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": "The denominator of a geometric progression is $\\frac{1}{3}$, the fourth term of this progression is $\\frac{1}{54}$, and the sum of all its terms is $\\frac{121}{162}$. Find the... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x_{1}$ and $x_{2}$ be the two roots of the equation $x^{2}-3x+k=0$ with respect to $x$, and $x_{1}=2x_{2}$. Find the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of the equation $10x + 210y = 2100$ is drawn on graph paper with each square representing one unit in each direction. Calculate the number of $1$ by $1$ graph paper squ... | math | {
"ground_truth": "941",
"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 in $\\bigtriangleup ABC$, $AB = 75$, and $AC = 120$. A circle with center $A$ and radius $AB$ intersects $\\overline{BC}$ at points $B$ and $X$. Moreover, $\\overline{BX}$ ... | math | {
"ground_truth": "117",
"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 vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|= \\sqrt {2}$, and $\\overrightarrow{a}\\perp (\\overrighta... | math | {
"ground_truth": "\\dfrac {\\pi}{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": "Determine the value of $q$ for the quadratic $6x^2 + 5x + q$ if its roots are $\\frac{-5 \\pm i\\sqrt{323}}{12}$.",
"role": "user"
}
] | math | {
"ground_truth": "14.5",
"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 how many ways can five people line up in a straight line if the youngest person cannot be first or last in the line?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers \\(36, 27, 42, 32, 28, 31, 23, 17\\) are grouped in pairs so that the sum of each pair is the same. Which number is paired with \\(32\\)?",
"role": "user"
}
] | math | {
"ground_truth": "27",
"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 $\\mathcal{F}$ be the set of continuous functions $f: \\mathbb{R} \\to \\mathbb{R}$ such that $$ e^{f(x)}+f(x) \\geq x+1, \\: \\forall x \\in \\mathbb{R} $$ For $f \\... | math | {
"ground_truth": "\\frac{3}{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": "Calculate:\n\\[\\sum_{k = 1}^\\infty \\frac{12^k}{(4^k - 3^k)(4^{k + 1} - 3^{k + 1})}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\{\\{\\text{2 4 1}\\} \\text{ [3 2] } 5\\}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{59}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $d$ be a positive number such that when $143$ is divided by $d$, the remainder is $11.$ Compute the sum of all possible two-digit values of $d$.",
"role": "user"
}
] | math | {
"ground_truth": "67",
"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 plane intersects a right circular cylinder of radius 1 forming an ellipse. If the major axis of the ellipse is 50% longer than the minor axis, determine the length of the major... | math | {
"ground_truth": "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": "Let $\\triangle A_0B_0C_0$ be an isosceles triangle with $\\angle B_0A_0C_0 = 50^\\circ$, $\\angle A_0B_0C_0 = 65^\\circ$, and $\\angle C_0A_0B_0 = 65^\\circ$. For each positive ... | math | {
"ground_truth": "\\textbf{(B)} 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fair die is rolled eight times. Find the probability of rolling at least a four at least six times.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{129}{256}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define a sequence $(x_{n})_{n\\geq 1}$ by taking $x_{1}\\in\\left\\{5,7\\right\\}$ ; when $k\\ge 1$ , $x_{k+1}\\in\\left\\{5^{x_{k}},7^{x_{k}}\\right\\}$ . Determine all pos... | math | {
"ground_truth": "25, 07, 43",
"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 note contains three two-digit numbers that are said to form a sequence with a fourth number under a cryptic condition. The numbers provided are 46, 19, and 63, but the fourth n... | 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": "How many whole numbers between $100$ and $400$ contain the digit $2$?",
"role": "user"
}
] | math | {
"ground_truth": "138",
