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": "A 10 × 10 grid is filled with numbers from 1 to 100 in a diagonal sweeping pattern towards the bottom-right corner. Find the sum of the smallest and the largest number in the las... | math | {
"ground_truth": "191",
"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": "An equilateral triangle has an area of $144\\sqrt{3}$ cm². If each side of the triangle is decreased by 5 cm, by how many square centimeters is the area decreased?",
"role": ... | math | {
"ground_truth": "53.75\\sqrt{3} \\text{ cm}^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": "Sandhya must save 35 files onto disks, each with 1.44 MB space. 5 of the files take up 0.6 MB, 18 of the files take up 0.5 MB, and the rest take up 0.3 MB. Files cannot be split ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A kitten, a rabbit, and a dog together weigh 30 pounds. The kitten and the rabbit together weigh exactly twice as much as the dog, and the kitten and the dog together weigh exact... | math | {
"ground_truth": "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": "Find the coefficient of the $x^3$ term in the expansion of $(1-x)^6(2-x)$.",
"role": "user"
}
] | math | {
"ground_truth": "-35",
"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 five-digit numbers are exactly divisible by 6, 7, 8, and 9?",
"role": "user"
}
] | math | {
"ground_truth": "179",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( p \\) and \\( q \\) be real numbers. One of the roots of the polynomial \\( x^3 + px + q = 0 \\) is \\( 2 + i \\sqrt{2} \\). Find \\( p + q \\).",
"role": "user"
}
... | math | {
"ground_truth": "14",
"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 $i$ as the imaginary unit, calculate the result of the complex number $\\left(1-i\\right)\\left(2-i\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "1-3i",
"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": "$3^3+3^3+3^3=$",
"role": "user"
}
] | math | {
"ground_truth": "3^4",
"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": "Let \\(a_{1}, a_{2}, a_{3}, \\ldots \\) be the sequence of all positive integers that are relatively prime to 75, where \\(a_{1}<a_{2}<a_{3}<\\cdots\\). (The first five terms of ... | math | {
"ground_truth": "3764",
"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": "If $x$ and $y$ are real numbers such that\n\\[ |x|-y = 5 \\qquad \\text{and} \\qquad |x|y - x^2 = -12, \\]\ndetermine the integer nearest to $x+y$.\nA) -6 \nB) -5 \nC) -1 \... | math | {
"ground_truth": "B) -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": "In the Cartesian coordinate system $xOy$, given three points $A\\left(0, \\frac{4}{3}\\right), B(-1,0), C(1,0)$, the distance from point $P$ to line $BC$ is the geometric mean of... | math | {
"ground_truth": "\\{0, \\pm \\frac{1}{2}, \\pm \\frac{2\\sqrt{34}}{17}, \\pm \\frac{\\sqrt{2}}{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 the equation of the circle with the minimum area that is tangent to the curve $y=\\frac{2}{x} (x > 0)$ and the line $2x+y+1=0$.",
"role": "user"
}
] | math | {
"ground_truth": "(x - 1)^2 + (y - 2)^2 = 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": "Given that $\\binom{18}{8}=43758$, $\\binom{18}{9}=48620$ and $\\binom{18}{10}=43758$, calculate $\\binom{20}{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "184756",
"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 circle of radius \\( r \\) is concentric with and outside a regular square of side length \\( 4 \\). What is the radius \\( r \\) such that the probability that two entire side... | math | {
"ground_truth": "C) \\( \\frac{8\\sqrt{3}}{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 the sequence \\(\\{x_n\\}\\) satisfying \\(x_0 = 0, x_{n+1} = x_n + a + \\sqrt{b^2 + 4ax_n}\\) for \\(n = 0, 1, 2, \\ldots\\), where \\(a\\) and \\(b\\) are given positive ... | math | {
"ground_truth": "x_n = a n^2 + b n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the quadratic equation $x^2 + 2mx + 3n = 0$, with roots $r_1$ and $r_2$. Determine the coefficients $p$ and $q$ for a new quadratic equation $x^2 + px + q = 0$ such that... | math | {
"ground_truth": "A) \\( p = 8m^3 - 18mn, q = 27n^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": "For every positive integer $ n$ determine the highest value $ C(n)$ , such that for every $ n$ -tuple $ (a_1,a_2,\\ldots,a_n)$ of pairwise distinct integers\r\n\r $ (n \\p... | math | {
"ground_truth": "n(n-1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two lines with slopes $\\frac{2}{3}$ and $\\frac{3}{2}$ intersect at the point $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$.",
"ro... | math | {
"ground_truth": "\\frac{171}{50}",
