data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all non-negative integers $ x,y,z$ such that $ 5^x \\plus{} 7^y \\equal{} 2^z$ .\r\n :lol: \r\n(*Daniel Kohen, University of Buenos Aires - Buenos Aires,Argentina*)",
... | math | {
"ground_truth": "(0, 0, 1), (0, 1, 3), (2, 1, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are two categorical variables $x$ and $y$, with one set of observations in a $2\\times 2$ contingency table as follows:\n\n| | $y_{1}$ | $y_{2}$ | Total |\n|-------... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any positive integer \\( n \\), consider the function \n\\[ g(n) =\\left\\{\\begin{matrix} \\log_{4}{n}, & \\text{if } \\log_{4}{n} \\text{ is rational,} \\\\ 0, & \\text{oth... | math | {
"ground_truth": "The correct answer is **A) \\( \\frac{55}{2} \\)**.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $\\frac{x^2 - 2bx + d}{3ax - 4c} = \\frac{m - 2}{m + 2}$, determine the value of $m$ such that the roots of the equation are numerically equal but of opposite ... | math | {
"ground_truth": "\\frac{4b}{3a - 2b}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the circle \\( C: (x - 2)^{2}+(y-2)^{2}=2 \\) and the fact that it passes through the origin to form two tangents \\( OT_{1} \\) and \\( OT_{2} \\) at \\( T_{1} \\) and \\(... | math | {
"ground_truth": "\\frac{12}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let there's a function $ f: \\mathbb{R}\\rightarrow\\mathbb{R}$ \r\nFind all functions $ f$ that satisfies:\r\na) $ f(2u)\\equal{}f(u\\plus{}v)f(v\\minus{}u)\\plus{}f(u\\min... | math | {
"ground_truth": "f(x) \\equiv 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a set of three distinct lines in a plane, there are exactly $M$ distinct points that lie on two or more of these lines. What is the sum of all possible values of $M$?",
"... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $5 \\times 13 \\times 31 \\times 73 \\times 137$",
"role": "user"
}
] | math | {
"ground_truth": "20152015",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the sequence where the first three terms are \\(2^{1/2}, 2^{1/4}, 2^{1/8}\\). If the pattern continues, calculate the value of the fourth term.",
"role": "user"
}
... | math | {
"ground_truth": "2^{-1/8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ and $k$ be positive integers such that $k\\leq 2^n$ . Banana and Corona are playing the following variant of the guessing game. First, Banana secretly picks an integ... | math | {
"ground_truth": "k \\leq 2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ p$ be an odd prime number. How many $ p$ -element subsets $ A$ of $ \\{1,2,\\dots,2p\\}$ are there, the sum of whose elements is divisible by $ p$ ?",
"role": "... | math | {
"ground_truth": "2 + \\frac{1}{p} \\left( \\binom{2p}{p} - 2 \\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = (1+x)^m + (1+x)^n$ where the coefficient of $x$ in the expansion is 19, and $m, n \\in \\mathbb{N}^*$. \n(1) Find the minimum value of the coefficient of $x^2$ in th... | math | {
"ground_truth": "156",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the function $f(x) = \\lg(2-x)$, then the domain of the function $f(x)$ is.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sequence of vertices $v_1,v_2,\\ldots,v_k$ in a graph, where $v_i=v_j$ only if $i=j$ and $k$ can be any positive integer, is called a $\\textit{cycle}$ if $v_1$ is ... | math | {
"ground_truth": "1001",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If Arjun has a $5 \\times 7$ index card, and if he shortens one side of this card by 2 inches, the card would have an area of 21 square inches, find the area of the card in squar... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all integers $m$ with $1 \\le m \\le 300$ such that for any integer $n$ with $n \\ge 2$ , if $2013m$ divides $n^n-1$ then $2013m$ also divides $n-1$... | math | {
"ground_truth": "4650",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $i$ is the imaginary unit, find the imaginary part of the complex number $\\frac{2i}{1-i}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $x$: $3 \\cdot (5^x) = 1875$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In rectangle ABCD, AB = 3 ⋅ AD. Points P and Q are on AB such that AP = PQ = QB. Let E be the midpoint of CD. If lines PE and QE are drawn to meet CD at points R and S respective... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The set $X$ of $N$ four-digit numbers formed from the digits $1,2,3,4,5,6,7,8$ satisfies the following condition:\n\n\n*for any two different digits from $1,2,3,4,,6,7,8$ ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For quadrilateral \\(A B C D\\), it is known that \\(\\angle B A C = \\angle C A D = 60^\\circ\\), and \\(A B + A D = A C\\). It is also known that \\(\\angle A C D = 23^\\circ\\... | math | {
