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": "For which maximal $N$ there exists an $N$ -digit number with the following property: among any sequence of its consecutive decimal digits some digit is present once only?\n\t\... | math | {
"ground_truth": "1023",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a set containing 8 elements, let $S$ be the total number of subsets of this set, and let $T$ be the number of subsets consisting of 3 elements. The value of $\\frac{T}{S}$ ... | math | {
"ground_truth": "\\frac{7}{32}",
"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 functions $f: R \\to R$ and $g:R \\to R$ such that $f(x-f(y))=xf(y)-yf(x)+g(x)$ for all real numbers $x,y$ .\n\nI.Voronovich",
"role": "user"
}
] | math | {
"ground_truth": "f(x) = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In coordinate space, points are given as $P = (3, -9, 6),$ $Q = (13, -19, 11),$ $R = (1, 4, -7),$ and $S = (3, -6, 9).$ Find the intersection point of lines $PQ$ and $RS.$",
... | math | {
"ground_truth": "\\left( -\\frac{19}{3}, \\frac{10}{3}, \\frac{4}{3} \\right)",
"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": "At Lincoln High School, the number of boys and girls is equal. $\\frac{5}{6}$ of the boys and $\\frac{2}{3}$ of the girls went on a field trip. What fraction of the students on t... | math | {
"ground_truth": "\\frac{4}{9}",
"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 all reals $\\lambda$ for which there is a nonzero polynomial $P$ with real coefficients such that $$ \\frac{P(1)+P(3)+P(5)+\\ldots+P(2n-1)}n=\\lambda P(n) $$ for all p... | math | {
"ground_truth": "\\lambda = \\frac{2^k}{k+1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer $N$ with four digits in its base ten representation is chosen at random, \nwith each four-digit number having an equal chance of being chosen. The probability ... | math | {
"ground_truth": "\\textbf{(A)}\\ \\frac{1}{4500}",
"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": "$ABCDE$ is inscribed in a circle with $AB = BC = CD = DE = 6$ and $AE = 2.$ Compute $(1 - \\cos \\angle C)(1 - \\cos \\angle ACE).$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle is tangent to one leg of an isosceles right triangle and passes through the vertex of the opposite acute angle. Find the radius of the circle if its center is on the hyp... | math | {
"ground_truth": "a(2 - \\sqrt{2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ryan borrows \\$8,000 to pay for his motorcycle. The annual interest rate on the loan is \\(10\\%\\). He makes no payments for 5 years, but has to pay back all the money he owes ... | math | {
"ground_truth": "\\$147.04",
"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 value of $2m+3b$ for the line that passes through the points $(-1,\\frac{1}{2})$ and $(2, -\\frac{3}{2})$ when it is expressed in the form $y = mx + b$.",
"role... | math | {
"ground_truth": "-\\frac{11}{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": "Let $\\{b_n\\}$ be a sequence of positive numbers defined by $b_1 = b$, $b_2 = kb$, and $b_{n+2} = b_n b_{n+1}$ for all positive integers $n$. Determine under what conditions the... | math | {
"ground_truth": "\\text{(A) }b = 1 \\text{ and } k = 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": "An 8 x 8 board is divided into unit squares. Each unit square is painted red or blue. Find the number of ways of doing this so that each 2 x 2 square (of four unit squares) has t... | math | {
"ground_truth": "1022",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sequence $\\{a\\_n\\}$ is an arithmetic sequence with first term $1$ and common difference $2$, and the sequence $\\{b\\_n\\}$ is a geometric sequence with first t... | math | {
"ground_truth": "17411",
"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": "Compose the equations of the tangent and normal lines to the curve at the point corresponding to the parameter value \\( t = t_{0} \\).\n\n\\[\n\\left\\{\n\\begin{array}{l}\nx = ... | math | {
"ground_truth": "y = -3x",
"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 $n>5$ be an integer. There are $n$ points in the plane, no three of them collinear. Each day, Tom erases one of the points, until there are three points left. On the $i$... | math | {