"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": "Define a sequence of positive integers $\\{a_n\\}$ through the recursive formula: $a_{n+1}=a_n+b_n(n\\ge 1)$ ,where $b_n$ is obtained by rearranging the digits of $a_n$ (in... | math | {
"ground_truth": "a_7 \\text{ cannot be a prime number}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of \\( y = \\frac{r(x)}{s(x)} \\) is given, where \\( r(x) \\) and \\( s(x) \\) are quadratic polynomials. It's known that there is a hole at \\( x = 4 \\), a zero at \... | 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 Madeline has 80 fair coins. She flips all the coins. Any coin that lands on tails is tossed again. Additionally, any coin that lands on heads in the first two tosses is als... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sample data: \n15 11 13 15 17 19 15 18 20 19 \n16 14 15 17 16 12 14 15 16 18 \nIf we create a frequency distribution table with an interval of 2, t... | 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": "Given the number $3150$, calculate the sum of its prime factors.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"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 maximum number of queens you could put on $2017 \\times 2017$ chess table such that each queen attacks at most $1$ other queen.",
"role": "user"
}
] | math | {
"ground_truth": "673359",
"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 fly is being chased by three spiders on the edges of a regular octahedron. The fly has a speed of $50$ meters per second, while each of the spiders has a speed of $r$ meter... | math | {
"ground_truth": "25",
"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 the $xy$-plane, the segment with endpoints $(-8,0)$ and $(32,0)$ is the diameter of a circle. If the point $(x, 20)$ is on the circle, then $x=$\nA) 10\nB) 12\nC) 14\nD) 16\nE... | math | {
"ground_truth": "B) 12",
"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": "Which of the following is the set of all perfect squares that can be written as sum of three odd composite numbers? $\\textbf{a)}\\ \\{(2k + 1)^2 : k \\geq \u0015 0\\}$ $\\textb... | math | {
"ground_truth": "\\{(2k + 1)^2 : k \\geq 3\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest whole number $b$ such that 125 can be expressed in base $b$ using only three digits?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the product of Kiana's age and the ages of her two older siblings is 256, and that they have distinct ages, determine the sum of their ages.",
"role": "user"
}
] | math | {
"ground_truth": "38",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The set of solutions to the inequality \\(\\log _{a}\\left(a-\\frac{x^{2}}{2}\\right)>\\log _{a}(a-x)\\) is \\(A\\), and \\(A \\cap \\mathbf{Z}=\\{1\\}\\). Determine the range of... | math | {
"ground_truth": "a \\in (1, +\\infty)",
"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": "Convex quadrilateral $ABCD$ has $AB = 9$ and $CD = 12$. Diagonals $AC$ and $BD$ intersect at $E$, $AC = 14$, and $\\triangle AED$ and $\\triangle BEC$ have equal areas. Find $AE... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $F$ be the focus of parabola $y^2=2px(p>0)$ , with directrix $l$ and two points $A,B$ on it. Knowing that $\\angle AFB=\\frac{\\pi}{3}$ , find the maximal value of $... | 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": "Find the number of sets of two or more consecutive positive integers whose sum is 156.\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B)}\\ 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": "Let the hyperbola $C$: $\\dfrac {x^{2}}{a^{2}} - \\dfrac {y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) have its left and right foci as $F_{1}$ and $F_{2}$, respectively. Suppose there exi... | math | {
"ground_truth": "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": "Find all pairs of natural numbers \\(a\\) and \\(b\\) such that \\(3^{a} + 4^{b}\\) is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 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": "The sum of the numerical coefficients in the complete expansion of $(x^2 - 2xy + y^2)^7$, calculate this sum.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "According to market research, the relationship between the selling price (in yuan) of a certain product in a supermarket and the time $t$ (in days) in the past month (30 days) is... | math | {
"ground_truth": "20200",
"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 minimum value of the function $$f(x)= \\frac {1}{ \\sqrt {x^{2}+2}}+ \\sqrt {x^{2}+2}$$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {3 \\sqrt {2}}{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": "Given that the sum of the first $n$ terms of the sequence $\\{a_{n}\\}$ is $S_{n}$, and the sequence $\\left\\{{\\frac{{{S_n}}}{n}}\\right\\}$ forms an arithmetic sequence with a... | math | {
"ground_truth": "397",
