data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a, b \\in \\mathbb{R}$, and $\\frac{1+i}{1-i} = a+bi$ (where $i$ is the imaginary unit), then the value of $b$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point $F$ is taken on the extension of side $BC$ of parallelogram $ABCD$. $AF$ intersects diagonal $BD$ at $E$ and side $CD$ at $G$. If $EF = 40$ cm and $GF = 30$ cm, determine t... | math | {
"ground_truth": "20\\text{ cm}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $f(x)$ is an even function defined on $\\mathbb{R}$, and $g(x) = f(x-1)$ is an odd function also defined on $\\mathbb{R}$, find the value of $f(2009) + f(2011)$.",
... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least positive integer \\( N > 1 \\) satisfying the following two properties:\n- There exists a positive integer \\( a \\) such that \\( N = a(2a - 1) \\).\n- The sum \\... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two children take turns writing a $k$-digit number: the first digit is written by the first child, the second digit by the second child, the third digit again by the first child,... | math | {
"ground_truth": "\\text{No, the second child cannot always ensure the number is divisible by 9.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lines with equation $ax+by=c$ such that $a, b, c$ form an arithmetic progression with a common difference $3d$ pass through a common point. Find the coordinates of that point.",
... | math | {
"ground_truth": "(-2, 2)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alberto, Bernardo, and Carlos are collectively listening to three different songs. Each is simultaneously listening to exactly two songs, and each song is being listened to by ex... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a revamped art design, the smallest circle has a radius of 3 inches, with each successive circle's radius increasing by 3 inches. The pattern of black and white circles has be... | math | {
"ground_truth": "C) 50\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the maximum number of possible points of intersection of a circle and a quadrilateral?",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(D) }8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P$ be the incenter of triangle $ABC$. Let $G_1$, $G_2$, and $G_3$ be the centroids of triangles $PBC$, $PCA$, and $PAB$, respectively. If the area of triangle $ABC$ is 36, t... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We have eight light bulbs, placed on the eight lattice points (points with integer coordinates) in space that are $\\sqrt{3}$ units away from the origin. Each light bulb can ei... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What are all values of $x$ such that for every $y > 0$, the inequality $$\\frac{4(x^2y^2+xy^3+4y^2+4xy)}{x+y} > 3x^2y + y$$ is satisfied? Express your answer in interval notation... | math | {
"ground_truth": "(1, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $A$ and $B$ are two points on the hyperbola ${x}^{2}-\\frac{{y}^{2}}{9}=1$, and the midpoint of the line segment $AB$ has coordinates $(-1,-4)$, then the slope of the ... | math | {
"ground_truth": "\\frac{9}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest possible value of $x$ for the equation $$\\left(\\frac{4x-16}{3x-4}\\right)^2+\\left(\\frac{4x-16}{3x-4}\\right)=6?$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{28}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n>1$ be an integer and let $f_1$ , $f_2$ , ..., $f_{n!}$ be the $n!$ permutations of $1$ , $2$ , ..., $n$ . (Each $f_i$ is a bijective function from $\\{1,2,..... | math | {
"ground_truth": "\\frac{n^2 - 1}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Natural numbers \\( a, b, c \\) are chosen such that \\( a < b < c \\). It is also known that the system of equations \\( 2x + y = 2033 \\) and \\( y = |x-a| + |x-b| + |x-c| \\) ... | math | {
"ground_truth": "1017",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\left(\\frac{2}{3}\\right)\\left(\\frac{3}{4}\\right)\\left(\\frac{4}{5}\\right)\\left(\\frac{5}{6}\\right)\\left(\\frac{6}{7}\\right)\\left(\\frac{7}{8}... | math | {
"ground_truth": "\\frac{-7}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which values of \\( n \\) is the polynomial \\( (x+1)^{n} + x^{n} + 1 \\) divisible by:\na) \\( x^{2} + x + 1 \\);\nb) \\( (x^{2} + x + 1)^{2} \\);\nc) \\( (x^{2} + x + 1)^{3... | math | {
"ground_truth": "\\begin{aligned}\n&\\text{a) } n = 6k \\pm 1; \\\\\n&\\text{b) } n = 6k - 2; \\\\\n&\\text{c) }Not possible;\n\\end{aligned}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve in integers: \\(6x^2 + 5xy + y^2 = 6x + 2y + 7\\). Specify the answer for which the value \\(|x| + |y|\\) is the largest. Write the answer in the form \\((x; y)\\).",
"... | math | {