"ground_truth": "83^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let points A = (0,0), B = (2,1), C = (5,4), and D = (6,0). A quadrilateral ABCD is divided into two equal area pieces by a line passing through A. This line intersects \\(\\overl... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Luca has four ropes whose lengths are 42 inches, 56 inches, 63 inches, and 77 inches. He wants to cut the ropes into equal length pieces for crafting, with no rope being wasted. ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "James made $8$ of his first $15$ free throw attempts. If he makes $1/2$ of his next $16$ attempts, by how many percentage points will he increase his overall success rate percent... | math | {
"ground_truth": "-2\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the number $825$, convert it into a factorial base of numeration, that is, $825 = a_1 + a_2 \\times 2! + a_3 \\times 3! + \\dots + a_n \\times n!$ where $0 \\le a_k \\le k$... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$\\textbf{Maria's Recent Collection}$\n\nMaria collects stamps and organizes them by country and by the decade in which they were issued. She bought the stamps at different price... | math | {
"ground_truth": "\\$2.50",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The complex number w has positive imaginary part and satisfies $|w| = 5$ . The triangle in the complex plane with vertices at $w, w^2,$ and $w^3$ has a right angle at $w$ . ... | math | {
"ground_truth": "-73",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, $AB=3$, $AC=2$, $BC= \\sqrt {10}$, then $\\overrightarrow{AB}\\cdot \\overrightarrow{AC}=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The device consists of a large number of independently operating elements with the same (very small) failure probability of each element over time $T$. Find the average number of... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a=2+\\sqrt{3}$ and $b=2-\\sqrt{3}$, find the value of $\\frac{a}{b}-\\frac{b}{a}$.",
"role": "user"
}
] | math | {
"ground_truth": "8\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The original price of a shirt is reduced by 50% to obtain a second price. The store advertises an additional sale, and so this second price is reduced by 40% to obtain a third pr... | math | {
"ground_truth": "70\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Does \\( n^2 \\) have more divisors that are congruent to \\( 1 \\mod 4 \\) or \\( 3 \\mod 4 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "1 \\mod 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\sqrt{2}, \\sqrt{5}, 2\\sqrt{2}, \\sqrt{11}, \\ldots$, find a general term formula for the sequence.",
"role": "user"
}
] | math | {
"ground_truth": "a_n=\\sqrt{3n-1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = 2\\sin{x}\\cos{x} - 2\\sin^2{x} + 1$ $($ for $x \\in \\mathbb{R}$ $)$, in a triangle $ABC$ where the sides opposite to angles $A$, $B$, and $C$ are $a$... | math | {
"ground_truth": "A: \\frac{3(\\sqrt{3} + \\sqrt{2})}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine maximum real $ k$ such that there exist a set $ X$ and its subsets $ Y_{1}$ , $ Y_{2}$ , $ ...$ , $ Y_{31}$ satisfying the following conditions: \r\n(1) for ev... | math | {
"ground_truth": "\\frac{25}{31}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A new logo designed by Mina consists of a large square and four identical circles. Each circle is tangent to two adjacent sides of the square and to two neighboring circles. If t... | math | {
"ground_truth": "900 - 225\\pi \\text{ square inches}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A workshop has 3 lathes, each working independently. Let $X$ be the number of lathes that fail simultaneously. Find the distribution of $X$ in the following two scenarios:<br/>$(... | math | {
"ground_truth": "0.002",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following equation:\n\n$$\n(x-1)(2x-3)(3x-4)(6x-5)=a,\n$$\n\nwhere the value of $a$ are $14$, $0.1$, and $-0.0544$, respectively.",
"role": "user"
}
] | math | {
"ground_truth": "x_1 = 1.458, x_2 = 0.876, x_3 = 1.4, x_4 = 0.933",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the first nonzero digit to the right of the decimal point of the fraction $\\frac{1}{127}$?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a square, inside which is inscribed a circle, inside which is inscribed a square, inside which is inscribed a circle, and so on, with the outermost square having a side ... | math | {
"ground_truth": "2 - \\frac{\\pi}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a shopping mall offers a discount promotion where the rules are as follows:\n1. If the total payment for a single shopping trip does not exceed 200 yuan, no discount w... | math | {