"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": "When Ringo, Paul, and George place their marbles into bags with 7 marbles per bag, and they have leftover marbles 2, 4, and 2 respectively, together with 5 marbles from Ringo, ca... | math | {
"ground_truth": "4",
"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 arithmetic mean of five numbers is 20. Three of the numbers are 22, 18, and 32, and the other two numbers are equal. What is the product of the two equal numbers?",
"role... | math | {
"ground_truth": "196",
"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": "Where are the points located in the plane for which the coordinates $(x, y)$ satisfy the inequality\n\n$$\n\\left(\\frac{x y+1}{x+y}\\right)^{2}<1?\n$$",
"role": "user"
}
] | math | {
"ground_truth": "-1 < x < 1 \\text{ and } (y < -1 \\text{ or } y > 1) \\text{ or } (x < -1 \\text{ or } x > 1) \\text{ and } -1 < y < 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": "Given the function f(x) = 1 + 2sin(2x - π/3).\n(1) Find the axis of symmetry and the center of symmetry.\n(2) Find the maximum and minimum values of f(x) when x ∈ [π/4, π/2].\n(3... | math | {
"ground_truth": "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": "Consider the system \\begin{align*}x + y &= z + u,2xy & = zu.\\end{align*} Find the greatest value of the real constant $m$ such that $m \\leq x/y$ for any positive integer ... | math | {
"ground_truth": "3 + 2\\sqrt{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": "Find the largest positive integer $m$ which makes it possible to color several cells of a $70\\times 70$ table red such that \n- There are no two red cells satisfying: the t... | math | {
"ground_truth": "32",
"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": "<u>Set 1</u>**p1.** Assume the speed of sound is $343$ m/s. Anastasia and Bananastasia are standing in a field in front of you. When they both yell at the same time, you hear A... | math | {
"ground_truth": "1715",
"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 $a_1, a_2, \\ldots$ and $b_1, b_2, \\ldots$ be arithmetic progressions such that $a_1 = 10, b_1 = 50$, and $a_{50} + b_{50} = 150$. Find the sum of the first fifty terms of t... | math | {
"ground_truth": "5205",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equations $2x + 7 = 3$ and $bx - 10 = -2$, find the value of $b$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"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": "Amy, Beth, and Jo listen to five different songs and discuss which ones they like. No song is liked by all three or disliked by all three. Furthermore, for each of the three pair... | math | {
"ground_truth": "**C)** 90",
"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": "Charles has three six-sided dice. One die is fair, the second die is biased so that it comes up six with probability $\\frac{2}{3}$ and each of the other five sides has probabili... | math | {
"ground_truth": "1803",
"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 $S_n$ and $T_n$ be the respective sums of the first $n$ terms of two arithmetic series. If $S_n:T_n=(7n^2+1):(4n^2+27)$ for all $n$, find the ratio of the fifteenth term of t... | math | {
"ground_truth": "\\frac{7}{4}",
"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 function $f(x) = 3\\sin x + \\cos x$ attains its maximum value when $x = \\alpha$, find the value of $\\tan 2\\alpha$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We call a graph with n vertices $k-flowing-chromatic$ if:\n1. we can place a chess on each vertex and any two neighboring (connected by an edge) chesses have different colors.\... | math | {
"ground_truth": "m = 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Connie performs an arithmetic operation on a number. She multiplies the number by 3 and then subtracts 10 getting 50 as her answer. However, she should have multiplied the number... | math | {
"ground_truth": "70",
"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 the sequence $\\left\\{a_{n}\\right\\}$ have a general term formula $a_{n} = n^2 + \\lambda n$ where $n \\in \\mathbf{N}_{+}$. If $\\left\\{a_{n}\\right\\}$ is a strictly inc... | math | {
"ground_truth": "\\lambda > -3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Approximate $2.534$ using rounding to the nearest hundredth, accurate to $0.01$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "2.53",
"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:<br/>$(1)-3^2+(-\\frac{1}{2})^2+(2023-π)^0-|-2|$;<br/>$(2)(-2a^{2})^{3}\\cdot a^{2}+a^{8}$;<br/>$(3)2023^{2}-2024\\times 2022.$ (Simplify the calculation)",
"role":... | 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": "Let $a,b,c$ be non-zero real numbers. The lines $ax + by = c$ and $bx + cy = a$ are perpendicular and intersect at a point $P$ such that $P$ also lies on the line $y=2... | math | {
