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": "Given the sequence \\(\\{a_{n}\\}\\) with the sum of the first \\(n\\) terms \\(S_{n} = n^{2} - 1\\) \\((n \\in \\mathbf{N}_{+})\\), find \\(a_{1} + a_{3} + a_{5} + a_{7} + a_{9}... | math | {
"ground_truth": "44",
"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": "We have $ 150$ numbers $ x_1,x_2, \\cdots , x_{150}$ each of which is either $ \\sqrt 2 \\plus{}1$ or $ \\sqrt 2 \\minus{}1$ \r\n\r\nWe calculate the following sum:\r\n\r ... | math | {
"ground_truth": "S = 111",
"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": "Determine all triples of real numbers $(a,b,c)$ such that \\begin{eqnarray*} xyz &=& 8 x^2y + y^2z + z^2x &=& 73 x(y-z)^2 + y(z-x)^2 + z(x-y)^2 &=& 98 . \\end{eqnarray*}",
... | math | {
"ground_truth": "(4, 4, \\frac{1}{2}), (4, \\frac{1}{2}, 4), (\\frac{1}{2}, 4, 4), (1, 1, 8), (1, 8, 1), (8, 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": "Let $\\theta$ be the angle between the planes $3x - 2y + z - 1 = 0$ and $9x - 6y - 4z + 3 = 0$. Find $\\cos \\theta$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{35}{\\sqrt{1862}}",
"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 complex number $z$ that satisfies the equation $z(1+i)=3+2i$, find the imaginary part of the complex number $z$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{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 wheel is divided into four parts labeled $D$, $E$, $F$, and $G$. The probability of the wheel stopping on $D$ is $\\frac{1}{4}$, and the probability of stopping on $E$ is $\\fr... | math | {
"ground_truth": "\\frac{1}{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": "**p1.** There are $32$ balls in a box: $6$ are blue, $8$ are red, $4$ are yellow, and $14$ are brown. If I pull out three balls at once, what is the probability that no... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the increasing interval of the function $y=\\ln x - ax$ is $(0, 1)$, determine the value of $a$.",
"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": "The domain of the function $y= \\sqrt {x+1}+ \\frac {1}{x+1}$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "(-1, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $(-2a^{2}b^{3})^{3}$ correctly.",
"role": "user"
}
] | math | {
"ground_truth": "-8a^{6}b^{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": "Given that for each positive integer n > 1, P(n) denote the greatest prime factor of n, find the number of positive integers n for which both P(n) = √n and P(n+48) = √(n+48).",
... | 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": "When two dice are continuously thrown, calculate the probability that the sum of the numbers facing up equals 6.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{36}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many values of $n$ are there for which you can insert $+$ signs into a string of $n$ $8$s, $8888\\cdots88$, so that the resulting expression equals $7700$?",
"role": "use... | math | {
"ground_truth": "101",
"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": "Evaluate the sum $(-2)^{-11} + (-2)^{-10} + (-2)^{-9} + \\cdots + (-2)^9 + (-2)^{10} + (-2)^{11}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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 $a+b=1$ and $ab=108$, find the value of $a^2b+ab^2$.",
"role": "user"
}
] | math | {
"ground_truth": "108",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\tan \\alpha = 3$, find the value of $\\frac{\\sin \\alpha + 2\\cos \\alpha}{\\sin \\alpha - 2\\cos \\alpha}$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions $f \\colon \\mathbb{R} \\to \\mathbb{R}$ that satisfy the following property for all real numbers $x$ and all polynomials $P$ with real coefficients:\n\n... | 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": "Determine the sum of the highest powers of $10$ and $6$ that divide $12!$.\nA) 5\nB) 6\nC) 7\nD) 8",
"role": "user"
}
] | math | {
"ground_truth": "C) 7",
"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 $\\triangle ABC$ be a triangle where $B$ is twice the measure of $A$, i.e., $B = 2A$. After drawing an altitude from the vertex $C$ to the base $AB$ which divides $C$ into $C... | math | {
