data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $(1296^{\\log_6 1728})^{\\frac{1}{4}}$, evaluate the resulting expression.",
"role": "user"
}
] | math | {
"ground_truth": "1728",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\ln(ax+1)+x^{3}-x^{2}-ax$ is increasing on the interval $[2,+\\infty)$, find the range of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "[0,4+2\\sqrt{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": "If $\\log_{b^3}x + \\log_{x^3}b = 1$ where $b>0, b \\neq 1, x \\neq 1$, then find $x$.\nA) $b^{\\frac{3+\\sqrt{5}}{2}}$\nB) $b^{\\frac{3-\\sqrt{5}}{2}}$\nC) $b^{\\sqrt{5}}$\nD) $... | math | {
"ground_truth": "b^{\\frac{3-\\sqrt{5}}{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": "The ratio of the short side to the long side of a certain rectangle plus \\(\\frac{1}{2}\\) equals the ratio of the long side to the diagonal. Find the square of this ratio.",
... | math | {
"ground_truth": "\\frac{3 - \\sqrt{5}}{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 $x$ and $y$ satisfy $|4-x|+\\sqrt{y-8}=0$, calculate the perimeter of an isosceles triangle with sides of length $x$ and $y$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"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 six-digit numbers that are perfect squares and meet the following criteria:\n(i) None of its digits are zero.\n(ii) All digits of the number are distinct.\n(iii) The first t... | math | {
"ground_truth": "A) 0",
"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": "Without using a calculator, determine which of the numbers \\( 33^{12} \\), \\( 63^{10} \\), and \\( 127^{8} \\) is the smallest.",
"role": "user"
}
] | math | {
"ground_truth": "127^{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest result that can be obtained by either adding or subtracting any two distinct numbers from the set $\\{ -20, -5, 1, 3, 7, 15 \\}$?",
"role": "user"
}
] | math | {
"ground_truth": "35",
"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": "Four A's, four B's, four C's, and four D's are placed in the sixteen spaces of a 4x4 grid so that each row and column contains one of each letter. If A is placed in the upper lef... | math | {
"ground_truth": "144",
"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 bug starts at a vertex of a square. On each move, it can either move to an adjacent vertex or diagonally to the opposite vertex. The probability of moving to an adjacent vertex... | math | {
"ground_truth": "59573",
"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 all real numbers \\( x_{1}, x_{2}, \\ldots, x_{60} \\in [-1, 1] \\), find the maximum value of \\( \\sum_{i=1}^{60} x_{i}^{2} (x_{i+1} - x_{i-1}) \\), where \\( x_{0} = x_{60... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the square of an integer \\( x \\) is 1849, what is the value of \\( (x+2)(x-2) \\)?",
"role": "user"
}
] | math | {
"ground_truth": "1845",
"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": "At the beginning of the school year, $40\\%$ of students in Mr. Well's class answered \"Yes\" to the question \"Do you love math?\" and $60\\%$ responded \"No\". Due to a school ... | math | {
"ground_truth": "C) 40%",
"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": "Fins all ordered triples $ \\left(a,b,c\\right)$ of positive integers such that $ abc \\plus{} ab \\plus{} c \\equal{} a^3$ .",
"role": "user"
}
] | math | {
"ground_truth": "(a, a - 1, a)",
"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 Gilda gives $20\\%$ of her original marbles to Pedro, then $10\\%$ of what is left to Ebony, and finally $25\\%$ of what remains to Jimmy, calculate the percentage of ... | math | {
"ground_truth": "54\\%",
"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": "1. If the proposition \"$\\exists x \\in \\mathbb{R}, x^2 + 2x + m \\leqslant 0$\" is a false statement, then the range of real number $m$ is ______. \n2. If the line $ax + 4y -... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(2m, 1)$, and $\\sin{\\alpha} = \\frac{1}{3}$.\n\n(1) Find the value of the real number $m$;\n\n(2) Find th... | math | {
