data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The arithmetic mean of a set of 75 numbers is 60. If two numbers from the set, namely 72 and 48, are removed, calculate the arithmetic mean of the remaining set of numbers.",
... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $|\\overrightarrow{a}|=2$, $|\\overrightarrow{b}|=\\overrightarrow{a}\\cdot\\overrightarrow{b}=1$, and $(... | math | {
"ground_truth": "\\frac{\\sqrt{7}-\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A flagpole is originally $8$ meters tall. A severe storm snaps the flagpole at a point $x$ meters above the ground so that the upper part, still attached to the base, touches the... | math | {
"ground_truth": "4.5625",
"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 $A$ be a subset of $\\{1, 2, 3, \\ldots, 50\\}$ with the property: for every $x,y\\in A$ with $x\\neq y$ , it holds that\n\\[\\left| \\frac{1}{x}- \\frac{1}{y}\\right|... | math | {
"ground_truth": "40",
"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 $x, y \\in \\mathbb{R}$, vectors $\\vec{a} = (x,1)$, $\\vec{b} = (1,y)$, and $\\vec{c} = (3, -6)$, and given that $\\vec{a}$ is perpendicular to $\\vec{c}$ and $\\vec{b}$ i... | math | {
"ground_truth": "15",
"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 total area of all the faces of a rectangular solid is $26\\text{cm}^2$, and the total length of all its edges is $28\\text{cm}$. Determine the length in cm of any one of its ... | math | {
"ground_truth": "\\sqrt{23}",
"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 triples $(a, b, c)$ of positive integers for which $\\frac{32a + 3b + 48c}{4abc}$ is also an integer.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 20, 1), (1, 4, 1), (3, 4, 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": "What is the maximum number of axes of symmetry that a union of three line segments in a plane can have?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the maximum of\n\\[\n\\sqrt{x + 16} + \\sqrt{20 - x} + 2\\sqrt{x}\n\\]\nfor \\( 0 \\le x \\le 20 \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{16\\sqrt{3} + 2\\sqrt{33}}{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": "Given that $\\text{1 kilometer} = \\text{5 hectometers}$, $\\text{1 hectometer} = \\text{10 dekameters}$, and $\\text{1 dekameter} = \\text{15 meters}$, calculate the number of m... | math | {
"ground_truth": "750",
"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 all positive integers \\( a \\) for which the equation\n\n\\[ 7an - 3n! = 2020 \\]\n\nhas a positive integer solution \\( n \\).\n\n(Note: For any positive integer \\( ... | math | {
"ground_truth": "a = 68 \\text{ or } a = 289",
"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 cube with 4-inch edges made of 64 cubes with 1-inch edges, where 48 are white and 16 are placed at the corners, calculate the fraction of the surface area of the larger c... | math | {
"ground_truth": "\\frac{3}{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": "A sphere with center \\(O\\) has a radius of \\(5\\). A triangle with sides of length \\(13, 13,\\) and \\(10\\) is situated in space such that each of its sides is tangent to th... | math | {
"ground_truth": "**C)** \\(\\frac{5\\sqrt{5}}{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": "Imagine a regular a $2015$ -gon with edge length $2$ . At each vertex, draw a unit circle centered at that vertex and color the circle’s circumference orange. Now, another unit... | math | {
"ground_truth": "2014",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "<u>Set 4</u> **p10.** Eve has nine letter tiles: three $C$ ’s, three $M$ ’s, and three $W$ ’s. If she arranges them in a random order, what is the probability that the string ... | math | {
"ground_truth": "\\frac{1}{28}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that\n\n\\[\nf(x y)=\\max \\{f(x+y), f(x) f(y)\\}\n\\]\n\nfor all \\( x, y \\in \\mathbb{R} \\).",
"ro... | math | {
"ground_truth": "f(x) = c \\text{, where } 0 \\leq c \\leq 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": "Toner Drum and Celery Hilton are both running for president. A total of $129$ million people cast their vote in a random order, with exactly $63$ million and $66$ million v... | math | {