"ground_truth": "2n - 8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence \\\\(\\{a_n\\}\\) with the sum of its first \\\\(n\\\\) terms denoted as \\\\(S_n\\\\), and \\\\(S_n = n^2 - 14n\\\\),\n\n\\\\((1)\\\\) Find the general formula ... | math | {
"ground_truth": "\\dfrac{682}{351}",
"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 $S$ be the set of all ordered triples $(p,q,r)$ of prime numbers for which at least one rational number $x$ satisfies $px^2+qx+r=0.$ Which primes appear in seven or m... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers a, b such that $ a^{n}\\plus{} b^{n} \\equal{} c^{n\\plus{}1}$ where c and n are naturals.",
"role": "user"
}
] | math | {
"ground_truth": "a = b = c = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice, Carol, and Bob repeatedly take turns tossing a die. Alice begins, then Carol follows Alice, and Bob follows Carol. Find the probability that Carol will be the first one to... | math | {
"ground_truth": "\\textbf{(C) } \\frac{30}{91}",
"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": "How many sets of three consecutive positive integers have a sum of 36?\nA) 0 \nB) 1 \nC) 2 \nD) 3 \nE) 4",
"role": "user"
}
] | 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": "In triangle $ABC$, $AB = 8$, $BC = 10$, and $CA = 12$. Let $D$ be a point in the interior of $\\overline{BC}$. Let points $I_B$ and $I_C$ denote the incenters of triangles $ABD$ ... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $981 + 983 + 985 + \\ldots + 999 = 5100 - M$, calculate the value of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "4800",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "a) Given that the decimal representation of \\(5^{2018}\\) has 1411 digits and begins with 3 (the leftmost non-zero digit is 3), for how many integers \\(1 \\leq n \\leq 2017\\) ... | math | {
"ground_truth": "2 \\text{ and } 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": "Given the function $f(x)=x^{3}-ax^{2}-x+6$, determine the range of the real number $a$ if the function is monotonically decreasing in the interval $(0,1)$.",
"role": "user"
... | math | {
"ground_truth": "a \\geqslant 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": "Caroline can make fifteen lassis from three mangoes. How many lassis can she make out of eighteen mangoes?",
"role": "user"
}
] | math | {
"ground_truth": "90",
"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": "John wishes to enclose a rectangular garden such that the length of the garden is 12 ft more than its width. He needs the area of the garden to be at least 120 sq. ft in order to... | 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": "If $x$ is such that $\\frac{1}{x}<3$ and $\\frac{1}{x}>-4$, and additionally $x \\neq 0$, find the range of possible values for $x$.\nA) $x \\in \\left(-\\infty, -\\frac{1}{4}\\r... | math | {
"ground_truth": "x \\in \\left(\\frac{1}{3}, \\infty\\right) \\cup \\left(-\\infty, -\\frac{1}{4}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an office at various times during the day, the boss gives the secretary a letter to type, each time putting the letter on top of the pile in the secretary's in-box. When ther... | math | {
"ground_truth": "256",
"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 $n, k \\geq 3$ be integers, and let $S$ be a circle. Let $n$ blue points and $k$ red points be\nchosen uniformly and independently at random on the circle $S$ . Deno... | math | {
"ground_truth": "\\frac{2nk}{n+k-1} - \\frac{2k!n!}{(n+k-1)!}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the rational function \\(\\frac{3x^7 + 4x^3 - 2x - 5}{p(x)}\\). Determine the smallest possible degree of \\(p(x)\\) such that the graph of the function has a horizontal... | math | {
"ground_truth": "7",
"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 there are $24$ students and $2$ pet guinea pigs in each fourth-grade classroom at Maple Grove Elementary, determine the total difference in the number of students and ... | math | {
"ground_truth": "110",
"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 all positive integers $k > 1$ for which there exists a positive integer $n$ such that $\\tbinom{n}{k}$ is divisible by $n$ , and $\\tbinom{n}{m}$ is not divisible b... | math | {