"ground_truth": "(-8 ; 25)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ be a real number such that $x^2 + 6x = 12$. Determine the value of $x^5 + 72x$.",
"role": "user"
}
] | math | {
"ground_truth": "2808x - 4320",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest value of $M$ for which for any choice of positive integer $n$ and positive real numbers $x_1<x_2<\\ldots<x_n \\le 2023$ the inequality $$ \\sum_{1\\... | math | {
"ground_truth": "4044",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the roots of $(x^2 - 5x + 6)(x - 3)(x + 1) = 0$.\nA) 2 and 3\nB) -1, 2, and 3\nC) 3\nD) 2",
"role": "user"
}
] | math | {
"ground_truth": "B) -1, 2, and 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $(3x + 25) - (2x - 5)$.",
"role": "user"
}
] | math | {
"ground_truth": "x + 30",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sides $AB,~ BC, ~CD$ and $DA$, respectively, of convex quadrilateral $ABCD$ are extended past $B,~ C ,~ D$ and $A$ to points $B',~C',~ D'$ and $A'$. Also, $AB = BB'/1.5 = 5,~ BC ... | math | {
"ground_truth": "C) 140",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of the squares of the coefficients of the expanded form of $3(x^4 + 2x^3 + 5x^2 + x + 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "315",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S=\\{(i,j) \\vert i,j=1,2,\\ldots ,100\\}$ be a set consisting of points on the coordinate plane. Each element of $S$ is colored one of four given colors. A subset $T$ ... | math | {
"ground_truth": "150,000",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a$ and $b$ are positive numbers such that \\( a^b = b^a \\) and \\( b=4a \\), find the value of \\( a \\).\nA) \\( \\sqrt[3]{9} \\)\nB) \\( \\sqrt[3]{4} \\)\nC) \\( \\sqrt[3]... | math | {
"ground_truth": "B) \\( \\sqrt[3]{4} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice’s age in years is twice Eve’s age in years. In $10$ years, Eve will be as old as Alice is now. Compute Alice’s age in years now.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the maximum value of the expression $-3r^2 + 36r - 9$ for real $r$?",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $n$ is a [positive integer](https://artofproblemsolving.com/wiki/index.php/Positive_integer) and $d$ is a single [digit](https://artofproblemsolving.com/wiki/index.php/Di... | math | {
"ground_truth": "750",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive factors of 60 are also multiples of 5 but not multiples of 3?\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"role": "user"
}
] | math | {
"ground_truth": "B) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the probability that A can solve the problem is $P\\_1$ and the probability that B can solve the problem is $P\\_2$, calculate the probability that at least one of the... | math | {
"ground_truth": "1-(1-P\\_1)(1-P\\_2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$ , $AB = AC$ . Its circumcircle, $\\Gamma$ , has a radius of 2. Circle $\\Omega$ has a radius of 1 and is tangent to $\\Gamma$ , $\\overline{AB}$ , and ... | math | {
"ground_truth": "595",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the minimum value of the expression $x^2 + y^2 - 8x + 6y + 25$ for real $x$ and $y$?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The value of $\\sqrt{102}$ is between two consecutive positive integers. What is the product of these two integers?",
"role": "user"
}
] | math | {
"ground_truth": "110",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1$ $(a > b > 0)$, where $M$ and $N$ are the left and right vertices of the ellipse, and $P$ is any point on the ell... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\\\(f(x)=a(x-5)^2+6\\ln x\\\\), where \\\\(a\\in\\mathbb{R}\\\\), the equation of the tangent line to the curve \\\\(y=f(x)\\\\) at the point \\\\((1,f(1))\\\\) is \\\\(2x-y... | math | {
"ground_truth": "2+6\\ln 3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be an equilateral triangle. $N$ is a point on the side $AC$ such that $\\vec{AC} = 7\\vec{AN}$ , $M$ is a point on the side $AB$ such that $MN$ is paral... | math | {
"ground_truth": "\\frac{1}{49}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each positive integer $n > 1$, let $P(n)$ denote the greatest prime factor of $n$. For how many positive integers $n$ is it true that both $P(n) = \\sqrt{n}$ and $P(n+72) = \... | math | {
"ground_truth": "\\textbf{(B) } 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Marcy has 15 coins, each of which is a 10-cent coin or a 25-cent coin. There are exactly 20 different values that can be obtained as combinations of one or more of her coins. How... | math | {
"ground_truth": "C) 7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define a sequence $(c_n)$ satisfying $c_0=1$ and for $n \\geq 0$, the recurrence relation $c_{n+1} = \\frac{5}{4}c_n + \\frac{7}{4}\\sqrt{4^n - c_n^2}$. Calculate $c_4$.",
