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": "If \\(\\frac{99!}{101! - 99!} = \\frac{1}{n}\\), determine the value of \\(n\\).",
"role": "user"
}
] | math | {
"ground_truth": "10099",
"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 last digit of the number \\(7^7\\).",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the quadratic equation $3x^2 - mx + 2x + 6 = 0$, find the values of $m$ for which the quadratic equation will have real and equal roots.",
"role": "user"
}
] | math | {
"ground_truth": "2 - 6\\sqrt{2} \\text{ and } 2 + 6\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $O$ be the center of an equilateral triangle $ABC$ of area $1/\\pi$ . As shown in the diagram below, a circle centered at $O$ meets the triangle at points $D$ , $E$... | math | {
"ground_truth": "\\frac{2 \\sqrt{3}}{27}",
"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": "All the cells in the top row of a $14 \\times 14$ square are filled with water, and one cell contains a sandbag. With each move, Vasya can place sandbags in any 3 unoccupied cell... | math | {
"ground_truth": "37",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a circle $C: x^2+y^2-4x+2y+m=0$ that intersects the y-axis at points $A$ and $B$, and $\\angle ACB = 90^\\circ$, find the value of the real number $m$.",
"role": "user"... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real solutions to the equation \\( 4x^2 - 40[x] + 51 = 0 \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{29}}{2}, \\frac{\\sqrt{189}}{2}, \\frac{\\sqrt{229}}{2}, \\frac{\\sqrt{269}}{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": "An automobile travels $a/6$ feet in $r$ seconds. If this rate is maintained for $3$ minutes, calculate the distance it travels in feet.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10a}{r}",
"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": "Read the following material and then answer the following questions: When simplifying algebraic expressions, sometimes we encounter expressions like $\\frac{5}{\\sqrt{3}}$, $\\fr... | math | {
"ground_truth": "\\frac{3\\sqrt{11}-1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the domain of the function \\( f(x) \\) is \\([-1,1]\\), find the domain of \\( f(a x) + f\\left(\\frac{x}{a}\\right) \\) where \\( a > 0 \\).",
"role": "user"
}... | math | {
"ground_truth": "\\left[ -\\frac{1}{a}, \\frac{1}{a} \\right] \\text{ if } a \\geq 1 \\text{ and } [-a,a] \\text{ if } 0 < a < 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": "Given \\( x y z + y + z = 12 \\), find the maximum value of \\( \\log_{4} x + \\log_{2} y + \\log_{2} z \\).",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $q_1 (x)$ and $r_1$ are the quotient and the remainder, respectively, when the polynomial $x^9$ is divided by $x - 1$, and if $q_2 (x)$ and $r_2$ are the quotient and ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\left(\\sqrt{8} - \\sqrt{4\\frac{1}{2}}\\right)^2$\nA) $\\frac{1}{2}$\nB) $\\frac{3\\sqrt{2}}{2}$\nC) $2$\nD) $\\frac{1}{4}$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the tetrahedron \\(ABCD\\), \\(AB = 2\\), \\(AC = 3\\), \\(AD = 4\\), \\(BC = \\sqrt{13}\\), \\(BD = 2\\sqrt{5}\\), and \\(CD = 5\\). Find the volume of the tetrahedron \\(ABC... | math | {
"ground_truth": "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": "If $f(x)$ is an odd function defined on $\\mathbb{R}$, and when $x \\geq 0$, $f(x) = x^2 + 2x$, then when $x < 0$, $f(x) = \\boxed{-x^2 + 2x}$.",
"role": "user"
}
] | math | {
"ground_truth": "-x^2 + 2x",
"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 tangent is drawn from a point on the line $y=x+1$ to the circle $(x-3)^2+y^2=1$. The minimum length of the tangent is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt {7}",
"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 trapezoid \\(A B C D\\) with right angles at \\(A\\) and \\(D\\). Let \\(A B = a\\), \\(C D = b\\), and \\(A D = h\\).\n\n1) What relationship must exist between \\(a\\),... | math | {
"ground_truth": "h^2 = 4ab",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Paula the painter had just enough paint for 30 identically sized rooms, but ended up with enough paint for only 25 rooms after losing three cans, determine the number ... | math | {
"ground_truth": "15",
"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": "Find the modular inverse of $35$, modulo $36$.\n\nExpress your answer as an integer from $0$ to $35$, inclusive.",
"role": "user"
}
] | math | {
"ground_truth": "35",
"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": "Two cars leave points A and B simultaneously and meet at 12 PM. If the speed of the first car is doubled while keeping the speed of the second car the same, the meeting will occu... | math | {
"ground_truth": "10:29 \\text{ AM}",