"ground_truth": "-\\frac{\\sqrt{2}}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a geometric sequence $\\{a_{n}\\}$ with a common ratio $q \\gt 1$, if $a_{2}+a_{3}+a_{4}=14$, and $a_{2}$, $a_{3}+1$, $a_{4}$ are the $1$st, $3$rd, and $5$th terms of an ar... | math | {
"ground_truth": "S_{n} = 8 - \\frac{1}{2^{n+1} - 1} - \\frac{3n + 7}{2^n}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A convex hexagon has interior angles with measures $x+2$, $2x+3$, $3x-1$, $4x+2$, $5x-4$, and $6x-3$ degrees. What is the measure of the largest angle?",
"role": "user"
}
] | math | {
"ground_truth": "203",
"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": "Three cones with a common vertex \\( A \\) are externally tangent to each other. The first two cones are identical, and the vertex angle of the third cone is \\( \\frac{\\pi}{4} ... | math | {
"ground_truth": "2 \\arctan \\frac{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": "When I saw Eleonora, I found her very pretty. After a brief trivial conversation, I told her my age and asked how old she was. She answered:\n\n- When you were as old as I am now... | math | {
"ground_truth": "15",
"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 sequence begins with 800,000 and each subsequent term is obtained by dividing the previous term by 2. What is the last integer in this sequence?",
"role": "user"
}
] | math | {
"ground_truth": "3125",
"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 ten 0's and ten 1's, how many 0-1 binary sequences can be formed such that no three or more consecutive 0's are together? For example, 01001001010011101011 is such a sequen... | math | {
"ground_truth": "24068",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( p \\) and \\( q \\) be real numbers so that the roots of\n\\[ z^2 + (6 + pi) z + (13 + qi) = 0 \\]\nare complex conjugates. Find the ordered pair \\( (p,q) \\).",
"ro... | math | {
"ground_truth": "(0,0)",
"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": "From the point \\((x, y)\\), a legal move is a move to \\(\\left(\\frac{x}{3}+u, \\frac{y}{3}+v\\right)\\), where \\(u\\) and \\(v\\) are real numbers such that \\(u^{2}+v^{2} \\... | math | {
"ground_truth": "\\frac{9\\pi}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three one-inch squares are placed with their bases on a line. The center square is lifted out and rotated 45 degrees, as shown. Then it is centered and lowered into its original ... | math | {
"ground_truth": "\\sqrt{2}+\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\frac{b}{a} = 3$ and $\\frac{c}{b} = 4$, calculate the ratio of $a + b$ to $b + c$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{15}",
"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": "Let $g(x)$ be a polynomial with leading coefficient $1$, whose four roots are the reciprocals of the roots of $f(x) = x^4 + ax^3 + bx^2 + cx + d$, where $a, b, c, d$ are positive... | math | {
"ground_truth": "\\frac{16 + 8a + 4b + 2c + d}{pqrs}",
"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": "Determine the units digit of $2^{1201} 4^{1302} 6^{1403}$.\nA) 1\nB) 2\nC) 4\nD) 6\nE) 8",
"role": "user"
}
] | math | {
"ground_truth": "B\\text{) } 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 a two-digit positive integer, determine how many integers satisfy the condition of being equal to the sum of its nonzero tens digit and the cube of its units digit.",
"... | math | {
"ground_truth": "0",
"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 point is chosen at random within the square on the coordinate plane whose vertices are $(0, 0), (1000, 0), (1000, 1000),$ and $(0, 1000)$. The probability that the point falls ... | math | {
"ground_truth": "0.5",
"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": "Let $x$ and $y$ be two positive real numbers such that $x + y = 50$. Find the ordered pair $(x, y)$ for which $x^3 y^4$ is maximized.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{150}{7}, \\frac{200}{7}\\right)",
"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 complex number $z=i(2-i)$, where $i$ is the imaginary unit, find the conjugate of $z$, denoted as $\\overline{z}$.",
