (Fill in the blank with a number).",
"role": "user"
}
] | math | {
"ground_truth": "-20",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\"Nine years to sharpen a sword, the blade is tested in June.\" To help with the high school entrance exam and effectively alleviate students' pre-exam pressure, a certain ninth-... | math | {
"ground_truth": "68",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "As shown in the diagram, there is a circle filled with the number 1. Fill the blank circles with the numbers 2, 3, 4, 5, and 6, ensuring no repeated numbers and that the differen... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A plane passes through the midpoints of edges $AB$ and $CD$ of pyramid $ABCD$ and divides edge $BD$ in the ratio $1:3$. In what ratio does this plane divide edge $AC$?",
"rol... | math | {
"ground_truth": "1:3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the slope $k$ of the angle bisector of the acute angle formed at the origin by the graphs of the lines $y = 2x$ and $y = -3x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-1 + \\sqrt{14}}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $F_1$ and $F_2$ are the two foci of the ellipse $\\frac{x^{2}}{4}+y^{2}=1$, and point $P$ is a moving point on this ellipse, determine the range of values for $\\overr... | math | {
"ground_truth": "[-2, 1]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system, the coordinates of the point $P(2,1)$ with respect to the origin are ______.",
"role": "user"
}
] | math | {
"ground_truth": "(-2,-1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs (a, b) of positive integers such that \\(ab^2 + b + 7\\) divides \\(a^2b + a + b\\).",
"role": "user"
}
] | math | {
"ground_truth": "(11, 1), (49, 1), (7k^2, 7k)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $3000 \\times (3000^{1999})$.",
"role": "user"
}
] | math | {
"ground_truth": "3000^{2000}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $h+k$ where $(h,k)$ is the center of the circle with the equation $x^2 + y^2 - 6x + 14y - 11 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When Cheenu was a boy, he could run 15 miles in 3 hours and 30 minutes. As an old man, he can now walk 10 miles in 4 hours. Calculate the number of minutes it takes for him to wa... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $2310$ is written as a product of two positive integers whose difference is as small as possible, then the difference is:\nA) 13\nB) 31\nC) 47\nD) 12\nE) 45",
"role": "use... | math | {
"ground_truth": "A) 13",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola $y^2 = 2px(p > 0)$, a point $M(3,m)$ on it is at a distance of $4$ from its focus $F$. Find the slope of the line $MF$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One player conceals a $10$ or $20$ copeck coin, and the other guesses its value. If he is right he gets the coin, if wrong he pays $15$ copecks. Is this a fair game? What a... | math | {
"ground_truth": "-\\frac{5}{12}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lines $L_1, L_2, \\dots, L_{120}$ are distinct. All lines $L_{5n}$, where $n$ is a positive integer, are parallel to each other. All lines $L_{5n-4}$, where $n$ is a positive int... | math | {
"ground_truth": "C)$ 5161",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two concentric circles have radii \\(3\\) and \\(5\\). Two points are chosen such that one point is uniformly at random on the outer circle and another is fixed on the inner circ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two brothers had tickets to a stadium located 20 km from their home. To reach the stadium, they decided to use their bicycle and agreed to start at the same time, one on the bicy... | math | {
"ground_truth": "10 \\text{ km}; 3 \\text{ hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x^2 + 2x = y - 4 \\) and \\( x = -6 \\), then what is the value of \\( y \\)?",
"role": "user"
}
] | math | {
"ground_truth": "28",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given lines $a$, $b$, $c$, and planes $\\alpha$, $\\beta$, $\\gamma$, consider the following propositions:\n1. If $a \\subset \\alpha$ and $b \\parallel \\alpha$, then $a \\paral... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the plane point set \\( A = \\{ (x, y) \\mid x = 2 \\sin \\alpha + 2 \\sin \\beta, y = 2 \\cos \\alpha + 2 \\cos \\beta \\} \\) and \\( B = \\{ (x, y) \\mid \\sin (x + y) \... | math | {
"ground_truth": "8\\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ 2^{1110} \\equiv n \\bmod{1111} $ with $ 0 \\leq n < 1111 $ . Compute $ n $ .",
"role": "user"
}
] | math | {
"ground_truth": "1024",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For an integer \\( n \\geq 2 \\) and non-negative real numbers \\( a_1, a_2, \\ldots, a_n \\) satisfying \\( \\sum_{i=1}^{n} a_i = 4 \\), find the maximum possible value of \\( 2... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A boat travels in still water at a speed of 10 mph. When it enters a river with a current of 3 mph, it travels a certain distance downstream and then returns upstream. The ratio ... | math | {
"ground_truth": "\\textbf{(B)}\\ \\frac{91}{100}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the degree of the polynomial $(x^5 + ax^8 + bx^2 + c)(2x^4 + dx^3 + e)(3x + f)$, where $a, b, c, d, e, f$ are non-zero constants, and additionally, $a + b = c$ and $d +... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(\\int_{0}^{\\pi / 2}\\left(\\sin ^{2}(\\sin x)+\\cos ^{2}(\\cos x)\\right) d x\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify: $|(-4)^2 - 3^2 + 2|$",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A natural number $k > 1$ is called *good* if there exist natural numbers $$ a_1 < a_2 < \\cdots < a_k $$ such that $$ \\dfrac{1}{\\sqrt{a_1}} + \\dfrac{1}{\\sqrt{a_2}} + \\c... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the number of ways to color $3$ cells in a $3\\times 3$ grid so that no two colored cells share an edge.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the power function $f(x) = x^{k}$ is a decreasing function on $(0, +\\infty)$, determine the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A truncated cone has horizontal bases with radii 24 and 4. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere?",