"ground_truth": "k \\ge 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the cartesian coordinate plane xOy, the focus of the parabola y^2 = 2px (p > 0) lies on the line 2x + y - 2 = 0. Find the value of p.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find all injective functions $f: \\mathbb R \\rightarrow \\mathbb R$ such that for every real number $x$ and every positive integer $n$ , $$ \\left|\\sum_{i=1}^n i\\left(f... | math | {
"ground_truth": "f(x) = x + 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": "Sasha was descending the stairs from his apartment to his friend Kolya who lives on the first floor. When he had descended a few floors, it turned out that he had covered one-thi... | math | {
"ground_truth": "7",
"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": "Find to 0.1-degree accuracy the angles of an isosceles triangle in which one angle bisector is twice as long as another by using a systematic trial-and-error method. Why can't we... | math | {
"ground_truth": "77.0^\\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": "Given the function $f(x)=2\\sin (ωx+φ)(ω > 0,|φ| < π)$ passes through the points $(\\frac{π}{12},-2)$ and $(\\frac{7π}{12},2)$, and is monotonic in the interval $(\\frac{π}{12}, ... | math | {
"ground_truth": "-10\\sqrt{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": "Tingting's solution to \"Simplify: $\\sqrt{8} \\times \\sqrt{18}$\" is as follows: \nSolution: Original expression $=2\\sqrt{2} \\times 3\\sqrt{2}=(2 \\times 3) \\times (\\sqrt{... | math | {
"ground_truth": "12",
"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": "Evaluate the following expression:\n\\[\\binom{50}{0} - 2\\binom{50}{1} + 3\\binom{50}{2} - \\dots + (-1)^{50}51\\binom{50}{50}\\]",
"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": "Given that $(a,b,c,d)$ is an ordered quadruple of not necessarily distinct integers, each one of them in the set ${0,1,2,3}$, determine the number of such quadruples for which $a... | math | {
"ground_truth": "96",
"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": "In the Cartesian coordinate system xOy, curve $C_1: x^2+y^2=1$ is given. Taking the origin O of the Cartesian coordinate system xOy as the pole and the positive half-axis of x as... | math | {
"ground_truth": "2\\sqrt{5}",
"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": "Observe the following expressions: $\\frac{2}{1} + 2 = 3\\frac{1}{1}$, $\\frac{3}{2} + 3 = 4\\frac{1}{2}$, $\\frac{4}{3} + 4 = 5\\frac{1}{3}$, $\\frac{5}{4} + 5 = 6\\frac{1}{4}$,... | math | {
"ground_truth": "\\frac{n+1}{n} + (n+1) = (n+2) + \\frac{1}{n}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers $a$ , $b$ and $c$ which satisfy the equation $$ a^2+b^2+1=c!. $$ *Proposed by Nikola Velov*",
"role": "user"
}
] | math | {
"ground_truth": "(a, b, c) = (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": "Find the number of natural numbers that do not exceed 2016 and are coprime with it. Recall that two integers are called coprime if they have no common natural divisors other than... | math | {
"ground_truth": "576",
"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": "There is a game of picking colored eggs at a market. In an opaque box, there are 9 eggs of the same size and shape, with 3 yellow, 3 red, and 3 blue eggs. The rules of the game a... | math | {
"ground_truth": "-\\frac{45}{14}",
"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 a rectangle $ABCD$ , let $M$ and $N$ be the midpoints of sides $BC$ and $CD$ , respectively, such that $AM$ is perpendicular to $MN$ . Given that the length of $AN... | math | {
"ground_truth": "720006",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the matrix product\n\\[\n\\begin{pmatrix} \n0 & d & -c \\\\ \n-d & 0 & b \\\\ \nc & -b & 0 \n\\end{pmatrix} \n\\begin{pmatrix} \nd^2 & dc & db \\\\ \ndc & c^2 & cb \\\\ \... | math | {
"ground_truth": "\\begin{pmatrix} 0 & 0 & 0 \\\\ 0 & 0 & 0 \\\\ 0 & 0 & 0 \\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 that $P(x, y, z)$ is a homogeneous degree 4 polynomial in three variables such that $P(a, b, c) = P(b, c, a)$ and $P(a, a, b) = 0$ for all real $a$ , $b$ , and $... | math | {
"ground_truth": "56",