"ground_truth": "\\frac{1}{43}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $P(x)$ is a monic polynomial of degree $2023$ such that $P(k) = k^{2023}P(1-\\frac{1}{k})$ for every positive integer $1 \\leq k \\leq 2023$ . Then $P(-1) = \\fra... | 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": "The sequence $\\{x_n\\}$ satisfies: $x_1=1$, $x_2=-1$, and $x_{n-1}+x_{n+1}=2x_n$ ($n\\geq2$), then $x_n=$ ___.",
"role": "user"
}
] | math | {
"ground_truth": "-2n+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": "Let $\\{a_n\\}$ be a sequence satisfying: $a_1=1$ and $a_{n+1}=2a_n+n\\cdot (1+2^n),(n=1,2,3,\\cdots)$ . Determine the general term formula of $\\{a_n\\}$ .",
"role": "... | math | {
"ground_truth": "a_n = 2^{n-2} (n^2 - n + 6) - 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": "Suppose the sequence $\\left\\{a_{n}\\right\\}$, where all terms are positive numbers, satisfies $a_{1}=2$ and $a_{n}=a_{n+1}+a_{n+2}$ for $n \\in \\mathbf{N}^{*}$. Let $b_{n} = ... | math | {
"ground_truth": "b_n = 2^{2 - \\frac{1}{2^{n-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": "Find the result of $3\\begin{pmatrix} -3 \\\\ 2 \\\\ 6 \\end{pmatrix} + \\begin{pmatrix} 4 \\\\ -5 \\\\ 2 \\end{pmatrix}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} -5 \\\\ 1 \\\\ 20 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the tower function of twos, defined recursively as $T(1) = 2$ and $T(n + 1) = 2^{T(n)}$ for $n \\ge 1$, let $A = (T(2009))^{T(2009)}$ and $B = (T(2009))^A$. Express the lar... | math | {
"ground_truth": "2010",
"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": "Three primes $p,q$, and $r$ satisfy $p+q = r$ and $1 < p < q$. Find the value of $p$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Five identical squares are arranged in a row and cut by two horizontal lines. The sum of the perimeters of the resulting 15 rectangles is 800 cm. Indicate the side length of the ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a regular hexagon where each of its $6$ sides and the $9$ diagonals are colored randomly and independently either red or blue, each color with the same probability. What... | math | {
"ground_truth": "\\frac{1048575}{1048576}",
"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 electronic clock on the International Space Station displayed time in the format HH:MM. Due to an electromagnetic storm, the device malfunctioned, and each digit on the displ... | math | {
"ground_truth": "11:18",
"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": "Stefan Banach and Matches. An improbable legend says that once in a small shop in downtown Lviv, Stefan Banach bought two matchboxes and put them in his jacket pocket. Each box c... | math | {
"ground_truth": "7.795",
"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 is a chessboard 8x8. We have to place $n$ black queens and $n$ white queens, so that no two queens attack. Find the maximal possible $n$ . \n(Two queens attack each ot... | math | {
"ground_truth": "8",
"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 collegiate basketball game, the Tigers and Lions were tied at the end of the first quarter, and the point difference at the end of the fourth quarter is 4 points. The Tigers... | math | {
"ground_truth": "23",
"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 poles, one 30 feet high and the other 90 feet high, are 150 feet apart. Halfway between the poles, there is an additional smaller pole of 10 feet high. The lines go from the ... | math | {
"ground_truth": "22.5",
"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": "Determine how many lattice points lie on the graph of the equation $x^2-y^2=65$ in the $x,y$-plane.",
"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": "Each edge of a cube is increased by 50%. Calculate the percent increase of the surface area of the cube.",
"role": "user"
}
] | math | {
"ground_truth": "125",