... | math | {
"ground_truth": "\\sqrt{96}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a diagram, the visible gray area within a larger circle is four times the area of the white circular region. What is the ratio of the radius of the smaller circle to the radiu... | math | {
"ground_truth": "\\frac{\\sqrt{5}}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(2013•Sichuan) Given that $f(x)$ is an even function defined on $\\mathbb{R}$, and when $x \\geq 0$, $f(x) = x^2 - 4x$, then the solution set of the inequality $f(x+2) < 5$ is.",... | math | {
"ground_truth": "(-7, 3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three friends, Chris, Silva, and Alex, are playing a game with six balls arranged in a circle. Each one of them, in turn, chooses two adjacent balls and swaps their positions. Th... | math | {
"ground_truth": "\\(\\textbf{C}) \\: 2.0\\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that the equality \\( f([x] y) = f(x)[f(y)] \\) holds for all \\( x, y \\in \\mathbb{R} \\). (Here, \... | math | {
"ground_truth": "f(x) = 0 \\text{ or } f(x) = c \\text{ where } [c] = 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three standard dice are rolled, yielding numbers $a, b, c$. Find the probability that the sum of these numbers is $a+b+c=15$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{108}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Railway routes. The diagram shows a simplified scheme of railway tracks. We want to determine how many different ways one can travel from \\(A\\) to \\(E\\) without traveling ove... | math | {
"ground_truth": "2501",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each point in the hexagonal lattice shown is one unit from its nearest neighbor. How many equilateral triangles have all three vertices in the lattice, where the lattice is exten... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $\\text{rem}\\left(\\tfrac{5}{7}, -\\tfrac{3}{11}\\right)?$ Define the remainder for all real numbers $x$ and $y$ with $y \\neq 0$ by \\[\\text{rem} (x ,y)=x... | math | {
"ground_truth": "-\\frac{8}{77}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A 6-digit number is called flippy if its digits alternate between two distinct digits. How many 6-digit flippy numbers are divisible by 40?\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"r... | math | {
"ground_truth": "\\textbf{(B) }2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $a=\\sqrt{3}$, $\\sin B=\\frac{1}{2}$, and $C=\\frac{\\pi }{... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\( x \\) and \\( y \\) are positive numbers with \\( xy = \\frac{1}{9} \\), \\( x(y+1) = \\frac{7}{9} \\), and \\( y(x+1) = \\frac{5}{18} \\), calculate the value of ... | math | {
"ground_truth": "\\frac{35}{18}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $3^{\\left(0^{\\left(2^2\\right)}\\right)}+\\left(\\left(3^1\\right)^0\\right)^2?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the roots of the quadratic equation $2x^2 + 14x + d = 0$ are $x = \\frac{-14 \\pm \\sqrt{14}}{4}$, what is the value of $d$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{91}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You flip a fair coin which results in heads ( $\\text{H}$ ) or tails ( $\\text{T}$ ) with equal probability. What is the probability that you see the consecutive sequence $\\tex... | math | {
"ground_truth": "\\frac{7}{8}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of the first eight terms in the geometric sequence starting with $\\frac13$ and halving each subsequent term. Express your answer as a common fraction.",
"role":... | math | {
"ground_truth": "\\frac{255}{384}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer divisor of $12!$ is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are rel... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The arithmetic mean of forty successive positive integers beginning at 7 is what value?",
"role": "user"
}
] | math | {
"ground_truth": "26.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a,b,c > 0$, find the smallest possible value of\n\\[\n\\left\\lfloor{\\frac{2a+b}{c}}\\right\\rfloor + \\left\\lfloor{\\frac{b+2c}{a}}\\right\\rfloor + \\left\\lfloor{\\frac{... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All of the digits of a seven-digit positive integer are either $7$ or $8.$ If this integer is divisible by $9,$ what is the sum of its digits?",
"role": "user"
}
] | math | {
"ground_truth": "54",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$i^{2016} = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of ways to arrange the letters of the word EXCEED.",
"role": "user"
}
] | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers $x$ and $y$ are inversely proportional. If the sum of $x$ and $y$ is 35, and $y$ is three times $x$, find the value of $x$ when $y=-21$.",
"role": "user"
}
] | math | {
"ground_truth": "-10.9375",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)=4\\sin(x- \\frac {π}{6})\\cos x+1$$.\n(Ⅰ) Find the smallest positive period of f(x);\n(Ⅱ) Find the maximum and minimum values of f(x) in the interval $$... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The cost of the 2000 candy bars is four for $3$dollars, so calculate the total cost of the candy bars.",
"role": "user"
}
] | math | {
"ground_truth": "-200",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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