"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 three wheels with Wheel One having three even and one odd number, Wheel Two having two even and two odd numbers, and Wheel Three having one even and three odd numbers, calc... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When three different numbers from the set $\\{-4, -3, -1, 5, 6\\}$ are multiplied, calculate the largest possible product.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"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 bagel is cut into sectors. After making 10 cuts, how many pieces are there?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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 \\( f: \\mathbf{R}_{+} \\rightarrow \\mathbf{R}_{+} \\), and it satisfies the following conditions:\n(1) For any \\( x, y \\in \\mathbf{R}_{+} \\), we have\n\\[ f(x f(y)) =... | math | {
"ground_truth": "f(x) = \\frac{1}{x}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that an arbitrary power function passes through the fixed point $A(m,n)$, the function $f(x) = \\log_a(x - m) + n$ passes through the fixed point $\\_\\_\\_\\_\\_\\_\\_\\_\... | math | {
"ground_truth": "(2, 1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all pairs $(m, n)$ of positive integers such that $m^2 + 2n^2 = 3(m + 2n)$",
"role": "user"
}
] | math | {
"ground_truth": "(m, n) = (3, 3), (4, 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": "Estimate \\( A \\), the number of unordered triples of integers \\( (a, b, c) \\) so that there exists a nondegenerate triangle with side lengths \\( a, b \\), and \\( c \\) fitt... | math | {
"ground_truth": "187500",
"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 all positive integers $n$ for which the number \n\n \\[\n N = \\frac{1}{n \\cdot (n + 1)}\n \\]\n can be represented as a finite decimal fraction.",
... | math | {
"ground_truth": "n = 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": "Let \\(k, a_2, a_3\\) and \\(k, b_2, b_3\\) be two nonconstant geometric sequences with different common ratios. It is given that \\(a_3 - b_3 = 7(a_2 - b_2)\\). Find the sum of ... | math | {
"ground_truth": "7",
"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": "Every card in a deck displays a shape (circle, square, or triangle), a color (red, blue, or green), a shade (light, medium, or dark), and a pattern (plain, striped, or dotted). T... | math | {
"ground_truth": "630",
"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 land area of China is approximately $9600000 km^{2}$, and the water area is approximately $370000 km^{2}$. Express the land area of China in scientific notation.",
"role"... | math | {
"ground_truth": "9.6 \\times 10^{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": "Mina is creating a similar logo for her brand but with a different design. She uses a square and eight smaller circles, each being tangent to two sides of the square and two adja... | math | {
"ground_truth": "576 - 72\\pi",
"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 function $f(x)= \\begin{cases} 2^{x}-4,x > 0 \\\\ 2x\\;\\;\\;,x\\leqslant 0 \\end{cases}$, find the value of $f(f(1))$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to arrange numbers from 1 to 8 in circle in such way the adjacent numbers are coprime?\n\nNote that we consider the case of rotation and turn over as dist... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the measure of the smaller angle formed by the minute and hour hands of a clock when the time is 3:15 p.m.",
"role": "user"
}
] | math | {
"ground_truth": "7.5^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $2b$ men can lay $3f$ bricks in $c$ days, calculate the number of days it will take $4c$ men to lay $6b$ bricks.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{b^2}{f}",
"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 $ABCD$ be a square and $O$ is your center. Let $E,F,G,H$ points in the segments $AB,BC,CD,AD$ respectively, such that $AE = BF = CG = DH$ . The line $OA$ intersect... | 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": "The mean (average) of a set of six numbers is 10. Given that one of the numbers is 25, find the mean of the remaining five numbers.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl}\n3x + 4 & \\text{if } x < -3, \\\\\n-x^2 - 2x + 2 & \\text{if } x \\ge -3.\n\\end{array}\n\\right.\\]Find the sum of all values of $x$... | math | {
"ground_truth": "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": "Compute the smallest positive integer $n$ such that\n\\[\\sum_{k = 0}^n \\log_{10} \\left( 1 + \\frac{1}{2^{2^k}} \\right) \\ge 1 + \\log_{10} \\frac{1}{2}.\\]",
"role": "use... | math | {
"ground_truth": "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": "The slant height of a cone is \\( l \\), and the angle between the slant height and the base is \\( \\theta \\). Find the side length of the largest cube that can be inscribed in... | math | {