"ground_truth": "546.6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=|x+7|+|x-1|$, for any real number $x$, the inequality $f(x)\\geqslant m$ always holds.\n\n1. Find the range of values for the real number $m$;\n2. When $... | math | {
"ground_truth": "x|x\\geqslant - \\frac {1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five colleagues received bonuses of $30, $40, $50, $60, and $70 respectively. Calculate the amount the colleague who received the $70 bonus needs to redistribute to the others.",... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In base 6, what is the digit $y$ in the number $24y2_6$ such that the number is divisible by 13?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Tara ran 3 miles in half the time it took Alex to run 4.5 miles. If it took Alex 27 minutes to run 4.5 miles, using the same rates, how many minutes would it take Tara to run 6 m... | math | {
"ground_truth": "27 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $(a,b)=(a_n,a_{n+1}),\\forall n\\in\\mathbb{N}$ all be positive interger solutions that satisfies $$ 1\\leq a\\leq b $$ and $$ \\dfrac{a^2+b^2+a+b+1}{ab}\\in\\mathbb{N... | math | {
"ground_truth": "(p, q, r) = (5, -1, -1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any positive integer $k$ denote by $S(k)$ the number of solutions $(x,y)\\in \\mathbb{Z}_+ \\times \\mathbb{Z}_+$ of the system $$ \\begin{cases} \\left\\lceil\\frac{x... | math | {
"ground_truth": "\\lceil 2\\sqrt{k} + 1 \\rceil",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A whole number was given. It was required to increase it by 200000 and triple the resulting number. Instead, the digit 2 was appended to the end of the given number's digital rec... | math | {
"ground_truth": "85714",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point (x, y) is to be chosen in the coordinate plane so that it is equally distant from the x-axis, the y-axis, and the line x+y=2. Find the value of x.",
"role": "user"
... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\mu\\) be a probability measure on \\(\\left(\\mathbb{R}^{n}, \\mathscr{B}\\left(\\mathbb{R}^{n}\\right)\\right)\\) with the distribution function \\(F = F(x)\\), \\(x \\... | math | {
"ground_truth": "\\int_{\\mathbb{R}^{n}} \\prod_{k=1}^{n}\\left[I_{\\left(a_{k}, b_{k}\\right)}+\\frac{I_{\\left\\{a_{k}\\right\\}}+I_{\\left\\{b_{k}\\right\\}}}{2}\\right] \\, d\\mu = \\lim _{c \\rightarrow \\infty} \\frac{1}{(2 \\pi)^{n}} \\int_{[-c, c]^{n}} \\prod_{k=1}^{n} \\frac{e^{-i t_{k} a_{k}}-e^{-i t_{k} ... | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\delta(x) = 5x + 6$ and $\\phi(x) = 7x + 3$, find the value of $x$ if $\\delta(\\phi(x)) = 20$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{35}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ N$ be the number of ordered pairs of nonempty sets $ \\mathcal{A}$ and $ \\mathcal{B}$ that have the following properties:\r\n\r\n• $ \\mathcal{A} \\cup \\mathcal{B}... | math | {
"ground_truth": "4094",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a679b$ is the decimal expansion of a number in base $10$ , such that it is divisible by $72$ , determine $a,b$ .",
"role": "user"
}
] | math | {
"ground_truth": "a = 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least positive four-digit solution to the following system of congruences:\n\\begin{align*}\n10x &\\equiv 30 \\pmod{20} \\\\\n2x + 10 &\\equiv 19 \\pmod{9} \\\\\n-3x + 1... | math | {
"ground_truth": "1296",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, the parametric equations of curve $C_{1}$ are $\\left\\{\\begin{array}{l}x=\\sin\\alpha\\\\ y=\\sqrt{3}\\cos\\alpha\\end{array}\\right.$... | math | {
"ground_truth": "P(\\frac{1}{2}, -\\frac{3}{2})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bertha has 8 daughters and no sons. Some of her daughters have 4 daughters each, and the rest have none. Bertha has a total of 40 daughters and granddaughters, and no great-grand... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bag contains 8 green balls, 5 red balls, and 3 blue balls. A ball is taken from the bag, its color recorded and then placed back in the bag. A second ball is taken and its colo... | math | {
"ground_truth": "\\dfrac{49}{128}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x)=\\log_{a}(x-3a)$ and the function $g(x)=\\log_{a}\\frac{1}{x-a}$ ($a>0$ and $a\\neq 1$) are defined in the interval $[a+2, a+3]$. \n(1) Find the range of valu... | math | {