"r... | math | {
"ground_truth": "\\frac{233}{512}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the lateral surface of a cylinder unfolds into a square, then the ratio of the height of the cylinder to the radius of the base circle is ____.",
"role": "user"
}
] | math | {
"ground_truth": "2\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer $n > 1$ is juicy if its divisors $d_1 < d_2 < \\dots < d_k$ satisfy $d_i - d_{i-1} \\mid n$ for all $2 \\leq i \\leq k$ . Find all squarefree juicy inte... | math | {
"ground_truth": "2, 6, 42, 1806",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Hannah has borrowed $200$ pearls from Irene at an $8\\%$ simple daily interest. Meanwhile, Julia has borrowed $300$ pearls from Kian at a $6\\%$ simple daily interest. In how man... | math | {
"ground_truth": "\\text{Julia: } 16.\\overline{6} \\text{ days}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $r$ and $s$ be the solutions to the equation $3x^2 - 4x - 7 = 0$. Compute the value of $(3r^3 - 3s^3)(r - s)^{-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{37}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given natural number n. Suppose that $N$ is the maximum number of elephants that can be placed on a chessboard measuring $2 \\times n$ so that no two elephants are mutually ... | math | {
"ground_truth": "2^{2015}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find a general formula, $a_n$, for the sequence 2, 22, 222, 2222, ...",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2(10^{n}-1)}{9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), side \\( AB = 13 \\), side \\( BC = 14 \\), and side \\( CA = 15 \\). An altitude \\( \\overline{AH} \\) is drawn from \\( A \\) to \\( BC \\)... | math | {
"ground_truth": "\\frac{8\\sqrt{12}}{21}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. What is the value of \\(\\frac{2}{5} + \\frac{2}{50} + \\frac{2}{500}\\)?\nA) 0.111\nB) 0.222\nC) 0.333\nD) 0.444\nE) 0.555",
"role": "user"
}
] | math | {
"ground_truth": "0.444 \\text{ (Option D)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two positive numbers, let x be the larger number and y be the smaller number. Express the sum of the two numbers and their difference as equations and find their ratio.",
... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $3x^3-9x^2+kx-12$ is divisible by $x-3$, determine the polynomial that it is also divisible by.",
"role": "user"
}
] | math | {
"ground_truth": "3x^2 + 4",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A boy and his father are standing on the seashore. If the boy stands on tiptoe, his eyes will be at a height of 1 meter above the sea surface, and if he sits on his father's shou... | math | {
"ground_truth": "1.4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive divisors of $180$ are not divisible by 3?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "I was planning to work 25 hours a week for 15 weeks this summer to earn $\\$4500$ to fund my education. Unfortunately, I was unable to work for the first three weeks of summer. H... | math | {
"ground_truth": "31.25",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the three numbers is what?",
"role": "user"
}
] | math | {
"ground_truth": "48",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the volume, in cubic inches, of a rectangular box, whose faces have areas of $36$ square inches, $18$ square inches, and $8$ square inches?",
"role": "user"
}
] | math | {
"ground_truth": "102",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the following expression:\n$$ \\frac {\\sin 47^{\\circ} -\\sin 17^{\\circ} \\cos 30^{\\circ}}{\\cos 17^{\\circ}} $$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right rectangular prism has integer side lengths $a$ , $b$ , and $c$ . If $\\text{lcm}(a,b)=72$ , $\\text{lcm}(a,c)=24$ , and $\\text{lcm}(b,c)=18$ , what is the sum of t... | math | {
"ground_truth": "3024",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Call a rational number *short* if it has finitely many digits in its decimal expansion. For a positive integer $m$ , we say that a positive integer $t$ is $m-$ *tastic* if th... | math | {
"ground_truth": "807",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the continuous function $ f(x)$ such that $ xf(x)\\minus{}\\int_0^x f(t)\\ dt\\equal{}x\\plus{}\\ln (\\sqrt{x^2\\plus{}1}\\minus{}x)$ with $ f(0)\\equal{}\\ln 2$ .",
... | math | {
"ground_truth": "f(x) = \\ln (1 + \\sqrt{x^2 + 1})",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $y = f(x)$ is the inverse function of $y = \\log_{\\frac{1}{2}}x$, find $f(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "f(x) = \\left( \\frac{1}{2} \\right)^x",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following system of equations in natural numbers:\n\n$$\n\\begin{aligned}\na^{3}-b^{3}-c^{3} & =3 a b c \\\\\na^{2} & =2(b+c)\n\\end{aligned}\n$$",