"role": "user"
}
] | math | {
"ground_truth": "1 - 2i",
"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": "Jane wishes to invest an amount in a bank that compounds interest monthly with an annual interest rate of 8%. How much should she invest to achieve a total of $75,000 at the end ... | math | {
"ground_truth": "\\$46,852",
"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 sequence $\\{b_n\\}$ defined by:\n$b_1 = 3$\n$b_{n + 1} = b_n + 3n + 1$, for $n \\geq 1$.\nCalculate $b_{50}$.\nA) 3725\nB) 3726\nC) 3727\nD) 3728",
"role": "use... | math | {
"ground_truth": "C) 3727",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\( n \\) is a positive integer and \\( n \\geq 4 \\). Find the largest positive integer \\( k \\) such that there exists a triangle with side lengths all being positi... | math | {
"ground_truth": "\\left\\lfloor \\frac{n-1}{3} \\right\\rfloor",
"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 smallest positive integer $n \\geq 10$ such that $n + 6$ is a prime and $9n + 7$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"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 twelve points are selected on the positive x-axis, and six points are selected on the positive y-axis, find the maximum possible number of points of intersection of the lin... | math | {
"ground_truth": "990",
"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 plane intersects the faces and the edge of a dihedral angle, such that the projection of the edge onto this plane coincides with the angle bisector formed by the intersection o... | math | {
"ground_truth": "\\tan \\frac{\\gamma}{2} = \\frac{\\tan \\frac{\\beta}{2}}{\\sin \\alpha}",
"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": "Petya inscribed two squares in a right triangle with sides 3, 4, and 5. One vertex of the first square coincides with the right-angle vertex of the triangle, while one side of th... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what value of $n$ does $|6 + ni| = 6\\sqrt{5}$?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**Fill in the Blank:** \nWhen a plane intersects a cube, the resulting cross-section is a polygon. The maximum number of sides this polygon can have is ____.",
"role": "user... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cell phone plan costs $30$ dollars each month, plus $10$ cents per text message sent, plus $20$ cents for each minute used over $50$ hours. In February, John sent $150$ text me... | math | {
"ground_truth": "\\69",
"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 two three-digit numbers $x$ and $y$ such that the sum of all other three digit numbers is equal to $600x$ .",
"role": "user"
}
] | math | {
"ground_truth": "x = 823",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the quadratic equation $ax^2 + 8x + c = 0$ which has exactly one solution. Given that $a + 2c = 14$, and $a < c$, determine the ordered pair $(a, c)$.",
"role": "use... | math | {
"ground_truth": "\\left(\\frac{7 - \\sqrt{17}}{2}, \\frac{7 + \\sqrt{17}}{2}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a string of lights with a recurrent pattern of three blue lights followed by four yellow lights, spaced 7 inches apart. Determine the distance in feet between the 4th bl... | math | {
"ground_truth": "28",
"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": "Consider simplifying the expression $\\left[ \\sqrt[4]{\\sqrt[3]{a^{16}}} \\right]^3\\left[ \\sqrt[3]{\\sqrt[4]{a^{16}}} \\right]^2$.\n**A)** $a^{\\frac{15}{3}}$ \n**B)** $a^{\\... | math | {
"ground_truth": "\\textbf{(B)}\\ a^{\\frac{20}{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": "For a geometric sequence $\\{a_n\\}$ with the first term $a_1=-1$ and the sum of the first $n$ terms denoted as $S_n$, if $\\frac {S_{10}}{S_{5}}= \\frac {31}{32}$, then the comm... | math | {
"ground_truth": "- \\frac {1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parabola $y^{2}=2px(p > 0)$, the distance between the focus and the directrix is $4$, and a line passing through the point $P(1,-1)$ intersects the parabola at points $A$... | math | {