"ground_truth": "\\left( - \\frac{3}{5}, - \\frac{6}{5} \\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": "David, Delong, and Justin each showed up to a problem writing session at a random time during the session. If David arrived before Delong, what is the probability that he also ar... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider $9$ points in space, no four of which are coplanar. Each pair of points is joined by an edge (that is, a line segment) and each edge is either colored blue or red or l... | 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": "Find all solutions to\n\\[\\sqrt[4]{60 - 3x} + \\sqrt[4]{20 + 3x} = 4.\\]",
"role": "user"
}
] | math | {
"ground_truth": "20, -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": "Using the digits 1, 2, 3, 5, 6, and 8 exactly once, form the smallest possible even five-digit number and determine the digit in the tens place.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sphere of radius $\\sqrt{85}$ is centered at the origin in three dimensions. A tetrahedron with vertices at integer lattice points is inscribed inside the sphere. What is the... | math | {
"ground_truth": "243",
"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": "How many zeros does $f(x) = \\cos(x^2)$ have on the interval $-2\\pi < x < 2\\pi$?\nA) 10 \nB) 25 \nC) 50 \nD) 15 \nE) Infinitely many",
"role": "user"
}
] | math | {
"ground_truth": "The final answer is B) 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": "Consider a function $f:\\mathbb{R} \\to \\mathbb{R}$ . Given that $f(0)=0$ . $\\lim_{x\\to0} \\frac{f(h)}{h}=7$ , and $f(x+y)=f(x)+f(y)+3xy$ for all $x,y\\in{\\mathbb{R}}$ ... | math | {
"ground_truth": "122.5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest positive integer $n$ such that $23n \\equiv 456 \\pmod{13}?$",
"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": "Using $n^{3}$ unit cubes, a cube with edge length $n$ is formed $(n \\in \\mathbf{N}, n \\geqslant 2)$. Find the maximum number of unit cubes that a single line can pass through.... | math | {
"ground_truth": "3n - 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": "Two dimensions of a cube are increased by $2$ and one dimension is decreased by $3$. The volume of the new rectangular solid is $19$ more than that of the cube. Find the volume o... | math | {
"ground_truth": "(4 + \\sqrt{47})^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": "Evaluate $\\left(\\sqrt{(\\sqrt{5})^4}\\right)^3$.",
"role": "user"
}
] | math | {
"ground_truth": "125",
"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 solution set of $6x^2+5x<4$ is the set of all values of $x$ such that the inequality $6x^2+5x<4$ is satisfied.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{3} < x < \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let\n\\[ g(x) = (\\arccos x)^2 + (\\arcsin x)^2. \\]\nFind the range of $g(x)$ for all $x \\in [-1,1]$. All functions are in radians.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[\\frac{\\pi^2}{8}, \\frac{\\pi^2}{4}\\right]",
"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 John drove 120 miles in 2 hours, with average speeds of 50 mph for the first 40 minutes and 60 mph for the next 40 minutes, calculate his average speed during the last... | math | {
"ground_truth": "70",
"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 sequence of positive integers $a_1, a_2, a_3, \\dots, a_{n}$ , define the \\emph{power tower function} \\[f(a_1, a_2, a_3, \\dots, a_{n})=a_1^{a_2^{a_3^{\\mathstrut^{ .^... | math | {
"ground_truth": "4983",
"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 $S$ be the set of integers of the form $2^x+2^y+2^z$ , where $x,y,z$ are pairwise distinct non-negative integers. Determine the $100$ th smallest element of $S$ .",
... | math | {
"ground_truth": "577",
"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 Ms. Li places all integers from 1 to 289 into a 17 × 17 grid, she places 1 in the middle square (ninth row and ninth column) and places other numbers one by one clockwise. ... | math | {
"ground_truth": "528",
"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 equation of a parabola is \\( y^2 - 4y + 2x + 9 = 0 \\). Find the vertex of the parabola.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(-\\frac{5}{2}, 2\\right)",
"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 product $\\left(1-\\frac{1}{3^{2}}\\right)\\left(1-\\frac{1}{4^{2}}\\right)\\ldots\\left(1-\\frac{1}{8^{2}}\\right).$\nA) $\\frac{1}{2}$\nB) $\\frac{3}{4}$\nC) $\\fr... | math | {
"ground_truth": "\\textbf{(B)}\\ \\frac{3}{4}",
"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": "What is the angle of inclination of the line $x - \\sqrt{3}y + 3 = 0$?",
"role": "user"
}
] | math | {
"ground_truth": "30^{\\circ}",
