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": "There are $15$ people, including Petruk, Gareng, and Bagong, which will be partitioned into $6$ groups, randomly, that consists of $3, 3, 3, 2, 2$ , and $2$ people (orders... | math | {
"ground_truth": "\\frac{3}{455}",
"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 $m$ be a positive integer. Find the number of real solutions of the equation $$ |\\sum_{k=0}^{m} \\binom{2m}{2k}x^k|=|x-1|^m $$",
"role": "user"
}
] | math | {
"ground_truth": "m-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": "α is a fixed real number. Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) (where \\( \\mathbb{R} \\) is the reals) which are continuous, have a continuous derivative, ... | math | {
"ground_truth": "\\begin{array}{rl}\n1. & \\alpha = 0 \\rightarrow \\text{No solutions} \\\\\n2. & \\alpha < 0 \\rightarrow \\text{No solutions} \\\\\n3. & \\alpha = 1 \\rightarrow \\text{Any } f(x) \\text{ with continuous derivative} \\\\\n4. & \\alpha > 0 \\text{ (not } \\frac{p}{q}\\text{, both odd)} \\rightarro... | {
"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 ordered triplets $(p,q,r)$ of positive integers such that $p$ and $q$ are two (not necessarily distinct) primes, $r$ is even, and \n\\[p^3+q^2=4r^2+45r+103.\\]",... | math | {
"ground_truth": "(7, 2, 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": "Calculate the value for the expression $\\sqrt{25\\sqrt{15\\sqrt{9}}}$.",
"role": "user"
}
] | math | {
"ground_truth": "5\\sqrt{15}",
"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 function $f(x)= \\sqrt {3}(\\sin ^{2}x-\\cos ^{2}x)+2\\sin x\\cos x$.\n(I) Find the smallest positive period of $f(x)$;\n(II) If $x\\in\\[- \\frac {π}{3}, \\frac {π}{3}... | math | {
"ground_truth": "\\left[-\\frac{\\pi}{12},\\frac{\\pi}{3}\\right]",
"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 expression $48! + 49! + 50!$, evaluate the largest integer $n$ for which $5^n$ is a factor of this expression.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"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 the non-decreasing sequence of positive integers $1,2,2,3,3,3,4,4,4,4,5,5,5,5,\\cdots$ in which the $n^{th}$ positive integer appears $n$ times. Calculate the remainder ... | math | {
"ground_truth": "3",
"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 that $|\\vec{a}|=1, |\\vec{b}|=1,$ the angle between $\\vec{a}$ and $\\vec{b}$ is $\\frac{\\pi}{3}$, $\\vec{x}=2 \\vec{a}-\\vec{b}$, $\\vec{y}=3 \\vec{b}-\\vec{a}$, find th... | math | {
"ground_truth": "-\\frac{3}{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 center of the circle with the equation $4x^2 - 8x + 4y^2 - 16y + 20 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 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": "If 7500 yen equals 65 dollars, find the number of yen the tourist will receive for 40 dollars.",
"role": "user"
}
] | math | {
"ground_truth": "4615",
"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 the equation $2kx^2-2x-3k-2=0$ with two real roots, one is less than 1 and the other is greater than 1, the range of the real number $k$ is.",
"role": "user"
}
] | math | {
"ground_truth": "k < -4 \\text{ or } k > 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 mean (average) height of a group of children would be increased by 6 cm if 12 of the children in the group were each 8 cm taller. Find the number of children in the group.",
... | 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": "Given a line passing through points $\\begin{pmatrix} -3 \\\\ 2 \\end{pmatrix}$ and $\\begin{pmatrix} 2 \\\\ -3 \\end{pmatrix}$, find the value of $b$ such that the line's direct... | 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": "For how many integers $x$ is the number $x^4 - 55x^2 + 54$ negative?\nA) 8\nB) 10\nC) 12\nD) 14\nE) 16",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(C)}\\ 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": "Let $k, a_2, a_3$ and $k, b_2, b_3$ be two distinct nonconstant geometric sequences with different common ratios. It is given that $$a_3 - b_3 = 5(a_2 - b_2).$$ Find the sum of t... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the coefficient of \\( x^4 \\) when the expression \\( 4(x^4 - 2x^3 + x^2) + 2(3x^4 + x^3 - 2x^2 + x) - 6(2x^2 - x^4 + 3x^3) \\) is simplified.",
"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": "A function $g: \\mathbb{Z} \\to \\mathbb{Z}$ is called adjective if $g(m)+g(n)>max(m^2,n^2)$ for any pair of integers $m$ and $n$ . Let $f$ be an adjective function such... | math | {
"ground_truth": "498",
"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": "Insert \\( n \\) real numbers between 1 and 100 such that these \\( n+2 \\) numbers form an increasing geometric sequence. Let the product of these \\( n+2 \\) numbers be denoted... | math | {