"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": "How many ordered triples \\((x, y, z)\\) of positive integers satisfy \\(\\text{lcm}(x,y) = 180\\), \\(\\text{lcm}(x,z) = 1000\\), and \\(\\text{lcm}(y,z) = 450\\)?\n**A)** 6\n**... | math | {
"ground_truth": "The correct answer is **D) 9**.",
"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": "**Q14.** Let be given a trinagle $ABC$ with $\\angle A=90^o$ and the bisectrices of angles $B$ and $C$ meet at $I$ . Suppose that $IH$ is perpendicular to $BC$ ( $H$... | math | {
"ground_truth": "40",
"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 sum of the interior angles of a convex polygon is 1958°, determine the degree measure of the omitted angle.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"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": "Compute $(\\cos 205^\\circ + i \\sin 205^\\circ)^{72}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2} - i\\frac{\\sqrt{3}}{2}",
"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": "Three machines perform certain work. If the first machine works alone, it will finish the work $a$ days later than if all machines worked together. If the second machine works al... | math | {
"ground_truth": "a + \\frac{-(a + b) + \\sqrt{(a - b)^2 + 4 a b c^2}}{2 (c + 1)}, \\quad b + \\frac{-(a + b) + \\sqrt{(a - b)^2 + 4 a b c^2}}{2(c + 1)}, \\quad \\frac{-c (a + b) + c \\sqrt{(a - b)^2 + 4 a b c^2}}{2(c + 1)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\frac{20 \\times 2 + 10}{5 + 3 - 1}$, calculate the result.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{50}{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": "Two distinct 2-digit prime numbers $p,q$ can be written one after the other in 2 different ways to form two 4-digit numbers. For example, 11 and 13 yield 1113 and 1311. If the ... | math | {
"ground_truth": "\\{13, 53\\}, \\{19, 47\\}, \\{23, 43\\}, \\{29, 37\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the function $f(x)=a⋅3^{x}+\\frac{1}{3^{x}}$ is an even function, then the real number $a=$____.",
"role": "user"
}
] | math | {
"ground_truth": "a=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 $S_n$ be number of ordered sets of natural numbers $(a_1;a_2;....;a_n)$ for which $\\frac{1}{a_1}+\\frac{1}{a_2}+....+\\frac{1}{a_n}=1$ . Determine \n1) $S_{10} mod(2)$ ... | math | {
"ground_truth": "S_{10} \\mod 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": "Let $a,$ $b,$ and $c$ be the roots of the equation $x^3 - 15x^2 + 13x - 8 = 0.$ Find the value of $\\frac{a}{\\frac{1}{a}+bc} + \\frac{b}{\\frac{1}{b}+ca} + \\frac{c}{\\frac{1}{c... | math | {
"ground_truth": "\\frac{199}{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": "Elective 4-5: Special Topics on Inequalities\n\nLet the function \\\\(f(x) = |x - a| + x\\\\), where \\\\(a > 0\\\\),\n\n\\\\((1)\\\\) When \\\\(a = 1\\\\), find the solution set... | math | {
"ground_truth": "6",
"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 an ellipse $C_1: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ ($a > b > 0$) and a hyperbola $C_2: \\frac{x^2}{2} - \\frac{y^2}{8} = 1$ share a common focus. One of the asymptot... | math | {
"ground_truth": "11",
"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 shortest distance in miles the hiker must travel to refill his water bottle at the river and then return to the shelter.",
"role": "user"
}
] | math | {
"ground_truth": "3 + \\sqrt{157}",
"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 all positive roots of the equation \\( x^{x} + x^{1-x} = x + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "x = 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": "How many rearrangements of $wxyz$ are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either $... | math | {
"ground_truth": "C) 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": "In $\\triangle ABC$, $a=2$, $c=4$, and $3\\sin A=2\\sin B$, then $\\cos C=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "- \\dfrac {1}{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": "Let $n$ be a positive integer and let $P$ be the set of monic polynomials of degree $n$ with complex coefficients. Find the value of \n\\[ \\min_{p \\in P} \\left \\{ \\max... | math | {
"ground_truth": "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": "If \\( g(x) = -\\dfrac{1}{x} \\), compute \\( g(g(g(g(g(7))))) \\).",