"ground_truth": "\\frac{\\sqrt{2} l \\sin \\theta}{\\tan \\theta + \\sqrt{2}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the cubic polynomial\n\\[16x^3 - 4x^2 - 4x - 1 = 0\\]\nwhich has a real root of the form $\\frac{\\sqrt[3]{p} + \\sqrt[3]{q} + 1}{r},$ where $p,$ $q,$ and $r$ are positi... | math | {
"ground_truth": "288",
"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 function $g(x)$ satisfies $g(3+x) = g(3-x)$ for all real numbers $x$. If $g(x) = 0$ has exactly three distinct real roots, find the sum of these roots.",
"role": "user"
... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A store sells 9 pencils and 10 notebooks for $\\mathdollar 5.35$ and 6 pencils and 4 notebooks for $\\mathdollar 2.50$. If a special offer allows buying pencils in packs of 4 for... | math | {
"ground_truth": "9.24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points $A$ and $B$ are on a circle of radius $5$ and $AB=6$. Point $C$ is the midpoint of the minor arc $AB$. Calculate the length of the line segment $AC$.",
"role": "user"
... | math | {
"ground_truth": "\\sqrt{10}",
"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": "Laura has six assignment scores: 93, 87, 90, 94, 88, and 92. What is the arithmetic mean of these six scores?",
"role": "user"
}
] | math | {
"ground_truth": "90.67",
"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 \\( p(x) \\) be the product of the digits of the decimal number \\( x \\). Find all positive numbers \\( x \\) for which \\( p(x) = x^2 - 10x - 22 \\).",
"role": "user"
... | math | {
"ground_truth": "12",
"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 $ABCD$ be a rectangle and $E$ be a point on segment $AD$ . We are given that quadrilateral $BCDE$ has an inscribed circle $\\omega_1$ that is tangent to $BE$ at $... | math | {
"ground_truth": "\\frac{3 + \\sqrt{5}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence, if $a_1 = -3$ and $11a_5 = 5a_8$, then the value of $n$ that minimizes the sum of the first $n$ terms, $S_n$, is $\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions $f:\\mathbb{N}\\to \\mathbb{N}$ so that for every natural numbers $m,n$ : $f(n)+2mn+f(m)$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "f(n) = (n + 2\\ell)^2 - 2\\ell^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": "Koalas absorb only $20\\%$ of the fiber they eat. If a koala absorbed 12 ounces of fiber in one day, how many ounces of fiber did he eat that day?",
"role": "user"
}
] | 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": "Let \\( n \\) be a positive integer. Consider an \\( n \\times n \\) grid \\( T_n \\) with the grid lines' intersection points (a total of \\( (n+1)^2 \\) intersection points) as... | math | {
"ground_truth": "\\left[ \\frac{n^2 + 2n - 1}{2} \\right]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $\\triangle ABC$, point $D$ lies on side $AB$ such that $BD=3DA$. Let $\\overrightarrow{CA}=\\overrightarrow{a}$ and $\\overrightarrow{CD}=\\overrightarrow{b}$. Find ... | math | {
"ground_truth": "4\\overrightarrow{b} - 3\\overrightarrow{a}",
"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": "Integers $x_1,x_2,\\cdots,x_{100}$ satisfy \\[ \\frac {1}{\\sqrt{x_1}} + \\frac {1}{\\sqrt{x_2}} + \\cdots + \\frac {1}{\\sqrt{x_{100}}} = 20. \\]Find $ \\displaystyle\\prod_{... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the ratio of the longer side to the shorter side of the rectangle is $7:4$, and the shorter side measures $20$ inches, determine the ratio of the area of the rectangle to t... | math | {
"ground_truth": "\\frac{7}{4\\pi}",
"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": "Makarla's workday is 10 hours long, and she attended three meetings. The first meeting lasted 40 minutes, the second meeting lasted twice as long as the first, and the third meet... | math | {
"ground_truth": "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": "Suppose that $x$ and $y$ are nonzero real numbers such that $\\frac{4x-3y}{x+4y} = 3$. Find the value of $\\frac{x-4y}{4x+3y}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{11}{63}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In all the cells of a $6 \\times 8$ table, except the corner ones, non-negative numbers are placed such that the sum of the numbers in each cross of five cells is no more than 10... | math | {
"ground_truth": "160",
"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 full container of water undergoes a series of pourings where in each pouring, a fraction of the remaining water is removed according to the sequence: first one third is removed... | math | {
"ground_truth": "\\text{C) 14}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cylindrical log has diameter $ 12$ inches. A wedge is cut from the log by making two planar cuts that go entirely through the log. The first is perpendicular to the axis of t... | math | {