"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 fair 8-sided die is rolled until a number 5 or greater appears. What is the probability that both numbers 2 and 4 appear at least once before any number from 5 to 8 is rolled?\... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a convex quadrilateral $ABCD$, sides $AB = 10$ and $CD = 15$. Diagonals $AC$ and $BD$ intersect at point $E$. If $AC = 18$ and the area of $\\triangle AED$ is twice the area o... | math | {
"ground_truth": "12",
"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": "Sienna rode her bicycle for 45 minutes at a speed of 12 mph, and then rollerbladed for 75 minutes at a speed of 8 mph. Calculate her overall average speed in miles per hour.",
... | math | {
"ground_truth": "9.5",
"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 cube has edge length 30 units. Points $P, Q,$ and $R$ are on $\\overline{AB}, \\overline{BC},$ and $\\overline{CD},$ respectively, forming the edges of the cube. It is given th... | math | {
"ground_truth": "525\\, \\text{square units}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality $|x| < 5\\pi$ and the equation $x^2 - 4x + 4 = 0$, find the number of integer solutions to this system.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the polynomial $x^2 - px + 18$ has only positive integer roots, find the average of all distinct possibilities for $p$.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = x^3 + ax^2 + (a+6)x + 1$ has both a maximum and a minimum value, find the range of values for $a$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, -3) \\cup (6, +\\infty)",
"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": "Two rectangles have integer dimensions, and both have a perimeter of 160 cm. What is the greatest possible difference between the areas of two such rectangles?",
"role": "use... | math | {
"ground_truth": "1521",
"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 segment \\( AD \\) is the bisector of the right triangle \\( ABC \\) (\\(\\angle C=90^{\\circ}\\)). A circle with radius \\(\\sqrt{15}\\) passes through points \\( A, C, D \\... | math | {
"ground_truth": "32",
"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": "Simplify $\\frac{9x^3y^2}{12x^2y^4}$ with $x=3$ and $y=2.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area of the equilateral triangle ABC is $\\frac{\\sqrt{3}}{4}$. Find the ratio of the area of the region where point P is closer to point A than to points B and C.",
"rol... | math | {
"ground_truth": "\\frac{\\sqrt{3}\\pi}{18}",
"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 right triangle $\\triangle ABC$ where $\\angle BAC = 90^\\circ$ and the lengths of sides $AB = 3$ and $AC = 4$, $M$ is the midpoint of the hypotenuse $BC$, and $D$ is a point ... | math | {
"ground_truth": "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": "Given the ellipse $C: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \\left(a > b > 0\\right)$, $A,B$ are the two endpoints of the major axis of $C$, and point $M$ is a point on $C$ sat... | math | {
"ground_truth": "1 - \\frac{\\sqrt{3}}{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": "Esteban the alchemist have $8088$ copper pieces, $6066$ bronze pieces, $4044$ silver pieces and $2022$ gold pieces. He can take two pieces of different metals and use a m... | math | {
"ground_truth": "20218",
"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": "Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. Determine the time at ... | math | {
"ground_truth": "3:30 \\text{ PM}",
"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": "Determine all pairs $(k,n)$ of non-negative integers such that the following inequality holds $\\forall x,y>0$ :\n\\[1+ \\frac{y^n}{x^k} \\geq \\frac{(1+y)^n}{(1+x)^k}.\\]",
... | math | {
"ground_truth": "(0, k)",
"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": "What is the sum of the tens digit and the units digit in the decimal representation of \\(8^{2003}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a \\heartsuit b = \\frac{3a}{b} \\cdot \\frac{b}{a}$. What is $(4 \\heartsuit (2 \\heartsuit 5)) \\heartsuit 3$?",
"role": "user"
}
] | 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": "Given an arithmetic sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first 12 terms being 60, find the minimum value of $\\left|a_{1}\\right| + \\left|a_{2}\\right| + \\cd... | math | {