"ground_truth": "\\frac{\\tan (n+3) - \\tan 3}{\\tan 1} - 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": "A regular hexagon $ABCDEF$ with side length 2 is given. Two circles are positioned outside the hexagon. The first circle is tangent to line $\\overline{AB}$ and the second circle... | 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": "Given the parabola $y=-x(x+2)$, translate it $2$ units to the right, then $3$ units down and find its equation.",
"role": "user"
}
] | math | {
"ground_truth": "y=-\\left(x-1\\right)^{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": "Parameterize the line segment connecting points $(1,3)$ and $(4,9)$ with equations $x = at + b$, $y = ct + d$ where $t = 0$ corresponds to $(1,3)$ and $t = 1$ corresponds to $(4,... | math | {
"ground_truth": "55",
"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 another experimental determination, a scientific constant $K$ is observed to be $3.71729$ with a margin of error of $\\pm 0.00247$. \nAn experimenter wishes to publish the val... | math | {
"ground_truth": "\\textbf{(C)}\\ 3.7",
"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": "Given vectors $a$, $b$, and $c$ that satisfy $|a|=1$, $|b|=2$, $c=a+b$, and $c \\perp a$, find the angle between $a$ and $b$.",
"role": "user"
}
] | math | {
"ground_truth": "120^{\\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": "A man commutes between work and home using either the train or the bus, with the following rules: if he takes the train to work in the morning, he takes the bus home in the after... | math | {
"ground_truth": "\\textbf{(C)}\\ 23",
"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 $S$ be the set of all positive integers between 1 and 2017, inclusive. Suppose that the least common multiple of all elements in $S$ is $L$ . Find the number of elements... | math | {
"ground_truth": "44",
"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 we write 0 in the first column, then we have to write 1 in the second column. Similarly, we have to write 0 in the third column and 1 in the fourth column, and so on.",
"r... | math | {
"ground_truth": "198",
"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 function f(x) = |x - 1|.\n\n1. Find the solution set of the inequality f(x) < x + |x + 1|.\n2. If the domain of the function g(x) = log₂[f(x + 3) + f(x) - 2a] is R, fin... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the set $S = \\{1, 2, \\cdots, 50\\}$. $X$ is any subset of $S$ and $|X| = n$. Find the smallest positive integer $n$ such that the subset $X$ must contain three numbers that... | math | {
"ground_truth": "42",
"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 $S=\\{(x,y) : x\\in \\{0,1,2,3\\}, y\\in \\{0,1,2,3\\},\\text{ and } (x,y)\\ne (2,2)\\}$. Let $T$ be the set of all right triangles whose vertices are in $S$. For every right... | 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": "Given points $M(-2,7)$ and $N(10,-2)$, point $P$ lies on segment $MN$ and $\\overrightarrow{PN}=-2 \\overrightarrow{PM}$. Determine the coordinates of point $P$.",
"role": "u... | math | {
"ground_truth": "(2,4)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point $Q$ is chosen in the interior of $\\triangle DEF$ such that when lines are drawn through $Q$ parallel to the sides of $\\triangle DEF$, the resulting smaller triangles $u... | math | {
"ground_truth": "1155",
"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": "Each of two boxes contains both black and white marbles, and the total number of marbles in the two boxes is $25.$ One marble is taken out of each box randomly. The probability... | math | {
"ground_truth": "61",
"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 each of $m$ distinct points on the positive part of the $x$ -axis be joined to $n$ distinct points on the positive part of the $y$ -axis. Obtain a formula for the numbe... | math | {
"ground_truth": "\\frac{mn(m-1)(n-1)}{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": "Divide a cube with edge length of $3 \\mathrm{~cm}$ into $n$ smaller cubes, where the smaller cubes do not all have the same volume and have edge lengths that are whole centimete... | math | {
"ground_truth": "20",
"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 arithmetic mean of the prime numbers in this list: 34, 37, 39, 41, 43.",
"role": "user"
}
] | math | {
"ground_truth": "40.33",
"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 sets $A=\\{x|y=ln(x-2)\\}$ and $B=\\{y|y=\\sqrt{x}+4\\}$, find $A\\cap B$.",
"role": "user"
}
] | math | {
"ground_truth": "[4, +\\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": "Let $a + 2 = b + 3 = c + 4 = d + 5 = a + b + c + d + 6$. Calculate the value of $a + b + c + d$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{10}{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": "A right cylinder and a right cone have equal bases and heights. Their lateral surface areas are in the ratio $8:5$. The area of the axial cross-section of the cone is $588 \\math... | math | {