"ground_truth": "C_1 - C_2 = A",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers $n$ for which the number $2^{n} + 65$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "10, 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 that two different square roots of a positive number are $3a-14$ and $a+2$, and the cube root of $b+11$ is $-3$; \n$(1)$ Find the values of $a$ and $b$; \n$(2)$ Find the ... | math | {
"ground_truth": "\\pm 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 \\(a, b, c \\geq 0\\), \\(t \\geq 1\\), satisfying\n\\[\n\\left\\{\n\\begin{array}{l}\na + b + c = \\frac{1}{2}, \\\\\n\\sqrt{a + \\frac{1}{2}(b - c)^{2}} + \\sqrt{b} + \\s... | math | {
"ground_truth": "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": "What is the least number of moves it takes a knight to get from one corner of an $n\\times n$ chessboard, where $n\\ge 4$ , to the diagonally opposite corner?",
"role": "u... | math | {
"ground_truth": "f(n) = 2 \\left\\lfloor \\frac{n+1}{3} \\right\\rfloor",
"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 $|\\overrightarrow{a}|=2$, $|\\overrightarrow{b}|=3$, and the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $60^{\\circ}$, with $\\overrightarrow{c}... | math | {
"ground_truth": "k=-\\frac{29}{14}",
"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 $f(x)=\\sqrt{ax^2-3x+2}$, its domain is $\\{x|x < 1$ or $x > b\\}$.\n\n$(1)$ Find the values of $a$ and $b$; \n\n$(2)$ Solve the inequality $\\frac{x-c}{ax-b}... | math | {
"ground_truth": "\\text{When } c > 2: \\{x|x > c \\text{ or } x < 2\\}, \\text{When } c < 2: \\{x|x > 2 \\text{ or } x < c\\}, \\text{When } c=2: \\{x|x\\neq 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": "In \\( \\triangle PQR \\), point \\( T \\) is on side \\( QR \\) such that \\( QT = 4 \\) and \\( TR = 12 \\). What is the ratio of the area of \\( \\triangle PQT \\) to the area... | math | {
"ground_truth": "1:3",
"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": "The sum of the first $n$ terms of an arithmetic progression is given by the formula $3n + 4n^2$. What is the $r$th term of this progression?\n**A)** $7r + 1$ \n**B)** $8r + 1$ ... | math | {
"ground_truth": "8r - 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": "Let \\( S = \\{1, 2, \\ldots, 9\\} \\). Compute the number of functions \\( f: S \\rightarrow S \\) such that, for all \\( s \\in S \\), \\( f(f(f(s))) = s \\) and \\( f(s) - s \... | math | {
"ground_truth": "288",
"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": "$(1)$ Given $25x^{2}-36=0$, find the value of $x$;<br/>$(2)$ The two different square roots of a positive number $a$ are $x+2$ and $3x-10$, find the values of $x$ and $a$.",
... | math | {
"ground_truth": "a = 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": "On a checkerboard composed of 100 unit squares arranged in a 10x10 grid, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?\nA... | math | {
"ground_truth": "\\frac{16}{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": "How many 4-digit positive integers, which consist only of even digits, are divisible by either 5 or 3?\nA) 190\nB) 200\nC) 210\nD) 220",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(A) } 190",
"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 $f : \\mathbb{N} \\to \\mathbb{N}$ be a function such that the following conditions hold: $\\qquad\\ (1) \\; f(1) = 1.$ $\\qquad\\ (2) \\; \\dfrac{(x + y)}{2} < f(x + y) \... | math | {
"ground_truth": "1012",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is $120 \\div 5 \\div 2 \\div 3$?",
"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": "If the real coefficient polynomial \\( f(x) = x^4 + (a-1)x^2 + 1 \\) is non-negative for all real numbers \\( x \\), determine the range of values for \\( a \\).",
"role": "u... | math | {
"ground_truth": "a \\geqslant -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": "Calculate the value in simplest form of the following expression given $x \\neq 2$, $y \\neq 3$, and $z \\neq 4$:\n\\[\\frac{x-2}{4-z} \\cdot \\frac{y-3}{2-x} \\cdot \\frac{z-4}{... | math | {