"ground_truth": "60",
"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 $ABC$ be a right isosceles triangle with right angle at $A$ . Let $E$ and $F$ be points on A $B$ and $AC$ respectively such that $\\angle ECB = 30^o$ and $\\angl... | math | {
"ground_truth": "90^\\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": "Find the coefficient of $x^2$ after expansion and collecting the terms of the following expression (there are $k$ pairs of parentheses): $((... (((x - 2)^2 - 2)^2 -2)^2 -...... | math | {
"ground_truth": "\\frac{4^k - 1}{3} \\cdot 4^{k-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 $x \\in \\mathbb{R}$. If the function $f(x)$ is monotonically increasing and for any real number $x$, it satisfies $f[f(x) - e^x] = e + 1$ (where $e$ is the base of natural l... | 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": "Given $a \\gt 0$ and $a\\neq 1$, the function $f(x)=\\frac{{{a^x}-{a^{-x}}}{{a^x}+{a^{-x}}}+b$ is a monotonically decreasing function on $R$, and satisfies two of the following t... | math | {
"ground_truth": "(2\\sqrt{2}-2, \\frac{17}{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 all positive integers $n$ that have distinct positive divisors $d_1, d_2, \\dots, d_k$ , where $k>1$ , that are in arithmetic progression and $$ n=d_1+d_2+\\cdots+d_k.... | math | {
"ground_truth": "n = 6m",
"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": "Moor has $3$ different shirts, labeled $T, E,$ and $A$ . Across $5$ days, the only days Moor can wear shirt $T$ are days $2$ and $5$ . How many different sequences of... | 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": "In Example 1-7, there are 5 characters: $a, b, c, d, e$. Form a string of 6 characters with the following requirements:\n1. The 1st and 6th characters must be consonants $b, c, d... | math | {
"ground_truth": "648",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the even function $f(x)$ is monotonically decreasing in the interval $(-\\infty, 0]$, and $f(-1) = \\frac{1}{2}$, find the range of values for $x$ that satisfies $2f(2... | math | {
"ground_truth": "(0, 1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the equation given by $132_A+43_B=69_{A+B}$, where $A$ and $B$ are consecutive positive integers and represent number bases, determine the sum of the bases $A$ and $B$.",
... | math | {
"ground_truth": "13",
"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 plane passes through a vertex of the base of a regular triangular pyramid. This plane is perpendicular to the opposite lateral face and parallel to the opposite side of the bas... | math | {
"ground_truth": "2 \\arctan (\\sqrt{3} \\cdot \\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": "Mr. Deschamps has chickens and cows; the chickens have two legs each, and the cows have four. In preparation for winter, he has to make slippers for them. He has a total of 160 a... | 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": "Bananas are sold at the market at a rate of $\\$6$ per three kilograms. According to this rate, how many dollars does it cost to buy 12 kilograms of bananas?",
"role": "user"... | math | {
"ground_truth": "\\$24",
"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 \\( y = f(x) \\) which has an inverse function \\( y = f^{-1}(x) \\), find the equation of the curve obtained after rotating the graph of \\( y = f(x) \\) coun... | math | {
"ground_truth": "y = f^{-1}(-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": "Given Paul has a set of $5$ uniquely designed keychains, the Star and the Sun are not placed next to each other, calculate the total number of possible arrangements.",
"role"... | 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": "Given that a 3-inch-by-5-inch photo is to cover a 3-foot-by-5-foot poster, calculate the number of photos needed to completely cover the poster.",
"role": "user"
}
] | math | {
"ground_truth": "144",
"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": "Refer to the diagram, $P$ is any point inside the square $O A B C$ and $b$ is the minimum value of $P O + P A + P B + P C$. Find $b$.",