"ground_truth": "m = 28 \\, \\text{cm} \\text{ and } r = 21 \\, \\text{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": "Let \\(\\mathbf{a} = \\begin{pmatrix} 4 \\\\ -7 \\\\ 2 \\end{pmatrix}\\), \\(\\mathbf{b} = \\begin{pmatrix} -2 \\\\ 3 \\\\ -1 \\end{pmatrix}\\), and \\(\\mathbf{c} = \\begin{pmat... | math | {
"ground_truth": "-66",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$ be a point on the parabola $y = x^2 - 4x + 4,$ and let $B$ be a point on the line $y = 2x - 3.$ Find shortest possible distance $AB.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2\\sqrt{5}}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In each cell of an \\( n \\times m \\) table, there is a number one. It is allowed to take any \\( 2 \\times 2 \\) square and change the signs of all the numbers in it. Is it pos... | math | {
"ground_truth": "n \\text{ and } m \\text{ are simultaneously divisible by 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 sequence is defined by $b_1=b_2=b_3=1$, and for all integers $n \\geq 1$, $b_{n+3} = b_{n+2} + b_{n+1} + b_n$. Given that $b_{28}= 6090307$, $b_{29}=11201821$, and $b_{30}=2060... | math | {
"ground_truth": "45127216 \\mod 500 = 216",
"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 sequence $\\{a_n\\}$ whose sum of the first $n$ terms $S_n$ satisfies: $S_n + S_m = S_{n + m}$, and $a_1 = 1$, calculate the value of $a_{10}$.",
"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 fourth term of the geometric progression with first three terms $\\sqrt 3$, $\\sqrt[3]3$, and $\\sqrt[6]3$ can be calculated.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A=\\{1,2,\\ldots, 2006\\}$ . Find the maximal number of subsets of $A$ that can be chosen such that the intersection of any 2 such distinct subsets has 2004 elements.",
... | math | {
"ground_truth": "2006",
"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 an odd function \\( f(x) \\) satisfies the condition \\( f(x+3) = f(x) \\). When \\( x \\in [0,1] \\), \\( f(x) = 3^x - 1 \\). Find the value of \\( f\\left(\\log_1 36... | math | {
"ground_truth": "-\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in rectangle ABCD, point E is the midpoint of side AD and point G is one-third the length of side CD from point C, and the area of rectangle ABCD is 108 square meters,... | math | {
"ground_truth": "27",
"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 $P(x)$ is a degree $n$ monic polynomial with integer coefficients such that $2013$ divides $P(r)$ for exactly $1000$ values of $r$ between $1$ and $2013$ ... | math | {
"ground_truth": "50",
"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 sum of all $x$ such that $1\\leq x\\leq 99$ and \\[\\{x^2\\}=\\{x\\}^2.\\] Compute $\\lfloor S\\rfloor$ .",
"role": "user"
}
] | math | {
"ground_truth": "68294",
"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 function $f(x)=ax^{3}+b\\sin x+4$ $(a,b\\in\\mathbb{R})$, and $f(\\lg (\\log _{2}10))=5$, find the value of $f(\\lg (\\lg 2))$.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the expansion of ${(\\sqrt{x}+\\frac{2}{x^2})^{10}}$, the constant term is ____.",
"role": "user"
}
] | math | {
"ground_truth": "180",
"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 you have $27$ identical unit cubes colored such that $3$ faces adjacent to a vertex are red and the other $3$ are colored blue. Suppose further that you assemble th... | math | {
"ground_truth": "53",
"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 column of infantry stretched out over 1 km. Sergeant Kim, riding on a hoverboard from the end of the column, reached its front and returned to the end. During this time, the in... | math | {
"ground_truth": "3.6 \\text{ km}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a non-empty subset A of the set of integers, A is said to possess property M if the following conditions are satisfied: ① There exists a $k \\in A$ such that $k+1 \\in A$; ... | math | {
"ground_truth": "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": "How many multiples of 4 are between 70 and 300?",
"role": "user"
}
] | math | {
"ground_truth": "57",
"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": "Randy drove the first third of his trip on a gravel road, the next $20$ miles on pavement, and the remaining one-fifth on a dirt road. Let x be the total length of Randy's trip i... | math | {
"ground_truth": "\\frac{300}{7}",
"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 is a parallelogram $ABCD$ , with $AB <AC <BC$ . Points $E$ and $F$ are selected on the circumcircle $\\omega$ of $ABC$ so that the tangenst to $\\omega$ at the... | math | {
"ground_truth": "60^\\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": "Given the definition of a matrix transformation from vector $\\overrightarrow{OP\\_n} = (x\\_n, y\\_n)$ to vector $\\overrightarrow{OP_{n+1}} = (x_{n+1}, y_{n+1})$ as follows:\n\... | math | {
"ground_truth": "(2, 4030)",