"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": "Compute the sum:\n\\[ \\frac{1}{7} + \\frac{2}{7} + \\frac{3}{7} + \\dots + \\frac{14}{7} + \\frac{15}{7}, \\]\nbut only add terms where the numerator is an odd number.",
"ro... | math | {
"ground_truth": "9\\frac{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": "Let $a,$ $b,$ $c$ be the roots of the cubic $x^3 - 2x^2 + 4x - 1 = 0.$ Given that $Q(x)$ is a cubic polynomial such that $Q(a) = b + c - 3$, $Q(b) = a + c - 3$, $Q(c) = a + b - 3... | math | {
"ground_truth": "-\\frac{20}{7}x^3 + \\frac{34}{7}x^2 - \\frac{12}{7}x + \\frac{13}{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 $f(x) = \\begin{cases} -(x-a)^2, & x\\geq 0 \\\\ -x^2-2x-3+a, & x<0 \\end{cases}$, if $f(x) \\leq f(0)$ holds true for all $x \\in \\mathbb{R}$, then the range of $a$ is $\... | math | {
"ground_truth": "-2 \\leq a \\leq 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a triangle, two of the side lengths are 5 and 12, and the angle between them is $150^\\circ.$ Find the length of the third side.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{169 + 60\\sqrt{3}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many positive integers $n$ is $\\frac{n}{40-n}$ also a positive integer?\nA) 5\nB) 6\nC) 7\nD) 8\nE) 9",
"role": "user"
}
] | math | {
"ground_truth": "C) 7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A_1A_2...A_{101}$ be a regular $101$ -gon, and colour every vertex red or blue. Let $N$ be the number of obtuse triangles satisfying the following: The three vertices o... | math | {
"ground_truth": "202 \\binom{75}{25}",
"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 $a$ and $b$ are real numbers, and $b^{2}+(4+i)b+4+ai=0$ (where $i$ is the imaginary unit), find the value of $|a+bi|$.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{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": "There are 111 StarCraft programmers. The StarCraft team SKT starts with a given set of eleven programmers on it, and at the end of each season, it drops a progamer and adds a pro... | math | {
"ground_truth": "61593840",
"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": "Caroline can make fifteen lassis from three mangoes. If the cost for each mango is $2, how much will it cost her to make the lassis from nine mangoes?",
"role": "user"
}
] | math | {
"ground_truth": "45 \\text{ lassis}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $n\\geq 3$ pupils standing in a circle, and always facing the teacher that stands at the centre of the circle. Each time the teacher whistles, two arbitrary pupils th... | math | {
"ground_truth": "\\frac{(n-1)n}{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": "There are three tasks, A, B, and C. Task A requires 2 people, while tasks B and C each require 1 person. From a group of 10 people, the number of different ways to select 4 peopl... | math | {
"ground_truth": "2520",
"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": "Successive discounts of $10\\%$ and $20\\%$ are equivalent to a single discount of what percentage?",
"role": "user"
}
] | math | {
"ground_truth": "28\\%",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be a positive number. Suppose we increase $S$ by $x\\%$, add 15, and then decrease the result by $y\\%$. Determine when the resulting number exceeds $S$ by at least 10 un... | math | {
"ground_truth": "**B)** \\( x > y + \\frac{xy}{100} + 500 - \\frac{1500y}{S} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( k_{1} \\) be the smallest natural number that is a root of the equation\n\n\\[\n\\sin k^\\circ = \\sin 334 k^\\circ\n\\]\n\n(a) Find \\( k_{1} \\).\n\n(b) Find the smalle... | math | {
"ground_truth": "40",
"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": "If $m$ and $n$ are positive integers such that $\\gcd(m,n) = 18$, what is the smallest possible value of $\\gcd(12m, 20n)$?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of eight terms each of value $5^8$: $5^8 + 5^8 + 5^8 + 5^8 + 5^8 + 5^8 + 5^8 + 5^8$.",
"role": "user"
}
] | math | {
"ground_truth": "3125000",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x \\neq 0, \\frac{x}{3} = y^3$ and $\\frac{x}{6} = 3y$, find the value of $x$.\nA) $9\\sqrt{6}$\nB) $12\\sqrt{6}$\nC) $15\\sqrt{6}$\nD) $18\\sqrt{6}$\nE) $24\\sqrt{6}$",