"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 $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ such that for all real numbers $x$ and $y$ satisfies, $$ 2+f(x)f(y)\\leq xy+2f(x+y+1). $$",
"role": "user"
... | math | {
"ground_truth": "f(x) = x + 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": "$\\dfrac{13!-12!}{10!}$",
"role": "user"
}
] | math | {
"ground_truth": "1584",
"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 interval in which the zero of the function $f(x)=3^{x}+5x$ is located.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\frac{1}{5},0)",
"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 number of significant digits in the measurement of the side of a rectangle whose computed area is $0.07344$ square meters to the nearest hundred-thousandth of a square meter ... | math | {
"ground_truth": "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": "Let $R$ be the set of all possible remainders when a number of the form $3^n$, where $n$ is a nonnegative integer, is divided by 500. Let $S$ be the sum of all elements in $R$. D... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three fair coins are to be tossed once. For each head that results, one fair die is to be rolled. Calculate the probability that the sum of the die rolls is odd.",
"role": "u... | math | {
"ground_truth": "\\frac{7}{16}",
"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 poles, one 30 inches high and another 50 inches high, are 120 inches apart. Determine the height of the intersection of the lines joining the top of each pole to the foot of ... | math | {
"ground_truth": "18.75",
"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 focus of the parabola $x = -\\frac{1}{8} y^2.$",
"role": "user"
}
] | math | {
"ground_truth": "\\left( \\frac{1}{2}, 0 \\right)",
"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 $y = -x^2 + 2x + 8$ and $x$ is a real number, then what is the maximum value possible for $y$?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The degree measures of the angles of nondegenerate hexagon $ABCDEF$ are integers that form a non-constant arithmetic sequence in some order, and $\\angle A$ is the smallest a... | math | {
"ground_truth": "1500^\\circ",
"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": "Four friends share 12 identical pencils and each one has at least two pencils. In how many ways can this happen?",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There exist unique positive integers $x$ and $y$ that satisfy the equation $x^2 + 84x + 2008 = y^2$. Find $x + y$.",
"role": "user"
}
] | math | {
"ground_truth": "80",
"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": "7. Peggy picks three positive integers between $1$ and $25$ , inclusive, and tells us the following information about those numbers:\n\n\n- Exactly one of them is a multiple o... | math | {
"ground_truth": "126",
"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 small sphere with a radius of 1 is free to move in any direction inside a tetrahedral container with an edge length of \\(4 \\sqrt{6}\\). Determine the area of the container's ... | math | {
"ground_truth": "108 \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a \\odot b = a^2 + \\sqrt{b + \\sqrt{b + \\sqrt{b + ...}}}$ for $a, b \\geq 0$. If $4 \\odot g = 20$, find the value of $g$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Evaluate the expression: $2^4 \\times 2^2 + 2^4 \\div 2^2$.",
"role": "user"
}
] | math | {
"ground_truth": "68",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the line $l$: $\\begin{cases} x=a+t\\sin \\alpha \\\\ y=b+t\\cos \\alpha \\end{cases}(t$ is a parameter$)$\n(1) When $\\alpha= \\frac {\\pi}{3}$, find the slope of the line... | math | {
"ground_truth": "x^{2}+y^{2}=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 line $l$ passes through the focus $F$ of the parabola $y^{2}=ax(a > 0)$ and intersects the parabola at points $A$ and $B$. Calculate the value of $\\dfrac {|AF|\\cdot |BF|}{|AF... | math | {
"ground_truth": "\\dfrac {a}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of sequences of 0s and 1s of length $n$ containing the block 01 exactly $m$ times.",
"role": "user"
}
] | math | {
"ground_truth": "\\binom{n + 1}{2m + 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": "From one vertex of a parallelepiped - let this be $O$ - consider the 3 edge vectors denoted by $a$, $b$, and $c$. Find the midpoints of the three faces passing through the opposi... | math | {
"ground_truth": "\\mathbf{s}= \\frac{2}{3}(\\mathbf{a} + \\mathbf{b} + \\mathbf{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": "A $23 \\times 23$ square is tiled with $1 \\times 1, 2 \\times 2$ and $3 \\times 3$ squares. What is the smallest possible number of $1 \\times 1$ squares?",
"role": ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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