"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 that $\\triangle{ABC}$ is an equilateral triangle of side length $s$, with the property that there is a unique point $P$ inside the triangle such that $AP=1$, $BP=\\sqrt{... | math | {
"ground_truth": "\\sqrt{7}",
"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": "In the following alpha-numeric puzzle, each letter represents a different non-zero digit. What are all possible values for $b+e+h$ ?\n\n $ \\begin{tabular}{cccc} &a&b&c &d&e&f... | math | {
"ground_truth": "15",
"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 order of the three numbers 20.3, 0.32, and $\\log{0.32}$ must be determined.",
"role": "user"
}
] | math | {
"ground_truth": "\\log{0.32} < 0.32 < 20.3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Place each of the digits 7, 8, 9, and 0 in exactly one square to make the smallest possible product. What is this product?",
"role": "user"
}
] | math | {
"ground_truth": "623",
"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 cube \\( A B C D - A_{1} B_{1} C_{1} D_{1} \\), let the points \\( P \\) and \\( Q \\) be the reflections of vertex \\( A \\) with respect to the plane \\( C_{1} B D \\) and... | math | {
"ground_truth": "\\frac{\\sqrt{15}}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2,000,000,000,000 - 1,111,111,111,111$ is subtracted and then multiplied by 2. Calculate the result.",
"role": "user"
}
] | math | {
"ground_truth": "1,777,777,777,778",
"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 $m, n \\in \\mathbb{R}$. If the line $l: mx + ny - 1 = 0$ intersects the x-axis at point A and the y-axis at point B, and the chord formed by the intersection of $l$ with the... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Paul owes Paula $60$ cents and has a pocket full of $5$-cent coins, $10$-cent coins, $25$-cent coins, and $50$-cent coins that he can use to pay her. Calculate the difference bet... | math | {
"ground_truth": "10",
"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 $f(x+4)+f(x-4) = f(x)$ for all real $x$, find the least common positive period $p$ of all such functions $f$.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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": "A projection takes \\(\\begin{pmatrix} 2 \\\\ -3 \\end{pmatrix}\\) to \\(\\begin{pmatrix} 1 \\\\ -\\frac{3}{2} \\end{pmatrix}\\). Which vector does the projection take \\(\\begin... | math | {
"ground_truth": "\\begin{pmatrix} \\frac{18}{13} \\\\ -\\frac{27}{13} \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ and $b$ be two-digit positive integers. Find the greatest possible value of $a+b$ , given that the greatest common factor of $a$ and $b$ is $6$ .\n\n*Proposed b... | math | {
"ground_truth": "186",
"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 sum of every third odd number between $100$ and $300$?",
"role": "user"
}
] | math | {
"ground_truth": "6800",
"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": "Starting from 37, adding 5 before each previous term, forms the following sequence:\n\\[37,537,5537,55537,555537,...\\]\nHow many prime numbers are there in this sequence?",
... | 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": "Determine all positive integers $n$ such that $4k^2 +n$ is a prime number for all non-negative integer $k$ smaller than $n$ .",
"role": "user"
}
] | math | {
"ground_truth": "n = 3, 7",
"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 positive number $b$ is selected such that the terms $30, b, \\frac{9}{4}$ are the first, second, and third terms, respectively, of a geometric sequence. Determine the value o... | math | {
"ground_truth": "8.215838362",
"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 equation of the tangent line to the function $f(x)=2\\ln x+x^{2}$ at $x=1$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "4x-y-3=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 product of two 999-digit numbers $400400400...\\text{(300 times)}...400$ and $606606606...\\text{(300 times)}...606$ has tens digit \\( A \\) and units digit \\( B \\). What ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ defined on $[0,+\\infty)$ satisfies $f(x+1)=2f(x)$, and when $x\\in[0,1)$, $f(x)=-x^{2}+x$. Let $a_{n}$ denote the maximum value of $f(x)$ on $[n-1... | 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 the greatest integer $n < 1000$ for which $4n^3 - 3n$ is the product of two consecutive odd integers.",
"role": "user"
}
] | math | {
"ground_truth": "899",
"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": "Jon and Steve ride their bicycles along a path that parallels two side-by-side train tracks running the east/west direction. Jon rides east at $20$ miles per hour, and Steve ride... | math | {
"ground_truth": "49",
"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": "The natural number $a_n$ is obtained by writing together and ordered, in decimal notation , all natural numbers between $1$ and $n$ . So we have for example that $a_1 = 1$ ... | math | {