... | math | {
"ground_truth": "\\textbf{(D)}\\ 18\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f(x)$ is an odd function with a period of 5 on $\\mathbb{R}$, and it satisfies $f(1)=1$, $f(2)=2$, then $f(3)-f(4)=$ ?",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $2x-4=0$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Thirty percent less than 80 is half more than what number?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{112}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the total distance on a Cartesian coordinate plane from point \\(A = (2, -3)\\) to point \\(B = (8, 5)\\) and then from point \\(B\\) to point \\(C = (3, 9)\\).",
"... | math | {
"ground_truth": "10 + \\sqrt{41}",
"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 points \\( (2, 9), (14, 18) \\), and \\( (6, k) \\) where \\( k \\) is an integer, find the sum of the values of \\( k \\) for which the area of the triangle is a minimum."... | math | {
"ground_truth": "31",
"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": "To the 8-digit number 20172018, prepend and append a single digit on both sides so that the resulting number...",
"role": "user"
}
] | math | {
"ground_truth": "2201720184",
"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 all a positive integers $a$ and $b$ , such that $$ \\frac{a^b+b^a}{a^a-b^b} $$ is an integer",
"role": "user"
}
] | math | {
"ground_truth": "(a, b) = (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": "If the ratio of $b$ to $a$ is 4, then what is the value of $a$ when $b = 15 - 6a$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{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": "Given the sequence $\\{a_k\\}_{k=1}^{11}$ of real numbers defined by $a_1=0.5$, $a_2=(0.51)^{a_1}$, $a_3=(0.501)^{a_2}$, $a_4=(0.511)^{a_3}$, and in general,\n\n$a_k=\\begin{case... | math | {
"ground_truth": "30",
"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 $f : \\mathbb{N} \\to \\mathbb{N} $ such that $f(a) + f(b)$ divides $2(a + b - 1)$ for all $a, b \\in \\mathbb{N}$ .\n\nRemark: $\\mathbb{N} = \\{ 1, 2, 3, \\ldo... | math | {
"ground_truth": "f(x) = 2x - 1 \\; \\forall x \\in \\mathbb{N}",
"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": "Mafia is a game where there are two sides: The village and the Mafia. Every night, the Mafia kills a person who is sided with the village. Every day, the village tries to hunt do... | math | {
"ground_truth": "\\frac{1}{9}",
"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 triangle $ABC$, let the sides opposite to angles $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively. It is given that $2a\\cos C + b\\cos C + c\\cos B = 0$.\n(Ⅰ) Find the mea... | math | {
"ground_truth": "\\sqrt{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is $4^2 \\cdot 10 + 5 \\cdot 12 + 12 \\cdot 4 + \\frac{24}{3}\\cdot 9$?",
"role": "user"
}
] | math | {
"ground_truth": "340",
"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": "Find $7463_{8} - 3154_{8}$. Express your answer in base $8$.",
"role": "user"
}
] | math | {
"ground_truth": "4317_8",
"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 revised diagram, $EF$ and $GH$ are straight lines. In the new setup:\n- $\\angle VEK = 70^\\circ$\n- $\\angle KEW = 40^\\circ$\n- $\\angle EVG = 110^\\circ$\n\nWhat is the... | math | {
"ground_truth": "40^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the point M with coordinates (-3, 5, 2) reflected across the y-axis, calculate the new coordinates of the reflected point M.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{(3, 5, -2)}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given is a cube of side length $2021$ . In how many different ways is it possible to add somewhere on the boundary of this cube a $1\\times 1\\times 1$ cube in such a way that... | math | {
"ground_truth": "13612182",
"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 fraction \n\n\\[\\dfrac{1}{99^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},\\]\nwhere $n$ is the length of the period of the repeating decimal expansion. Express the sum ... | math | {