"ground_truth": "216",
"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": "For a certain complex number $d$, the polynomial\n\\[Q(x) = (x^2 - 3x + 3)(x^2 - dx + 5)(x^2 - 5x + 10)\\]\nhas exactly 5 distinct roots. What is $|d|$?\n**A)** $\\sqrt{24}$\n**B... | math | {
"ground_truth": "\\textbf{C) } \\sqrt{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": "Given the universal set $U=\\mathbb{R}$, set $A=\\{x\\mid 2^{x} > 1\\}$, and set $B=\\{x\\mid x^{2}-3x-4 > 0\\}$, find the intersection of sets A and B.",
"role": "user"
}
... | math | {
"ground_truth": "\\{x \\mid x > 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 fifty distinct natural numbers, twenty-five of which do not exceed 50, and the remaining are greater than 50 but do not exceed 100. Additionally, no two of these numbers di... | math | {
"ground_truth": "2525",
"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 real numbers $x > 1,$ determine the minimum value of\n\\[\n\\frac{x + 10}{\\sqrt{x - 1}}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{11}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Carla the Caterpillar lives on a coordinate plane and begins her journey at $(10, -10)$. She moves in the order of north, east, south, and west. Carla moves 2 units north in her ... | math | {
"ground_truth": "\\textbf{(C)}\\ (-191, -10)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every integer $r > 1$ find the smallest integer $h(r) > 1$ having the following property: For any partition of the set $\\{1, 2, . . ., h(r)\\}$ into $r$ classes, the... | math | {
"ground_truth": "h(r) = 2r",
"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": "Climbing from the first to the third floor, Petya walks up 36 steps. Climbing from the first to his floor in the same building entrance, Vasya walks up 72 steps. On which floor d... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\triangle DEF$ has a right angle at $E$, $DE = 15$, and squares $DEUV$ and $EFST$ have equal areas, calculate the perimeter of $\\triangle DEF$.",
"role": "user"... | math | {
"ground_truth": "30 + 15\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The school offers German and Chinese language classes. There are 30 students enrolled in at least one language class. 22 students are in the German class and 19 students are in t... | math | {
"ground_truth": "\\frac{352}{435}",
"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": "Team A and Team B play a series where the first team to win four games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the i... | math | {
"ground_truth": "\\frac{2}{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": "Given that hamburgers cost $\\$4$ each and milkshakes cost $\\$3$ each, find the total amount of money it will take to purchase $7$ hamburgers and $6$ milkshakes.",
"role": "... | math | {
"ground_truth": "46",
"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 $ABCD$ be a convex quadrilateral with $\\angle{DAC}= \\angle{BDC}= 36^\\circ$ , $\\angle{CBD}= 18^\\circ$ and $\\angle{BAC}= 72^\\circ$ . The diagonals and intersect a... | math | {
"ground_truth": "108^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $0.83= \\frac{y}{192+x}$, find the smallest value of $x$, if $x$ and $y$ are positive integers.",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (8, 166)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the positive integers less than or equal to $3020$ are in base-ten, calculate how many of these numbers contain the digit $0$.",
"role": "user"
}
] | math | {
"ground_truth": "572",
"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 all positive integers $n$ , let $f(n)$ return the smallest positive integer $k$ for which $\\tfrac{n}{k}$ is not an integer. For example, $f(6) = 4$ because $1$ , ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that x varies directly as y and inversely as the square of z, and that x = 10 when y = 4 and z = 14, find the value of x when y = 16 and z = 7.",
"role": "user"
}
] | math | {
"ground_truth": "160",
"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 expression $G = \\frac{5x^2 + 20x + 4n}{5}$, which is the square of an expression linear in $x$, determine the range between which $n$ must fall.",
"role": "user"
... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "a) For each $n \\ge 2$ , find the maximum constant $c_{n}$ such that\r $\\frac 1{a_{1}+1}+\\frac 1{a_{2}+1}+\\ldots+\\frac 1{a_{n}+1}\\ge c_{n}$ \r\nfor all positive reals $a... | math | {
"ground_truth": "c_n = 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": "Two years ago, a skateboard was priced at $120, and knee pads were $30. This year, the price of the skateboard increased by $8\\%$, while the price of the knee pads increased by ... | math | {