"role": "user"
}
] | math | {
"ground_truth": "-\\dfrac{1}{7}",
"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 $\\triangle ABC$, $BC=2$, $AB=2\\sqrt{3}$, $AC=b$, and the equation $x^{2}-4x+b=0$ has two equal real roots with respect to $x$. The length of the median on side $AC$... | 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": "In the geometric sequence $\\{ a_{n} \\}$, the common ratio $q=2$, and $a_{1}+a_{2}+a_{3}=21$. Find the value of $a_{3}+a_{4}+a_{5}$.",
"role": "user"
}
] | math | {
"ground_truth": "84",
"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 positive integers $n$ and $p$ if $p$ is prime and \\[ n^8 - p^5 = n^2+p^2 . \\] \r\n*Adrian Stoica*",
"role": "user"
}
] | math | {
"ground_truth": "(n, p) = (2, 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": "Given that Tom had two containers, and the first was $\\frac{3}{5}$ full of oil and the second was empty, then he poured all the oil from the first container into the second cont... | math | {
"ground_truth": "\\frac{10}{9}",
"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": "Six unit disks \\(C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}\\) are in the plane such that they don't intersect each other and \\(C_{i}\\) is tangent to \\(C_{i+1}\\) for \\(1 \\le... | math | {
"ground_truth": "\\sqrt{3} - 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": "Given the sequence ${{a_n}}$ that satisfies ${a_1=0, a_{n+1} = \\frac{a_n - \\sqrt{3}}{\\sqrt{3}a_n + 1}}(n \\in N^*)$, find the value of ${a_{30}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{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": "The sum of two numbers is $S$. Suppose each number is multiplied by $4$ and then each of the resulting numbers is doubled. What is the sum of the final two numbers?",
"role":... | math | {
"ground_truth": "8S",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a singing contest, a Rooster, a Crow, and a Cuckoo were contestants. Each jury member voted for one of the three contestants. The Woodpecker tallied that there were 59 judges,... | math | {
"ground_truth": "13",
"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": "Ditty can bench $80$ pounds today. Every week, the amount he benches increases by the largest prime factor of the weight he benched in the previous week. For example, since he ... | math | {
"ground_truth": "32",
"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 all real pairs $(a,b)$ that solve the system of equation \\begin{align*} a^2+b^2 &= 25, 3(a+b)-ab &= 15. \\end{align*} *(German MO 2016 - Problem 1)*",
"role": "user"... | math | {
"ground_truth": "(0, 5), (5, 0), (4, -3), (-3, 4)",
"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": "Two jars with different volumes (one with volume $V_1$ and the other $V_2$) are filled with alcohol solutions with different ratios. For the jar with volume $V_1$, the ratio of t... | math | {
"ground_truth": "\\frac{r(s+1)V_1 + s(r+1)V_2}{(s+1)V_1 + (r+1)V_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": "The angles in a particular triangle are in arithmetic progression, and the side lengths are $4,5,x$. Express the sum of the possible values of $x$ in the form $a+\\sqrt{b}+\\sqrt... | math | {
"ground_truth": "36",
"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": "Suppose $1 \\leq r \\leq n$. For an ordered tuple $\\left(x_{1}, x_{2}, \\cdots, x_{r}\\right)$ where each $x_{j} \\in\\{1,2, \\cdots, n\\}$, there are at most $i-1$ elements les... | math | {
"ground_truth": "(n-r) \\cdot n^{r-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": "Let $ABC$ be a triangle inscribed in circle $\\Gamma$ , centered at $O$ with radius $333.$ Let $M$ be the midpoint of $AB$ , $N$ be the midpoint of $AC$ , and $D$ ... | math | {
"ground_truth": "444",
"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": "Al takes one green pill and one pink pill each day for two weeks, and his pills cost a total of $\\textdollar 546$. If a green pill costs $\\textdollar g$ and a pink pill costs $... | math | {
"ground_truth": "20",