"ground_truth": "4x+y-3=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": "Given in $\\triangle ABC$, $\\angle A=120^{\\circ}$, and $AB=AC=2$, then $BC=$ ______, $\\overrightarrow{BC}\\cdot \\overrightarrow{CA}=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area of the newly designed shaded shapes shown in the \\(7 \\times 7\\) grid?\n[asy] filldraw((3.5,3.5)--(0,2)--(2,2)--(2,0)--(3.5,3.5)--(5,0)--(5,2)--(7,2)--(3.5,3.5... | math | {
"ground_truth": "\\textbf{(B)}\\: 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": "Let \\(\\left(a_{n}\\right)\\) be defined by \\(a_{1}=3\\), \\(a_{2}=2\\), and for \\(n \\geqslant 1\\), \\(a_{n+2}\\) is the remainder of the Euclidean division of \\(a_{n}+a_{n... | 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": "What is the smallest four-digit multiple of 8 whose digits' sum is 20?",
"role": "user"
}
] | math | {
"ground_truth": "1071",
"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": "Simplify and then evaluate the expression: $$\\frac{{{x}^{2}}-4xy+4{{y}^{2}}}{{{x}^{2}}-xy}\\div (x+y-\\frac{3{{y}^{2}}}{x-y})+\\frac{1}{x}$$, where $(x, y)$ is the solution to t... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the twelve-sided regular polygon \\(A_1A_2A_3A_4A_5A_6A_7A_8A_9A_{10}A_{11}A_{12}\\), how many distinct equilateral triangles in the plane of the polygon have at least two ... | math | {
"ground_truth": "124",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence $\\{{a_n}\\}$ is an arithmetic sequence with a common difference of $\\frac{1}{2}$. The sum of its first $100$ terms is $145$. Find the value of $({a_1}+{a_3}+{a_5}+... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with radius $\\frac{\\sqrt{2}}{2}$ and a regular hexagon with side length 1 share the same center. Calculate the area inside the circle, but outside the hexagon.",
"... | math | {
"ground_truth": "\\frac{\\pi}{2} - \\frac{3\\sqrt{3}}{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": "The coefficient of $x^2$ in the expansion of $(2-x)(1-3x)^4$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "120",
"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 diagram shows two equilateral triangles with side length $4$ mounted on two adjacent sides of a square also with side length $4$ . The distance between the two vertices ma... | math | {
"ground_truth": "80",
"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 three-dimensional Cartesian coordinate system, find the coordinates of the point symmetrical to point A(3, 4, -5) with respect to the x-axis.",
"role": "user"
}
] | math | {
"ground_truth": "(3, -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": "We call a pair of natural numbers \\((a, p)\\) good if the number \\(a^3 + p^3\\) is divisible by \\(a^2 - p^2\\), with \\(a > p\\).\n\n(a) (1 point) Specify any possible value o... | math | {
"ground_truth": "24",
"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 distance between a pair of points P and Q, where P is on edge AB and Q is on edge CD, is minimized.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A wooden cube with side length $n$ units is painted green on all six faces and then cut into $n^3$ unit cubes. Exactly one-third of the total number of faces of the unit cubes ar... | math | {
"ground_truth": "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": "Santa Claus arrived at the house of Arnaldo and Bernaldo carrying ten distinct toys numbered from 1 to 10 and said to them: \"Toy number 1 is for you, Arnaldo, and toy number 2 i... | math | {
"ground_truth": "6305",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers $ n \\ge 3$ such that there are $ n$ points in space, with no three on a line and no four on a circle, such that all the circles pass through three points b... | math | {
"ground_truth": "n = 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": "Given Allison's birthday cake is in the form of a $5 \\times 5 \\times 3$ inch rectangular prism with icing on the top, front, and back sides but not on the sides or bottom, calc... | math | {