"ground_truth": "A) -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": "Samantha gets up at 7:00 a.m., catches the school bus at 8:00 a.m. and arrives home at 5:30 p.m. Given that she has 7 classes that last 45 minutes each, has 45 minutes for lunch,... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the endpoint $Q$ of line segment $PQ$ has coordinates $(4,3)$, and the endpoint $P$ moves on the circle $({(x+1)}^{2}+{{y}^{2}}=4)$, find the trajectory equation of th... | math | {
"ground_truth": "{\\left(x- \\frac{3}{2}\\right)}^{2}+{\\left(y- \\frac{3}{2}\\right)}^{2}=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": "Suppose $h(x)$ and $k(x)$ are two functions defined on $\\mathbb{R}$ such that the range of $h$ is $[-3, 5]$ and the range of $k$ is $[-1, 4]$. Determine the maximum possible val... | math | {
"ground_truth": "20",
"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 a country, there are $28$ cities and between some cities there are two-way flights. In every city there is exactly one airport and this airport is either small or medium or ... | math | {
"ground_truth": "286",
"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 an isosceles right triangle \\( \\triangle ABC \\) where the area of an inscribed square in diagram (1) is \\( 441 \\mathrm{~cm}^2 \\), find the area of another inscribed s... | math | {
"ground_truth": "392",
"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 parallelogram ABCD, the length of BC is 12 and the height from A to BC is 10. Points E and F are on BC such that BE = 5 and CF = 3. Compute the area of the shaded region DEFBC... | math | {
"ground_truth": "80",
"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": "If $-3 \\le x < \\frac{3}{2}$ and $x \\ne 1$ , define $C(x) = \\frac{x^3}{1 - x}$ . The real root of the cubic $2x^3 + 3x - 7$ is of the form $p C^{-1}(q)$ , where $p$ ... | math | {
"ground_truth": "(p, q) = \\left(\\frac{7}{3}, \\frac{27}{98}\\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": "Joann rides her bike at an average speed of 15 miles per hour for 5 hours. To travel the same distance as Joann, Fran rides her bike for 4 hours. At what average speed, in miles ... | math | {
"ground_truth": "18.75 \\text{ mph}",
"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 equilateral $\\triangle ABC$ let points $D$ and $E$ trisect $\\overline{BC}$ . Then $\\sin \\left( \\angle DAE \\right)$ can be expressed in the form $\\tfrac{a\\sq... | math | {
"ground_truth": "20",
"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 triangular section with side lengths DB=EB=2 is cut from an equilateral triangle ABC with a side length of 5. Calculate the perimeter of the remaining quadrilateral.",
"rol... | math | {
"ground_truth": "13",
"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": "Execute the following program: \n```\nINPUT a \ni=1 \nDO \na=2*a-1 \ni=i+1 \nLOOP UNTIL i>10 \nPRINT a|END\n``` \nIf the input value of $a$ is from the first ten positiv... | math | {
"ground_truth": "0.2",
"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": "Three flower beds, X, Y, and Z, contain X = 600, Y = 480, and Z = 420 plants, respectively. The plants are shared as follows: Beds X and Y share 60 plants, Beds Y and Z share 70 ... | math | {
"ground_truth": "1320",
"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 lengths of the three sides $a, b, c$ with $a \\le b \\le c$ , of a right triangle is an integer. Find all the sequences $(a, b, c)$ so that the values of perimeter and a... | math | {
"ground_truth": "(5, 12, 13)",
"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 right triangle has sides $ka$, $lb$, and hypotenuse $c$. If $k$ and $l$ are positive constants, find the largest possible value of\n\\[\\frac{ka + lb}{c}.\\]",
"role": "use... | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( f(x) = 3x - 3 \\) and \\( g(x) = x^2 + 1 \\). What is the value of \\( f(1 + g(2)) \\)?",
"role": "user"
}
] | math | {
"ground_truth": "15",
"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": "Calculate the product of the 10 factors $\\Big(1 - \\frac{1}{2}\\Big)\\Big(1 - \\frac{1}{3}\\Big)\\Big(1 - \\frac{1}{4}\\Big)\\cdots\\Big(1 - \\frac{1}{11}\\Big)$.",