"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": "Write 3.36 as a simplified fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{84}{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": "In triangle $ABC$ , side $AC$ is $8$ cm. Two segments are drawn parallel to $AC$ that have their ends on $AB$ and $BC$ and that divide the triangle into three parts of... | math | {
"ground_truth": "\\frac{8 \\sqrt{3}}{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": "Given that the expanded fraction $F_1$ and $F_2$ become $.373737\\cdots$ and $.737373\\cdots$ in base $R_1$, and $.252525\\cdots$ and $.525252\\cdots$ in base $R_2$, calculate th... | math | {
"ground_truth": "19",
"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": "Given that $m$ is an integer such that $1 < 3m \\leq 45$, what is the sum of all possible integer values of $m$?",
"role": "user"
}
] | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A labor employment service center has 7 volunteers ready to provide labor employment guidance on the streets over the weekend, with 6 people to be arranged for duty on Saturday a... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets of consecutive integers where each set starts with one more element than the preceding one and the first element of each set is one more than the last element of t... | math | {
"ground_truth": "4641",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The standard equation of a circle with the center at $(2,-3)$ and intercepted by the line $2x+3y-8=0$ with a chord length of $4\\sqrt{3}$ is __________.",
"role": "user"
}
... | math | {
"ground_truth": "(x-2)^{2}+(y+3)^{2}=25",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the $ xy$ plane, the line $ l$ touches to 2 parabolas $ y\\equal{}x^2\\plus{}ax,\\ y\\equal{}x^2\\minus{}2ax$ , where $ a$ is positive constant.\r\n\r\n(1) Find the equ... | math | {
"ground_truth": "\\frac{9a^3}{8}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $D$ be the circle with the equation $x^2 - 4y - 34 = -y^2 + 12x + 74$. Determine the center $(c,d)$ and radius $r$ of $D$, and calculate $c + d + r$.",
"role": "user"
}... | math | {
"ground_truth": "4 + 2\\sqrt{17}",
"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 is a sequence of numbers $+1$ and $-1$ of length $n$ . It is known that the sum of every $10$ neighbouring numbers in the sequence is $0$ and that the sum of every... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The roots of the quadratic equation $x^2+px+19=0$ are exactly 1 greater than the roots of the equation $x^2-Ax+B=0$, where $A$, $B$, and $p$ are integers. Find the value of $A+B$... | math | {
"ground_truth": "18",
"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 quotient of dividing a certain three-digit number by 11 is equal to the sum of the squares of the digits of the dividend. Find this number.",
"role": "user"
}
] | math | {
"ground_truth": "550",
"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": "There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrically situated (that is each room is exactly opposite to one other room... | 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": "Joe now chooses randomly with equal probabilities from four types of fruits (apple, orange, banana, grape) for his four meals (breakfast, lunch, tea, and dinner). What is the pro... | 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 the Rutherford and Geiger observations, a radioactive substance emitted an average of $3.87 \\alpha$-particles over a period of 7.5 seconds. Find the probability that this sub... | math | {
"ground_truth": "0.596",
"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 $\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{6} = x$, calculate $12 \\cdot x^{-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sum of the first $10$ terms of an arithmetic progression is $100$ and the sum of the first $100$ terms is $10$, find the sum of the first $110$ terms.",
"role": "us... | math | {
"ground_truth": "-110",
"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 the right focus of the hyperbola $\\dfrac{x^2}{a^2} - \\dfrac{y^2}{b^2} = 1 (a > 0, b > 0)$ be $F$. A line $l$ perpendicular to the $x$-axis and passing through point $F$ int... | math | {
"ground_truth": "\\dfrac{3\\sqrt{2}}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
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