"ground_truth": "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 ratio of the boat’s average speed for the round trip to its speed in still water.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the boundary value problem \\(x^{2} y^{\\prime \\prime} + 2x y^{\\prime} - 6y = 0\\), given \\(y(1) = 1\\), and \\(y(x)\\) is bounded as \\(x \\rightarrow 0\\).",
"role... | math | {
"ground_truth": "y(x) = x^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": "A line segment is divided into two parts such that the ratio of the lesser part to the greater part is as the cube of the greater part is to the square of the whole segment. Let ... | math | {
"ground_truth": "D) -3/2",
"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": "An $\\textrm{alien}$ script has $n$ letters $b_1,b_2,\\dots,b_n$ . For some $k<n/2$ assume that all words formed by any of the $k$ letters (written left to right) are me... | math | {
"ground_truth": "600",
"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\n$$\nf(x) = \\left|8x^3 - 12x - a\\right| + a\n$$\n\nThe maximum value of this function on the interval \\([0, 1]\\) is 0. Find the maximum value of the real n... | 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": "Determine the set of $x$-values for which the equation $x^{\\log_{10} x} = \\frac{x^2}{10}$ holds true.\nA) 10, only\nB) 100, only\nC) Both 10 and 100\nD) 1, only\nE) More than t... | math | {
"ground_truth": "A) 10, only",
"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 rope of length 10 *m* is tied tautly from the top of a flagpole to the ground 6 *m* away from the base of the pole. An ant crawls up the rope and its shadow moves at a rate of ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $3 \\times 3^4 - 27^{65} \\div 27^{63}$",
"role": "user"
}
] | math | {
"ground_truth": "-486",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ be a positive integer; a divisor of $N$ is called *common* if it's great than $1$ and different of $N$ . A positive integer is called *special* if it has, at least... | math | {
"ground_truth": "6, 8, 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": "Let $r$ be a complex number such that $r^7 = 1$ and $r \\neq 1.$ Compute\n\\[\n(r - 1)(r^2 - 1)(r^3 - 1)(r^4 - 1)(r^5 - 1)(r^6 - 1).\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the coefficient of $x$ in the expansion of $(x^{2}- \\frac {1}{x})^{5}$.",
"role": "user"
}
] | math | {
"ground_truth": "-10",
"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 $f(x)=|x-a|$, where $a\\in R$.\n\n(1) If $a=1$, solve the inequality $f(x)\\geqslant \\frac{1}{2}(x+1)$;\n\n(2) Let the range of the function $g(x)=f(x)-|x-2|$... | 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": "Find the reciprocal of $\\left( \\frac{1}{4} - \\frac{1}{5} \\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"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": "Two mirror walls are placed to form an angle of measure $\\alpha$ . There is a candle inside the angle. How many reflections of the candle can an observer see?",
"role": "us... | math | {
"ground_truth": "\\left\\lfloor \\frac{360^\\circ}{\\alpha} \\right\\rfloor - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of \\(a\\) for which the system of equations \n\\[\n\\begin{cases}\nx - 4 = a(y^3 - 2), \\\\\n\\frac{2x}{|y^3| + y^3} = \\sqrt{x}\n\\end{cases}\n\\]\nhas at least... | math | {
"ground_truth": "a \\in (-\\infty, 0) \\cup \\{4\\}, a \\in [0,2] , a \\in (2, 4) \\cup (4, + \\infty)",
"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 the coordinate grid displayed below, there are six triangles. Determine how many of these triangles are isosceles.\n[asy] for(int a=0; a<=10; ++a) { draw((a,0)--(a,8)); } for... | math | {
"ground_truth": "E) 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": "A rectangular box $Q$ is inscribed in a sphere of radius $r$. The surface area of $Q$ is 432, and the sum of the lengths of its 12 edges is 120. What is $r$?",
"role": "user"... | math | {
"ground_truth": "\\sqrt{117}",
"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 circle is circumscribed around an acute-angled triangle \\(ABC\\). Point \\(K\\) is the midpoint of the smaller arc \\(AC\\) of this circle, and point \\(L\\) is the midpoint o... | math | {