"ground_truth": "883",
"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 triangle $XYZ,$ $y = 7,$ $z = 6,$ and $\\cos (Y - Z) = \\frac{15}{16}.$ Find $x.$",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{22}",
"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": "\\[\n\\left(\\left(1 \\frac{1}{7}-\\frac{23}{49}\\right): \\frac{22}{147}-\\left(0.6: 3 \\frac{3}{4}\\right) \\cdot 2 \\frac{1}{2}+3.75: 1 \\frac{1}{2}\\right): 2.2\n\\]",
"r... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The price of paper A is 3 coins for 2 sheets, while the price of paper B is 2 coins for 3 sheets. Determine the ratio of the unit prices of paper A and B.",
"role": "user"
... | math | {
"ground_truth": "\\text{The ratio of the unit prices of paper A and B is 9:4.}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five years from now, Billy's age will be twice Joe's current age. Currently, the sum of their ages is 60. How old is Billy right now?",
"role": "user"
}
] | math | {
"ground_truth": "38\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the parabola \\( y = p x^{2} \\) has a common point with the square whose vertices are \\( A(1,1) \\), \\( B(2,1) \\), \\( C(2,2) \\), and \\( D(1,2) \\), then the range of th... | math | {
"ground_truth": "\\left[ \\frac{1}{4}, 2 \\right]",
"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 two whole numbers, $\\diamondsuit$ and $\\Delta$, have a product of 48 and $\\diamondsuit \\neq \\Delta$, find the largest possible value of $\\diamondsuit + \\Delta$.... | math | {
"ground_truth": "49",
"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 number $n^2 \\pm 3n + 5$ is not divisible by 121 for any integer $n$.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{There are no integer values of } n \\text{ such that } n^2 \\pm 3n + 5 \\text{ is divisible by } 121.",
"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 the sum of all positive integers such that their expression in base $3$ digits is the reverse of their expression in base $8$ digits. Express your answer in base $10$.",
... | math | {
"ground_truth": "1 + 2 + 20 = 23",
"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 $A$ be a set of numbers chosen from $1,2,..., 2015$ with the property that any two distinct numbers, say $x$ and $y$ , in $A$ determine a unique isosceles triangle (... | math | {
"ground_truth": "10",
"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 a senior grade of a school with 900 students, there are 0 female students. Using stratified sampling method based on the gender ratio, if a sample of 45 students is to be draw... | math | {
"ground_truth": "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": "Consider a sequence $\\{a_n\\}$ of integers, satisfying $a_1=1, a_2=2$ and $a_{n+1}$ is the largest prime divisor of $a_1+a_2+\\ldots+a_n$ . Find $a_{100}$ .",
"role"... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many even integers $n$ between 1 and 200 is the greatest common divisor of 18 and $n$ equal to 4?",
"role": "user"
}
] | math | {
"ground_truth": "34",
"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": "On a chessboard composed of 100 unit squares (10x10 board), what is the probability that a randomly chosen unit square does not touch the outer edge of the board?\nA) $\\frac{9}{... | math | {
"ground_truth": "\\frac{16}{25}",
"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 a new set of weights comprising 1 lb, 4 lb, and 9 lb, determine the maximum weight that can be measured using this set, and how many different weights can be achieved using... | math | {
"ground_truth": "C) 14 lb and 7 weights",
"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 graph of the function y = log<sub>a</sub>(x - 3) + 1 (where a > 0 and a ≠ 1) always passes through a fixed point P. Determine the coordinates of point P.",
"role": "user"... | math | {
"ground_truth": "(4, 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": "Of the odd numbers 1, 3, 5, ..., 25 (including all odd integers between these limits), which number has the greatest number of divisors?",
"role": "user"
}
] | math | {
"ground_truth": "15 \\text{ and } 21",