"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": "In an alley of width $w$, a ladder rests against two walls. At one end, say point $Q$, the ladder makes a $30^\\circ$ angle with the ground, and on the opposite wall at $R$, it m... | math | {
"ground_truth": "2h",
"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": "Among all sets of four natural numbers \\((k, l, m, n)\\) where \\(k > l > m > n\\), find the set such that the sum \\(\\frac{1}{k}+\\frac{1}{l}+\\frac{1}{m}+\\frac{1}{n}\\) is l... | math | {
"ground_truth": "(2, 3, 7, 43)",
"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": "Compute\n\\[\\begin{vmatrix} -7 & 5 \\\\ 6 & -2 \\end{vmatrix}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "-16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Out of an original group of 15 items, 11 need to be selected for approval for a new policy to take effect. What is this ratio, eleven to fifteen, rounded to the nearest tenth?",
... | math | {
"ground_truth": "0.7",
"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": "Let $b_1$ , $b_2$ , $b_3$ , $c_1$ , $c_2$ , and $c_3$ be real numbers such that for every real number $x$ , we have\n\\[\n x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 = (x^2 + b... | 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": "Let $a,b,c$ be positive real numbers such that $a+b+c=3$ . Determine, with certainty, the largest possible value of the expression $$ \\frac{a}{a^3+b^2+c}+\\frac{b}{b^3+c^2... | 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": "Nine points are evenly spaced out on a circle and connected as shown below to form a 9-pointed star by connecting every fourth point. What is the sum of the angle measurements of... | math | {
"ground_truth": "1440^\\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": "The shaded region shown consists of 15 unit squares and rests along the $x$-axis and the $y$-axis. The shaded region is rotated about the $y$-axis to form a solid. In cubic units... | math | {
"ground_truth": "54\\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": "Two kangaroos, A and B, are jumping in a specific area as shown in a diagram. Kangaroo A jumps in the sequence $A, B, C, D, E, F, G, H, I, A, B, C, \\cdots$ in a loop. Kangaroo B... | math | {
"ground_truth": "226",
"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 $\\begin{vmatrix} x & y \\\\ z & w \\end{vmatrix} = 12,$ find $\\begin{vmatrix} 3x & 3y \\\\ 3z & 3w \\end{vmatrix}.$",
"role": "user"
}
] | math | {
"ground_truth": "108",
"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 $p$ be a monic cubic polynomial such that $p(0)=1$ and such that all the zeroes of $p^\\prime (x)$ are also zeroes of $p(x)$ . Find $p$ . Note: monic means that the... | math | {
"ground_truth": "p(x) = (x + 1)^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": "Solve the equation:\n\n$$\n\\frac{1}{x}+\\frac{1}{x+2}-\\frac{1}{x+4}-\\frac{1}{x+6}-\\frac{1}{x+8}-\\frac{1}{x+10}+\\frac{1}{x+12}+\\frac{1}{x+14}=0\n$$",
"role": "user"
}... | math | {
"ground_truth": "x=-7, \\quad x=-7 \\pm \\sqrt{19 \\pm 6 \\sqrt{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": "Determine the number of distinct ordered pairs $(x,y)$, where $x$ and $y$ are positive integers, satisfying the equation $x^4y^4 - 24x^2y^2 + 35 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain new energy vehicle factory plans to produce 60 new energy vehicles per day this week. Due to the implementation of rotating rest days for workers, the number of workers... | math | {
"ground_truth": "35 \\text{ vehicles}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S_n$ and $T_n$ be the respective sums of the first $n$ terms of two arithmetic series. If $\\frac{S_n}{T_n} = \\frac{9n+5}{6n+31}$ for all $n$, find the ratio of the fifteen... | math | {
"ground_truth": "B) \\( \\frac{92}{71} \\)",
"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 clock takes 7 seconds to strike 7 times at 7 o'clock. How long does it take for the clock to strike 10 times?\nA) 9.5 seconds\nB) 10 seconds\nC) 10.5 seconds\nD) 11 seconds",
... | math | {
"ground_truth": "C) 10.5 seconds",