"ground_truth": "\\frac{9-\\sqrt{57}}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anna has five circular discs, each of a different size. She decides to build a tower using three of her discs so that each disc in her tower is smaller than the disc below it. Ho... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\Gamma$ be the maximum possible value of $a+3b+9c$ among all triples $(a,b,c)$ of positive real numbers such that\n\\[ \\log_{30}(a+b+c) = \\log_{8}(3a) = \\log_{27} ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let triangle $ABC$ be a right triangle with right angle at $B$. Let $D$ and $E$ be points on $\\overline{AC}$ such that $D$ is between $A$ and $E$ and $\\overline{BD}$ bisects $\... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = x^2 + 2x + 1$, if there exists $t$, such that for $x \\in [1, m]$, $f(x+t) \\leq x$ always holds, then the maximum value of the real number $m$ is.",
... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two cubes with an edge length of $a$ share a segment that connects the centers of two opposite faces. One cube is rotated by $45^{\\circ}$ relative to the other. Find the volume ... | math | {
"ground_truth": "2a^3(\\sqrt{2} - 1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The merchant purchased goods at a discount of 30% off the list price. He wishes to mark them up so that after offering a discount of 10% on this new marked price, he still achiev... | math | {
"ground_truth": "111.1\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A child possesses a set of 64 distinct blocks. Each block is made from one of 2 materials (plastic or wood), 2 sizes (small or large), 4 colors (blue, green, red, yellow), 4 shap... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $U = \\{0, 1, 2, 3\\}$, and $A = \\{x \\in U | x^2 + mx = 0\\}$. If the complement of $A$ in $U$, $C_UA = \\{1, 2\\}$, then the real number $m$ equals \\_\\_\\_\\_\\_\\_.",
... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\sin x + \\cos x = \\frac{1}{5}$, and $0 < x < \\pi$, find the value of $\\tan x$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ such that for any integer $k$ there exists an integer $a$ for which $a^3+a-k$ is divisible by $n$ .\n\n*Warut Suksompong, Thailand*",
... | math | {
"ground_truth": "n = 3^k",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The inscribed circle of triangle $DEF$ is tangent to $\\overline{DE}$ at $P,$ and its radius is $15$. Given that $DP=15$ and $PE=18,$ find the perimeter of the triangle.",
"r... | math | {
"ground_truth": "280.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least positive integer such that when its leftmost digit is deleted, the resulting integer is 1/25 of the original integer.",
"role": "user"
}
] | math | {
"ground_truth": "900",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the polynomial\n\\[ ax^4 + bx^3 + cx^2 + dx + e = 0 \\]\nwith integer coefficients and roots $-4$, $6$, $10$, and $-1/2$. If $e$ is a positive integer, determine its sma... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It is known that $3 \\leq x \\leq 5$ and $4 \\leq y \\leq 6$. Find the maximum and minimum values of the expression $2x - 3y$. Provide the sum of these values in the answer.",
... | math | {
"ground_truth": "-14",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of \\( x \\) such that \\( \\sqrt{x + 15} = 12 \\).",
"role": "user"
}
] | math | {
"ground_truth": "129",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ for which both numbers \\[1\\;\\;\\!\\!\\!\\!\\underbrace{77\\ldots 7}_{\\text{ $n$ sevens}}\\!\\!\\!\\!\\quad\\text{and}\\quad 3\\;\\; \\!\\!\\... | math | {
"ground_truth": "n = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two concentric circles form a race track, where the outer circle is precisely 8 feet farther from the center than the inner circle. If the radius of the inner circle is 15 feet, ... | math | {
"ground_truth": "16\\pi \\text{ feet}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $$ \\frac{(2 + 2)^2}{2^2} \\cdot \\frac{(3 + 3 + 3 + 3)^3}{(3 + 3 + 3)^3} \\cdot \\frac{(6 + 6 + 6 + 6 + 6 + 6)^6}{(6 + 6 + 6 + 6)^6} $$",
"role": "user"
}
] | math | {
"ground_truth": "108",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve in the set of real numbers the equation \\[ 3x^3 \\minus{} [x] \\equal{} 3,\\] where $ [x]$ denotes the integer part of $ x.$",
"role": "user"
}
] | math | {
"ground_truth": "x = \\sqrt[3]{\\frac{4}{3}}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a\\textdollar b = (a - b)^2$, calculate $(x - y)^2\\textdollar(y - x)^2$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Please observe the following set of equations: $(-1) \\times \\frac{1}{2} = (-1) + \\frac{1}{2}$; $(-2) \\times \\frac{2}{3} = (-2) + \\frac{2}{3}$; $(-3) \\times \\frac{3}{4} = ... | math | {
"ground_truth": "(-n) \\times \\frac{n}{n+1} = -n + \\frac{n}{n+1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(Selected Inequality Problems) \nThe solution set of the inequality $|x-4|+|3-x|<2$ is ___.",