"ground_truth": "90^\\circ",
"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": "Define $x$ $\\$$ $y$ to be $x(y + 2) + xy + x$. What is the value of $3$ $\\$$ $(-4)$?",
"role": "user"
}
] | math | {
"ground_truth": "-15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $T$ be the set of all points $(x, y, z)$ where $x, y, z \\in \\{0, 1, 2, 3\\}$. How many equilateral triangles all have their vertices in $T$?\nA) 100\nB) 115\nC) 125\nD) 130... | math | {
"ground_truth": "B) 115",
"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 dealer sold 300 cars, and some of these sales are recorded in the table below. If all remaining cars sold were Lexuses, how many Lexuses did she sell?\n\n\\begin{tabular}{|c | ... | math | {
"ground_truth": "60",
"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": "It is given that \\(a+b=c-1\\) and \\(ab=c^{2}-7c+14\\), find the largest possible value of \\(a^{2}+b^{2}\\).",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A round pizza is $\\frac{1}{2}$ of an inch thick and has a diameter of 10 inches. It is cut into 10 congruent pieces. What is the number of cubic inches in the volume of one piec... | math | {
"ground_truth": "\\frac{5\\pi}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of pairs $(n, q)$ , where $n$ is a positive integer and $q$ a non-integer rational number with $0 < q < 2000$ , that satisfy $\\{q^2\\}=\\left\\{\\frac{n!}... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sequence $\\{a\\_n\\}$ is an arithmetic sequence with the sum of the first $n$ terms denoted as $S\\_n$, and $a\\_3=6$, $S\\_3=12$.\n\n(I) Find $a\\_n$;\n\n(II) Fi... | math | {
"ground_truth": "n(n+1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2019$ students are voting on the distribution of $N$ items. For each item, each student submits a vote on who should receive that item, and the person with the most votes rec... | math | {
"ground_truth": "1009",
"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": "Calculate the length of the diagonal of a rectangle where one side is $30\\sqrt{2}$ cm and the other side is $30(\\sqrt{2} + 2)$ cm. Express your answer in simplest form.",
"... | math | {
"ground_truth": "\\sqrt{7200 + 3600\\sqrt{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": "The side lengths of both triangles are given in centimeters. What is the length of segment $PQ$?\n\n[asy]\npair P, Q, R, S, T, U, V;\n\nP = (0,0);\nQ = 15*dir(0);\nR = 25*dir(135... | math | {
"ground_truth": "20",
"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 pyramid has a triangular base with side lengths $20$, $20$, and $24$. The three edges of the pyramid from the three corners of the base to the fourth vertex of the pyramid all ... | math | {
"ground_truth": "803",
"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": "Let $g$ be a function defined for all real numbers that satisfies $g(3+x) = g(3-x)$ and $g(8+x) = g(8-x)$ for all $x$. If $g(0) = 0$, determine the least number of roots $g(x) = ... | math | {
"ground_truth": "402",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a $10 \\times 10$ grid, consisting of 100 squares. The rows of the grid are numbered from top to bottom in order from 1 to 10: the highest row is number 1, the lowest is... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ such that the number $$ n^6 + 5n^3 + 4n + 116 $$ is the product of two or more consecutive numbers.",
"role": "user"
}
] | math | {
"ground_truth": "n = 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": "Let $S = \\{1, 2,..., 8\\}$ . How many ways are there to select two disjoint subsets of $S$ ?",
"role": "user"
}
] | math | {
"ground_truth": "6561",
"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 set of balls contains $ n$ balls which are labeled with numbers $ 1,2,3,\\ldots,n.$ We are given $ k > 1$ such sets. We want to colour the balls with two colours, black a... | math | {
"ground_truth": "k^2 + k - 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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