"ground_truth": "n \\equiv 1 \\pmod{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": "A chord perpendicular to the diameter of a circle divides it in the ratio $1: 3$. At what angles is the chord visible from the ends of this diameter?",
"role": "user"
}
] | math | {
"ground_truth": "60^\\circ, 120^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sara lists the whole numbers from 1 to 50. Lucas copies Sara's numbers, replacing each occurrence of the digit '3' with the digit '2'. Calculate the difference between Sara's sum... | math | {
"ground_truth": "105",
"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 $\\lceil{\\sqrt{x}}\\rceil=20$, how many possible integer values of $x$ are there?",
"role": "user"
}
] | math | {
"ground_truth": "39",
"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 ellipse $\\dfrac{x^2}{a^2} + \\dfrac{y^2}{b^2} = 1$ $(a > b > 0)$, the symmetric point $Q$ of the right focus $F(c, 0)$ with respect to the line $y = \\dfrac{b}{c}x$ is... | math | {
"ground_truth": "\\dfrac{\\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": "What number, when added to ten times its square root, equals 39?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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 point B is the projection of point A(1, 2, 3) on the yOz coordinate plane, and O is the origin of the coordinates, find the value of |OB|.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{13}",
"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": "What is the minimum number of digits to the right of the decimal point needed to express the fraction $\\frac{987654321}{2^{15} \\cdot 5^7}$ as a decimal?",
"role": "user"
... | math | {
"ground_truth": "15",
"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 teacher states, \"If a whole number \\( n \\) is not prime, then neither \\( n-2 \\) nor \\( n+2 \\) are prime.\" Find a counterexample to this statement among the following nu... | math | {
"ground_truth": "\\textbf{B) 9}",
"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": "Alan, Barb, Cory, and Doug are on the golf team, Doug, Emma, Fran, and Greg are on the swim team, and Greg, Hope, Inga, and Alan are on the tennis team. These nine people sit in ... | math | {
"ground_truth": "2521",
"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 Chloe chooses a real number uniformly at random from the interval $[0, 1000]$ and Laurent chooses a real number uniformly at random from the interval $[0, 3000]$, find... | math | {
"ground_truth": "\\frac{7}{9}",
"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 α satisfies sin(α - π/6) = 1/3, calculate the value of cos(2π/3 - α).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "The solution set of the inequality $3 \\leq |5-2x| < 9$, determine the intervals that satisfy this inequality.",
"role": "user"
}
] | math | {
"ground_truth": "(-2,1] \\cup [4,7)",
"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 boy tells his friend: You can easily remember my phone number the following way. There is an increasing quadruple of natural numbers \\(a_{1}, a_{2}, a_{3}, a_{4}\\) where both... | math | {
"ground_truth": "681224",
"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": "Define a sequence $(a_n)$ recursively by $a_1=0, a_2=2, a_3=3$ and $a_n=\\max_{0<d<n} a_d \\cdot a_{n-d}$ for $n \\ge 4$ . Determine the prime factorization of $a_{197020... | math | {
"ground_truth": "3^{6567340}",
"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 function $y=\\log_a(x-3)-1$, the graph always passes through a fixed point $P$. Find the coordinates of point $P$.",
"role": "user"
}
] | math | {
"ground_truth": "(4, -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": "How many four-digit numbers have at least one 4 and at least one 7?",
"role": "user"
}
] | 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": "In triangle $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite angles $A$, $B$, and $C$ respectively. It is given that $\\frac {\\sin B}{2\\sin A-\\sin C}= \\frac ... | math | {
"ground_truth": "\\text{the area of triangle} ABC \\text{ is} \\frac{3\\sqrt{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": "Two transformations are applied to the complex number $-3 - 8i$:\n1. A $60^\\circ$ rotation around the origin in the counter-clockwise direction.\n2. A dilation, centered at the ... | math | {
"ground_truth": "-3 - 8\\sqrt{3} - (8 + 3\\sqrt{3})i",
"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 infinite sequence $a_0,a_1,\\ldots$ is given by $a_1=\\frac12$ , $a_{n+1} = \\sqrt{\\frac{1+a_n}{2}}$ . Determine the infinite product $a_1a_2a_3\\cdots$ .",
"role"... | math | {
"ground_truth": "\\frac{3\\sqrt{3}}{4\\pi}",
"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 Mrs. Smith is 39 years old, and she has nine children with consecutive ages from 5 to 13 inclusive, find the digit that is not the age of one of Mrs. Smith's children.... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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