"role": ... | math | {
"ground_truth": "\\frac{1}{11}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Fluffy the rabbit ate twice as many carrots each day from April 1st to April 3rd, and a total of 84 carrots over these three days, calculate the number of carrots Fluf... | math | {
"ground_truth": "48",
"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": "How many strings of ones and zeroes of length 10 are there such that there is an even number of ones, and no zero follows another zero?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the random variable $X$ follow a binomial distribution $X \\sim B\\left(5, \\frac{1}{2}\\right)$. Find the probability that the function $f(x)=x^{2}+4x+X$ has a root.",
"... | math | {
"ground_truth": "\\frac{31}{32}",
"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 $f(x) = e^x$, where $x \\in \\mathbb{R}$, and $g(x) = \\ln x$, where $x \\in (0, +\\infty)$.\n\n(I) If the line $y = kx + 2$ is tangent to the graph of $g(x)$,... | math | {
"ground_truth": "\\frac{f(a) + f(b)}{2} > \\frac{f(b) - f(a)}{b - a}",
"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\n\\[\n\\cos \\left( 8 \\arccos \\frac{1}{5} \\right).\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-15647}{390625}",
"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": "How many solutions does the equation \\( \\cos \\left( \\frac{\\pi}{3} \\sin x \\right) = \\sin \\left( \\frac{\\pi}{3} \\cos x \\right) \\) have in the closed interval \\([0, \\... | math | {
"ground_truth": "\\textbf{(A) }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": "Find the integral \\(\\int \\frac{\\cos x}{\\sqrt{1+4 \\sin x}} d t\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2} \\sqrt{1 + 4 \\sin x} + C",
"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 supermarket sells Huashan brand water cups for $x$ yuan each. During the National Day promotion, the price was reduced by $5$ yuan for the first time. After selling for one d... | math | {
"ground_truth": "0.8(x - 5) = 60",
"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": "Place four balls numbered 1, 2, 3, and 4 into three different boxes, with at least one ball in each box. How many different arrangements are there where exactly one box contains ... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression $\\sqrt{4 + \\left (\\frac{x^3 - 2}{3x}\\right)^2}$.\n**A)** $\\frac{\\sqrt{x^6 + 36x^2}}{3x}$ \n**B)** $\\frac{\\sqrt{x^6 - 4x^3 + 36x^2 + 4}}{3x}$ \n*... | math | {
"ground_truth": "\\frac{\\sqrt{x^6 - 4x^3 + 36x^2 + 4}}{3x}",
"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": "If $\\triangle B_1B_2B_3$ is isosceles with angles $45^\\circ$, $45^\\circ$, and $90^\\circ$ at $B_1$ and $B_2$, respectively, and $B_{n+3}$ is defined as the midpoint of the seg... | math | {
"ground_truth": "45^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two concentric circles have the same center \\(C\\). The radius of the larger circle is \\(12\\) and the radius of the smaller circle is \\(7\\). Determine the area of the ring b... | math | {
"ground_truth": "95\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse $\\Gamma$: $\\frac{{{x^2}}}{{{a^2}}}+\\frac{{{y^2}}}{{{b^2}}}=1(a>b>0)$, there is a point $P(1,1)$ inside the ellipse. Two lines $l_{1}$ and $l_{2}$ passing thro... | math | {
"ground_truth": "\\frac{\\sqrt{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": "Determine how many positive divisors are shared by the numbers 9240 and 8820.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Captain Zarnin of Planet Hvan has expanded his battle station and now has six job openings: Assistant Engineer, Weapons Maintenance, Field Technician, Radio Specialist, Navigatio... | math | {
"ground_truth": "3,\\!276,\\!000",
"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 sequence \\(y_1, y_2, y_3, \\dots\\) defined by\n\\begin{align*}\ny_1 &= \\sqrt[3]{2}, \\\\\ny_2 &= (\\sqrt[3]{2})^{\\sqrt[3]{2}},\n\\end{align*}\nand in general,\n\\[... | 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": "John, who is 16 years old, flips a fair coin whose sides are labeled 5 and 15. He then adds the number on the top of the flipped coin to the number he rolls on a standard die. Wh... | math | {