"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 point P is on the curve $y=x^2+1$ (where $x \\geq 0$), and point Q is on the curve $y=\\sqrt{x-1}$ (where $x \\geq 1$). Then the minimum value of the distance $|PQ|$ is _... | math | {
"ground_truth": "\\frac{3\\sqrt{2}}{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": "Suppose $\\overline{AB}$ is a segment of unit length in the plane. Let $f(X)$ and $g(X)$ be functions of the plane such that $f$ corresponds to rotation about $A$ $60^... | math | {
"ground_truth": "\\frac{1 + \\sqrt{3}}{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": "On the edges \\( AC, BC, BS, AS \\) of a regular triangular pyramid \\( SABC \\) with vertex \\( S \\), points \\( K, L, M, N \\) are chosen respectively. It is known that points... | math | {
"ground_truth": "CQ = \\frac{7}{3}",
"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": "Lucy has lots of identical lolly sticks. She arranges the lolly sticks end to end to make different triangles. Which number of lolly sticks could she not use to make a triangle?\... | math | {
"ground_truth": "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": "Evaluate the following sum up to the \\(2013^\\text{th}\\) term:\n$$\n\\left\\lfloor\\frac{1}{1}\\right\\rfloor + \\left\\lfloor\\frac{1}{2}\\right\\rfloor + \\left\\lfloor\\frac... | math | {
"ground_truth": "62",
"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": "Kelvin the Frog is hopping on a number line (extending to infinity in both directions). Kelvin starts at $0$ . Every minute, he has a $\\frac{1}{3}$ chance of moving $1$ uni... | math | {
"ground_truth": "\\frac{3\\sqrt{5} - 5}{5}",
"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": "One of the asymptotes of a hyperbola has the equation $y = 4x$. The foci of the hyperbola both lie on the line $x = 3$. Find the equation of the other asymptote of the hyperbola,... | math | {
"ground_truth": "y = -4x + 24",
"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 quadrilateral $ABCD$, side lengths $AB,~ BC,~$ and $CD$ are $5$, $7$, and $15$, respectively. If $\\sin B = -\\cos C = \\frac{7}{25}$ and both $\\angle B$ and $\\angle C$ are ... | math | {
"ground_truth": "4\\sqrt{13}",
"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 $\\triangle ABC$, $AB=\\sqrt{3}$, $AC=\\sqrt{5}$, $BC=2$, calculate the area of $\\triangle ABC$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{11}}{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": "Roberto has four pairs of trousers, nine shirts, three jackets, and five belts. How many different outfits can he make if an outfit consists of a pair of trousers, a shirt, a jac... | math | {
"ground_truth": "540",
"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 a triangular pyramid $S-ABC$ with a base that is an equilateral triangle, and point $A$'s projection $H$ on the side $SBC$ is the orthocenter of $\\triangle SBC$. If $SA = ... | math | {
"ground_truth": "\\frac{1}{6} a^3",
"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": "From this infinite list of numbers, how many are integers? $$\\sqrt{6561},\\sqrt[3]{6561},\\sqrt[4]{6561},\\sqrt[5]{6561},\\sqrt[6]{6561},\\ldots$$",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all integers $m\\ge2$ for which there exists an integer $n\\ge1$ with $\\gcd(m,n)=d$ and $\\gcd(m,4n+1)=1$ .\n\n*Proposed by Gerhard Woeginger, Austria*",
"r... | math | {
"ground_truth": "\\{ m : m \\equiv 0 \\pmod{d} \\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all polynomials of the form $$ P_n(x)=n!x^n+a_{n-1}x^{n-1}+\\dots+a_1x+(-1)^n(n+1) $$ with integer coefficients, having $n$ real roots $x_1,\\dots,x_n$ satisfying $... | math | {
"ground_truth": "P_1(x) = x - 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": "A positive integer is written on each corner of a square such that numbers on opposite vertices are relatively prime while numbers on adjacent vertices are not relatively prime. ... | math | {
"ground_truth": "60",
"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 $m$ be a positive integer and $a$ a positive real number. Find the greatest value of $a^{m_1}+a^{m_2}+\\ldots+a^{m_p}$ where $m_1+m_2+\\ldots+m_p=m, m_i\\in\\mathbb{N}... | math | {