"ground_truth": "9.4\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n \\ge 2$ such that equality $i+j \\equiv C_{n}^{i} + C_{n}^{j}$ (mod $2$ ) is true for arbitrary $0 \\le i \\le j \\le n$ .",
"role":... | math | {
"ground_truth": "n = 2^p - 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The average of 12 numbers is 90. If the numbers 82 and 95 are removed from the set of numbers, what is the average of the remaining 10 numbers?",
"role": "user"
}
] | math | {
"ground_truth": "90.3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using 2 unit squares (unit squares), we can form a 2-tile shape, commonly known as a domino. Clearly, after translations, rotations, and symmetric transformations, dominoes that ... | math | {
"ground_truth": "12",
"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 minimum value of the function \\( y = \\sqrt{x^2 + 2x + 2} + \\sqrt{x^2 - 2x + 2} \\).",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs of positive integers \\((n, k)\\) for which\n\n\\[ n! + n = n^k \\]\n\nholds.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 2), (3, 2), (5, 3)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $0, z,$ and $z^2$ are the three distinct vertices of an isosceles right triangle where $z$ and $z^2$ form the right angle, calculate the number of nonzero complex numb... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cagney can frost a cupcake every 20 seconds, Lacey can frost a cupcake every 30 seconds, and Jamie can frost a cupcake every 15 seconds. Working together, calculate the number of... | math | {
"ground_truth": "90",
"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": "Simplify the expression $(2x)^{-2} - 4$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{16x^2 - 1}{4x^2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the number is 12,650, calculate how many positive factors it has.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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 how many integer values of \\( n \\) is the value of \\( 8000 \\cdot \\left(\\frac{2}{5}\\right)^n \\) an integer?\nA) 8\nB) 9\nC) 10\nD) 11\nE) 12",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(C) }10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify first, then evaluate: $(2a^{2}b-4ab^{2})-2(ab^{2}+a^{2}b)$, where $a=2$ and $b=-1$.",
"role": "user"
}
] | math | {
"ground_truth": "-12",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a classroom of boys and girls, a student is randomly chosen to lead a project. The probability that a boy is chosen is $\\frac{3}{4}$ of the probability that a girl is chosen.... | math | {
"ground_truth": "\\frac{3}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a Cartesian coordinate system, for rectangle ABCD, if line AB is defined by the equation $x - 2y - 2 = 0$ and the diagonal line of the rectangle is relative to the point $(0,1... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the coordinate plane, the line passing through points $(2023,0)$ and $(-2021,2024)$ also passes through $(1,c)$ for a constant $c$ . Find $c$ .\n\n*Proposed by Andy Xu... | math | {
"ground_truth": "1012",
"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 $p$, $q$, and $r$ be polynomials such that $r(x) = p(x) \\cdot q(x)$. If the constant term of $p(x)$ is 6 and the constant term of $r(x)$ is -18, what is the value of $q(0)$?... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $l$ some line, that is not parallel to the coordinate axes. Find minimal $d$ that always exists point $A$ with integer coordinates, and distance from $A$ to $l$ is ... | math | {
"ground_truth": "\\frac{1}{2\\sqrt{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": "Evaluate $\\left\\lfloor |{-25.7}|\\right\\rfloor$.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a high school basketball game, students participate in pairs. Each round, both members of a pair take two shots each, and a pair is considered \"excellent\" if the total numbe... | math | {
"ground_truth": "27",
"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 domino is a $1\\times2$ or $2\\times 1$ rectangle. Diego wants to completely cover a $6\\times 6$ board using $18$ dominoes. Determine the smallest positive integer $k... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John drove 150 miles in 120 minutes. His average speed during the first 40 minutes was 70 mph, and for the next 40 minutes, he traveled at 75 mph. Determine the average speed dur... | math | {
"ground_truth": "80",
"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": "Dividing both sides of the inequality $-6x \\gt 2$ by $-6$, determine the resulting inequality.",
"role": "user"
}
] | math | {
"ground_truth": "x \\lt -\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.