"ground_truth": "\\frac{1}{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": "For all integers $n$ greater than 1, define $a_n = \\dfrac{1}{\\log_n 5005}$. Calculate $b = a_3 + a_4 + a_5 + a_6$ and $c = a_{15} + a_{16} + a_{17} + a_{18} + a_{19}$. Find the... | math | {
"ground_truth": "-\\log_{5005} 3876",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $ x^{4} - 2^{ - y^{2} } x^{2} - \\left\\| x^{2} \\right\\| + 1 \\equal{} 0$, where $ \\left\\| a\\right\\|$ denotes the greatest integer not exceeding $ a$, find t... | math | {
"ground_truth": "2",
"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": "Determine the value of $y$ for any real number $x$ given the expression:\n\\[ y = \\sqrt{x^2 + 4x + 4} + \\sqrt{x^2 - 6x + 9} \\]\nA) \\( x + 1 \\)\nB) \\( |x+2| - |x-3| \\)\nC) ... | math | {
"ground_truth": "C) \\( |x+2| + |x-3| \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a two-digit positive integer $N$, determine how many have the property that the sum of $N$ and the number obtained by reversing the order of the digits of $N$ is a prime nu... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x^2-2(k+1)x+4$ is a perfect square, then the value of $k$ is.",
"role": "user"
}
] | math | {
"ground_truth": "-3 \\text{ or } 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": "A natural number not exceeding 10 is chosen at random. What is the probability that this number is a prime number?",
"role": "user"
}
] | math | {
"ground_truth": "0.4",
"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": "A small container with a volume of 24 $\\text{cm}^3$ holds 60 paperclips. Determine the number of paperclips a larger container can hold if its volume is 54 $\\text{cm}^3$.",
... | math | {
"ground_truth": "135",
"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 parabola with its vertex $V$ and focus $F$. Let there be a point $B$ on this parabola such that the distance $BF$ is 25 and $BV$ is 26. Determine the sum of all possib... | math | {
"ground_truth": "\\frac{50}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose 2012 reals are selected independently and at random from the unit interval $[0,1]$ , and then written in nondecreasing order as $x_1\\le x_2\\le\\cdots\\le x_{2012}$ . ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In acute triangle \\(ABC\\), let \\(D, E\\), and \\(F\\) be the feet of the altitudes from \\(A, B\\), and \\(C\\) respectively, and let \\(L, M\\), and \\(N\\) be the midpoints ... | math | {
"ground_truth": "\\frac{ZB}{ZC} = \\frac{AB^2}{AC^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": "Find all pairs of integers $(a,b)$ such that $n|( a^n + b^{n+1})$ for all positive integer $n$",
"role": "user"
}
] | math | {
"ground_truth": "\\{(0, 0), (-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": "At noon, the temperature in Minneapolis is $N$ degrees warmer than in St. Louis. By 6:00 PM on the same day, the temperature in Minneapolis has fallen by 9 degrees while the temp... | math | {
"ground_truth": "195",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the ellipse \\(x^{2} + 4(y - a)^{2} = 4\\) and the parabola \\(x^{2} = 2y\\) have a common point, determine the range of values for \\(a\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\left[-1, \\frac{17}{8}\\right]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that a cubic function with respect to $x$ , $f(x)=ax^3+bx^2+cx+d$ satisfies all of 3 conditions:\n\\[f(1)=1,\\ f(-1)=-1,\\ \\int_{-1}^1 (bx^2+cx+d)\\ dx=1\\].\n\nFind ... | math | {
"ground_truth": "\\frac{81}{128}",
"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": "$A$ and $B$ travel around an elliptical track at uniform speeds in opposite directions, starting from the vertices of the major axis. They start simultaneously and meet first aft... | math | {
"ground_truth": "720",
"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 entire graph of the function $f(x)$ is shown below ($f$ is only defined when $x$ is between $-4$ and $4$ inclusive). How many values of $x$ satisfy $f(f(x)) = 1$?\n\n[asy]\ni... | math | {