"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 legs of a right triangle are 6 cm and 8 cm. Find the distance from the center of the inscribed circle to the center of the circumscribed circle.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{13}",
"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 a duck found that $5-2\\sqrt{3}i$ is one of the roots of $-259 + 107x - 17x^2 + x^3$ , what is the sum of the real parts of the other two roots?\n\n*2022 CCA Math B... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function f(x) = |2x + 1| + |x - 1|.\n1. Solve the inequality f(x) ≤ 3.\n2. Let the minimum value of the function f(x) be m. If a and b are both positive numbers, and a ... | math | {
"ground_truth": "\\frac{3 + 2\\sqrt{2}}{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": "How many ways are there to put 6 distinguishable balls into 3 distinguishable boxes?",
"role": "user"
}
] | math | {
"ground_truth": "729",
"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 all ordered pairs $(a,b)$ , of natural numbers, where $1<a,b\\leq 100$ , such that $\\frac{1}{\\log_{a}{10}}+\\frac{1}{\\log_{b}{10}}$ is a natural number.",
"role": ... | math | {
"ground_truth": "(2, 5), (5, 2), (4, 25), (25, 4), (10, 10), (20, 5), (5, 20), (10, 100), (100, 10), (20, 50), (50, 20), (25, 40), (40, 25), (100, 100)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that positive real numbers $a$ and $b$ satisfy $a+b=\\frac{5}{3}$, find the minimum value of $\\frac{4}{{a+2b}}+\\frac{9}{{2a+b}}$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that Erin the ant starts at a given corner of a cube and crawls along exactly 7 edges in such a way that she visits every corner exactly once and then finds that she is una... | math | {
"ground_truth": "6",
"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": "Two circles \\(x^2 + y^2 = a^2\\) and \\(x^2 + y^2 = 9a^2\\) intersect a group of parallel lines given by \\(y = \\pm a \\sqrt{3}\\) and \\(y = \\pm 3a \\sqrt{3}\\), where \\(a >... | math | {
"ground_truth": "A) \\(\\pi a^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": "Expand $(x^2-x+1)^6$ to get $a_{11}x^{12}+a_{11}x^{11}+\\ldots+a_{2}x^2+a_{1}x+a_{0}$, find the value of $a_{12}+a_{10}+\\ldots+a_{2}+a_{0}$.",
"role": "user"
}
] | math | {
"ground_truth": "365",
"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 below shows $\\vartriangle ABC$ with point $D$ on side $\\overline{BC}$ . Three lines parallel to side $\\overline{BC}$ divide segment $\\overline{AD}$ into ... | math | {
"ground_truth": "40",
"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 \\( f(n) = \\frac{x_{1} + x_{2} + \\cdots + x_{n}}{n} \\), where \\( n \\) is a positive integer, and \\( x_{k} = (-1)^{k} \\) for \\( k = 1,2, \\cdots, n \\), determine th... | math | {
"ground_truth": "\\left\\{0, -\\frac{1}{n}\\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": "The summation $\\sum_{k=1}^{360} \\frac{1}{k \\sqrt{k+1} + (k+1)\\sqrt{k}}$ is the ratio of two relatively prime positive integers $m$ and $n$ . Find $m + n$ .",
"role"... | math | {
"ground_truth": "37",
"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": "An old clock's minute and hour hands coincide every 66 minutes of standard time. Calculate the difference between this old clock's 24 hours and 24 hours of standard time.",
"... | 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": "A number consists of 3 different digits. The sum of the 5 other numbers formed with those digits is 2003. Find the number.",
"role": "user"
}
] | math | {
"ground_truth": "345",
"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 400-meter race, Sunny finishes 50 meters ahead of Windy. In their next competition, they participate in a new 500-meter race. Due to a change in the weather, the wind now as... | math | {
"ground_truth": "106.25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of \\[\\dfrac{3+6+9}{2+4+8} - \\dfrac{2+4+8}{3+6+9}?\\]\nA) $\\frac{81}{63}$\nB) $\\frac{49}{63}$\nC) $\\frac{32}{63}$\nD) $\\frac{23}{63}$\nE) $\\frac{1}{3}$",... | math | {
"ground_truth": "\\frac{32}{63}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.