"role": "user"
}
] | math | {
"ground_truth": "(2.5, 4.5)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "the code system of a new 'MO lock' is a regular $n$ -gon,each vertex labelled a number $0$ or $1$ and coloured red or blue.it is known that for any two adjacent vertices,eit... | math | {
"ground_truth": "3^n + 3 \\text{ if } n \\text{ is even, and } 3^n + 1 \\text{ if } n \\text{ is odd}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Students A, B, and C choose a group as a gift in turn. Student A likes ox and horse, student B likes ox, dog, and sheep, and student C likes all the mascots. If the gifts chosen ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the distance between the points $(3, 7)$ and $(3, -2)$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three people, \\( A \\), \\( B \\), and \\( C \\), visit their teacher \\( D \\)'s house. Teacher \\( D \\) gives each person a hat with a four-digit number written on it. It is ... | math | {
"ground_truth": "2704 + 2304 + 9604 = 14612",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the fractions $\\dfrac{2}{9}$ and $\\dfrac{5}{12}$, calculate the value halfway between them.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{23}{72}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the volume of a regular triangular pyramid whose height's midpoint is 2 units away from a lateral face and \\(\\sqrt{12}\\) units away from a lateral edge. If necessary, rou... | math | {
"ground_truth": "374.12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six positive integers from a list of twelve positive integers are $3, 5, 7, 9, 11, 13$. What is the smallest possible value of the median of this list of twelve positive integers... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "5 sheets of red card paper can be exchanged for 2 sheets of gold card paper. 1 sheet of gold card paper can be exchanged for 1 sheet of red card paper and 1 sheet of silver card ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $DEF$, the sides are given by $DE = 25$, $EF = 31$, and $FD = 34$. Points $P$ and $Q$ are on $\\overline{DF}$ with $P$ on $\\overline{DQ}$, points $R$ and $S$ are on ... | math | {
"ground_truth": "238",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all prime numbers between $1$ and $100$ that are simultaneously $1$ greater than a multiple of $4$ and $1$ less than a multiple of $5$.",
"role": "user"
}
] | math | {
"ground_truth": "139",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the indeterminate equation \\( 96x_{1} + 97x_{2} = 1000 \\), find the number of sets of non-negative integer solutions.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When three positive integers are divided by $53$, the remainders are $31$, $15$, and $7$, respectively.\n\nWhen the sum of the three integers is divided by $53$, what is the rema... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what value of $z$ does the function $h(z)=\\sqrt{1.44+0.8(z+0.3)^2}$ attain its minimum value?",
"role": "user"
}
] | math | {
"ground_truth": "-0.3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Marco Polo has created a map of Asia on the complex plane without distorting distances. Beijing corresponds to $0$ on this complex plane, and Tokyo corresponds to $3000i$. Meanwh... | math | {
"ground_truth": "1500",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest prime divisor of $1202102_5$.",
"role": "user"
}
] | math | {
"ground_truth": "307",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the point sets \\( A = \\left\\{(x, y) \\left\\lvert\\,(x-3)^{2}+(y-4)^{2} \\leqslant\\left(\\frac{5}{2}\\right)^{2}\\right.\\right\\} \\) and \\( B = \\left\\{(x, y) \\lef... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The circumference of a circle has 50 numbers written on it, each of which is either +1 or -1. We want to find the product of these numbers. What is the minimum number of question... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Observe the following equations: \n1=1 \n1-4=-（1+2）=-3 \n1-4+9=1+2+3=6 \n1-4+9-16=-（1+2+3+4）=-10 \nThen, the 5th equation is \nThe value of the 20th equation is \n... | math | {
"ground_truth": "-210",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any real number $k$, the graph of\n\\[ y = 3x^2 + kx - 2k \\] passes through a fixed point $(a,b)$. Find $(a,b)$.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 12)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest $n$ such that $(z+1)^n = z^n + 1$ has all its non-zero roots in the unitary circumference, e.g. $(\\alpha+1)^n = \\alpha^n + 1, \\alpha \\neq 0$ implies ... | math | {
"ground_truth": "n = 7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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