"ground_truth": "1",
"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": "Triangle $ABC$ has right angle at $B$ , and contains a point $P$ for which $PA = 10$ , $PB = 6$ , and $\\angle APB = \\angle BPC = \\angle CPA$ . Find $PC$ .\n\n[asy]\n... | math | {
"ground_truth": "33",
"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 right triangle has a side length of 30 inches and a hypotenuse of 34 inches. A second triangle is similar to the first and has a hypotenuse of 102 inches. Calculate the length ... | math | {
"ground_truth": "48 \\text{ 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": "Given that $ 2^{2004}$ is a $ 604$ -digit number whose first digit is $ 1$ , how many elements of the set $ S \\equal{} \\{2^0,2^1,2^2, \\ldots,2^{2003}\\}$ have a first di... | math | {
"ground_truth": "194",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the side length of a square is 5 cm, calculate the perimeter of the square.",
"role": "user"
}
] | math | {
"ground_truth": "20 \\, \\mathrm{cm}",
"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 smallest value of $x$ such that $5x^2 + 8x + 3 = 9$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-8 - 2\\sqrt{46}}{10}",
"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 designer has 3 fabric colors (red, green, and blue) he may use for a dress. Four different patterns and two types of sleeve lengths (short and long) are available for the dress... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A team of landscapers worked on a large and a small football field, and the area of the large field is twice the area of the small field. There were 6 more workers in the part of... | math | {
"ground_truth": "16",
"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": "For a real number $x,$ find the maximum value of\n\\[\n\\frac{x^4}{x^8 + 2x^6 + 4x^4 + 4x^2 + 16}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n \\geq 2$ be a natural number, and let $\\left( a_{1};\\;a_{2};\\;...;\\;a_{n}\\right)$ be a permutation of $\\left(1;\\;2;\\;...;\\;n\\right)$ . For any integer $k$ ... | math | {
"ground_truth": "2 \\leq n \\leq 8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $(x_1, y_1)$ be a point on the line $y = mx + k$ and $(x_2, y_2)$ be a point on the parabola $y = ax^2 + bx + c$. Given that $x_1 = p$ and $x_2 = q$, derive the distance betw... | math | {
"ground_truth": "|q - p|\\sqrt{1 + (aq^2 + bq + c - mp - k)^2/(q - p)^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": "Find the minimum value of $\\sqrt{x^2+y^2}$ given the constraints $3x+4y=24$ and $x \\geq 0$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{24}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Don has a container with $\\frac{1}{4}$ of a gallon of juice. His friend Steve drinks $\\frac{3}{4}$ of the juice in it. How many gallons of juice did Steve drink?",
"role": ... | math | {
"ground_truth": "\\frac{3}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $x^{2020}+y^2=2y$, find the number of ordered pairs of integers $(x, y)$ that satisfy the equation.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"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 set $A = \\{x \\in \\mathbb{R} | ax^2 - 3x + 2 = 0, a \\in \\mathbb{R}\\}$.\n\n(1) If $A$ is an empty set, find the range of values for $a$; \n(2) If $A$ contains only... | math | {
"ground_truth": "\\{a | a = 0 \\text{ or } a \\geq \\frac{9}{8}\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a_1(x+m)^4+a_2(x+m)^3+a_3(x+m)^2+a_4(x+m)+a_5=x^4$, let $m= \\int_{0}^{\\pi} (\\sin x - 1 + 2\\cos^2 \\frac{x}{2})dx$, then $a_2=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"... | math | {
"ground_truth": "-8",
"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": "There were electronic clocks on the International Space Station, displaying time in the format HH:MM. Due to an electromagnetic storm, the device started malfunctioning, and each... | math | {
"ground_truth": "11:48",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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