"ground_truth": "(p-1)a + a^{m - (p-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": "Find the largest natural number in which all digits are different and each pair of adjacent digits differs by 6 or 7.",
"role": "user"
}
] | math | {
"ground_truth": "60718293",
"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 all positive integer $n(\\ge 2)$ and rational $\\beta \\in (0,1)$ satisfying the following:\nThere exist positive integers $a_1,a_2,...,a_n$ , such that for any set $I... | math | {
"ground_truth": "n \\le 10",
"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 pairs $ (m,n)$ of positive integers with $ m < n$ fulfill the equation $ \\frac {3}{2008} \\equal{} \\frac 1m \\plus{} \\frac 1n$ ?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Suppose I randomly pick an integer \\( p \\) between 1 and 20 inclusive. What is the probability that I choose a \\( p \\) such that there exists an integer \\( q \\) so that \\(... | math | {
"ground_truth": "\\frac{4}{20} = \\frac{1}{5}",
"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": "Solve the system of equation $$ x+y+z=2; $$ $$ (x+y)(y+z)+(y+z)(z+x)+(z+x)(x+y)=1; $$ $$ x^2(y+z)+y^2(z+x)+z^2(x+y)=-6. $$",
"role": "user"
}
] | math | {
"ground_truth": "\\{(0, 3, -1), (0, -1, 3), (3, 0, -1), (3, -1, 0), (-1, 0, 3), (-1, 3, 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": "Let \\(x\\) and \\(y\\) be positive real numbers, and let \\(k\\) be a positive constant. Find the maximum value of\n\\[\n\\frac{(kx+y)^2}{x^2+y^2}.\n\\]",
"role": "user"
}... | math | {
"ground_truth": "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": "China Mathematical Olympiad 2018 Q6\nGiven the positive integer $n ,k$ $(n>k)$ and $ a_1,a_2,\\cdots ,a_n\\in (k-1,k)$ ,if positive number $x_1,x_2,\\cdots ,x_n$ satisfyi... | math | {
"ground_truth": "a_1 a_2 \\cdots a_n",
"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 is called \"oddly even\" if the sum of its digits is even. Find the sum of the first 2013 oddly even numbers.",
"role": "user"
}
] | math | {
"ground_truth": "4055187",
"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 $ABCD$ be a square with the side of $20$ units. Amir divides this square into $400$ unit squares. Reza then picks $4$ of the vertices of these unit squares. These ver... | math | {
"ground_truth": "\\{11, 20, 27, 32, 35, 36\\}",
"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 sum of two numbers is 50, and their product is 25. If the sum of their reciprocals is $a$, find $a$.\n\nIf the lines $ax + 2y + 1 = 0$ and $3x + by + 5 = 0$ are perpendicular... | math | {
"ground_truth": "136",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point $P$ is located 15 inches away from the center of a circle. A secant from $P$ intersects the circle at points $Q$ and $R$ such that the external segment $PQ$ is 10 inches ... | math | {
"ground_truth": "3\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A box contains seven cards, each numbered consecutively from 1 to 7. Four cards are selected randomly without replacement. Calculate the probability that 6 is the largest number ... | math | {
"ground_truth": "\\frac{3}{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": "In $\\triangle PQR$, $PQ = 93$, and $PR = 105$. A circle with center $P$ and radius $PQ$ intersects $\\overline{QR}$ at points $Q$ and $Y$. Moreover, $\\overline{QY}$ and $\\over... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the cross product of vectors $\\begin{pmatrix} 3 \\\\ -4 \\\\ 5 \\end{pmatrix}$ and $\\begin{pmatrix} -2 \\\\ 7 \\\\ 1 \\end{pmatrix}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} -39 \\\\ -13 \\\\ 13 \\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": "The circles with radii \\( R \\) and \\( r \\) touch each other externally. The lateral sides of an isosceles triangle are their common tangents, and the base of the triangle tou... | math | {
"ground_truth": "\\frac{2R^2}{\\sqrt{Rr}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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