"role": "user"
... | math | {
"ground_truth": "(a, b, c) = (2, 1, 1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a class, 18 students have a red notebook, 15 students have a blue bag, and 7 students have both. How many students are there (at least) in the class?",
"role": "user"
}
... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three variables, $x$, $y$, and $z$, are in the ratio $4:5:6$. Additionally, we know that $y = 15b - 5$. Determine the value of $b$ given that the sum of $x$, $y$, and $z$ is equa... | math | {
"ground_truth": "\\frac{7}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the projection of the vector $\\begin{pmatrix} 5 \\\\ 3 \\end{pmatrix}$ onto the vector $\\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} 5.4 \\\\ 1.8 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $A$ and $B$ are positive numbers such that $A = kB$ where $k > 1$. Given that $A$ is $x\\%$ greater than $B$, express $k$ in terms of $x$.\nA) $k = 1 + \\frac{x}{200}$ \n... | math | {
"ground_truth": "k = 1 + \\frac{x}{100}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ ABC$ is inscript in a circumference $ \\Gamma$ . A chord $ MN\\equal{}1$ of $ \\Gamma$ intersects the sides $ AB$ and $ AC$ at $ X$ and $ Y$ respectivel... | math | {
"ground_truth": "\\frac{7}{45}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Concentric circles $\\Omega_1$ and $\\Omega_2$ with radii $1$ and $100$ , respectively, are drawn with center $O$ . Points $A$ and $B$ are chosen independently at ran... | math | {
"ground_truth": "10004",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nikita and Egor run along a circular track, starting from the same point in opposite directions. It is known that Nikita completes a lap 12 seconds faster than Egor, but still ta... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It is known that the number \\( \\cos 6^\\circ \\) is a root of the equation \\( 32 t^5 - 40 t^3 + 10 t - \\sqrt{3} = 0 \\). Find the other four roots of this equation. (The answ... | math | {
"ground_truth": "\\cos 66^\\circ, \\cos 78^\\circ, \\cos 138^\\circ, \\cos 150^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of the following series: $$\\frac{1}{2^{1}}+\\frac{1}{2^{2}}+\\frac{1}{2^{3}}+\\frac{1}{2^{4}}+\\frac{1}{2^{5}}+\\frac{1}{2^{6}}.$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{63}{64}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In rectangle $EFGH$, we have $E=(-4,3)$, $F=(996,43)$, and $H=(-2,y)$ for some integer $y$. What is the area of rectangle $EFGH$?\nA) 50000\nB) 50050\nC) 50100\nD) 50200",
"r... | math | {
"ground_truth": "50050 \\text{ (B)}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An arithmetic sequence consists of $150$ numbers that are each at least $20$ and at most $120$. The sum of the numbers is $12,000$. Let $L$ be the least possible value of the $75... | math | {
"ground_truth": "\\frac{6000}{149}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ ABCD$ be a regular tetrahedron, and let $ O$ be the centroid of triangle $ BCD$ . Consider the point $ P$ on $ AO$ such that $ P$ minimizes $ PA \\plus{} 2(PB \... | math | {
"ground_truth": "\\sin \\angle PBO = \\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given four numbers: $\\left(-1\\right)^{2023}$, $|-2|$, $-\\left(-1.2\\right)$, $-3^{2}$, calculate the number of negative numbers among them.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The value of $x$ that satisfies $\\log_{2^x} 3^{20} = \\log_{2^{x+3}} 3^{2020}$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $... | math | {
"ground_truth": "103",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let's consider a three-digit number, whose digits are not necessarily non-zero and distinct; the number is formed as \\(100a + 10b + c\\) where \\(a, b, c\\) are integers such th... | math | {
"ground_truth": "The minimum value of the quotient, given the new setup, is \\( \\textbf{(E) }50.5 \\).",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest common factor of 450 and 210?",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two cars are driving on a highway at a speed of 80 km/h with an interval of 10 meters between them. Upon reaching a speed limit sign, the cars instantly reduce their speed to 60 ... | math | {
"ground_truth": "7.5 \\, \\text{m}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\[f(x) =\n\\begin{cases}\nx/2 & \\quad \\text{if } x \\text{ is even}, \\\\\n5x+1 & \\quad \\text{if } x \\text{ is odd}.\n\\end{cases}\n\\]\nWhat is $f(f(f(f(f(f(7))))))$?"... | math | {
"ground_truth": "116",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $15$ and $9$ are lengths of two medians of a triangle, what is the maximum possible area of the triangle to the nearest integer ?",
"role": "user"
}
] | math | {
"ground_truth": "86",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Tina is 3 years older than Alex and Max is 3 years old, and Tina's age is a perfect square multiple of Max's age for the second time today, calculate the sum of the di... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Express $543210_{7} - 43210_{8}$ in base 10.",
"role": "user"
}
] | math | {
"ground_truth": "76717",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( ABC \\), the median \\( BK \\) is half the length of side \\( AB \\) and forms an angle of \\( 32^\\circ \\) with it. Find angle \\( ABC \\).",
"role": "user"... | math | {
"ground_truth": "106^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\sin{347^{\\circ}}\\cos{148^{\\circ}} + \\sin{77^{\\circ}}\\cos{58^{\\circ}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers $n$ such that the sum of the three largest divisors of $n$ is $1457$ .",
"role": "user"
}
] | math | {
"ground_truth": "987, 1023, 1085, 1175",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\{a_{n}\\}$ with a non-zero common difference, let $S_{n}$ denote the sum of its first $n$ terms, where $n \\in \\mathbb{N}^*$. If $S_{3} = a_{4} +... | math | {
"ground_truth": "\\frac{n}{2n + 1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ represent the smallest integer that satisfies the following conditions:\n- $\\frac{n}{2}$ is a perfect square.\n- $\\frac{n}{3}$ is a perfect cube.\n- $\\frac{n}{5}$ is a... | math | {
"ground_truth": "\\sigma(2^{42} \\cdot 3^{42} \\cdot 5^{42})",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Someone buys two estates; one yields 1560 frt, and the other, which was 7000 frt cheaper and yields $\\frac{1}{2} \\%$ less, produces 515 frt less annually. How much did the two ... | math | {
"ground_truth": "\\text{One estate costs 26000 frt with a yield of 6\\%, and the other costs 84000 frt with a yield of } 1 \\frac{6}{7} \\text{\\%.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The pressure $(P)$ of wind on a sail varies jointly as the area $(A)$ of the sail and the square of the velocity $(V)$ of the wind. Initially, the pressure is 4 pounds on 2 squar... | math | {
"ground_truth": "20\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the sequence $(a_n)$ as follows: $a_0=a_1=1$ and for $k\\ge 2$ , $a_k=a_{k-1}+a_{k-2}+1$ .\nDetermine how many integers between $1$ and $2004$ inclusive can be e... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the maximum value of the function $f\\left( x \\right)=\\frac{{{\\left( x+1 \\right)}^{2}}+\\sin x}{{{x}^{2}}+1}$ be $M$, and the minimum value be $m$. Find the value of $M+m... | math | {
"ground_truth": "M+m=2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a_n\\}$ with the sum of the first $n$ terms denoted as $S_n$, if $a_1=2$ and $\\frac{S_n}{n}=a_{n+1}-(n+1)$ $(n\\in\\mathbb{N}^*)$, then the maximum positive... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$ , points $E$ and $F$ lie on $\\overline{AC}, \\overline{AB}$ , respectively. Denote by $P$ the intersection of $\\overline{BE}$ and $\\overline{CF}... | math | {
"ground_truth": "84",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the matrix $\\mathbf{N}$ if $\\mathbf{N} \\mathbf{i} = \\begin{pmatrix} 1 \\\\ 4 \\\\ -3 \\end{pmatrix}$, $\\mathbf{N} \\mathbf{j} = \\begin{pmatrix} -2 \\\\ 6 \\\\ 5 \\end{... | math | {
"ground_truth": "\\mathbf{N} = \\begin{pmatrix} 1 & -2 & 0 \\\\ 4 & 6 & 1 \\\\ -3 & 5 & 2 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are exactly 120 ways to color five cells in a \\( 5 \\times 5 \\) grid such that each row and each column contains exactly one colored cell.\n\nThere are exactly 96 ways to... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A jacket costs as much as trousers and a vest. But a jacket and two pairs of trousers would cost 175 dollars, and trousers and two vests would cost 100 dollars. How much does the... | math | {
"ground_truth": "150 \\text{ dollars}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)$ defined as follows:\n$$\nf(x) = \\begin{cases} \n\\log_{2}(8-x) & \\text{if } x \\leq 0 \\\\\nf(x-1) & \\text{if } x > 0\n\\end{cases}\n$$\nCalculate th... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a $10 \\times 15$ rectangle that is cut into two congruent pentagons, which are then reassembled to form a larger rectangle. If $y$ is one-third the length of the longer... | math | {
"ground_truth": "5\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Kara meant to multiply a number by $8$ but accidentally divined by $8$. Afterwards, instead of doubling the result, she squared the value. As a result of these mishaps, Kara ende... | math | {
"ground_truth": "D) 896",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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