data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "Archer Zhang Qiang has the probabilities of hitting the 10-ring, 9-ring, 8-ring, 7-ring, and below 7-ring in a shooting session as 0.24, 0.28, 0.19, 0.16, and 0.13, respectively. Calculate the probability that this archer in a single shot:\n(1) Hits either the 10-ring or the 9-ring;\n(2) Hits at l... | {
"ground_truth": "0.29",
"style": "rule"
} | {
"index": "1800",
"split": "train"
} |
math | [
{
"content": "A net for hexagonal pyramid is constructed by placing a triangle with side lengths $x$ , $x$ , and $y$ on each side of a regular hexagon with side length $y$ . What is the maximum volume of the pyramid formed by the net if $x+y=20$ ? Please output the final answer within \\boxed{}.",
"ro... | {
"ground_truth": "128\\sqrt{15}",
"style": "rule"
} | {
"index": "1801",
"split": "train"
} |
math | [
{
"content": "Consider a circle of radius $4$ with center $O_1$ , a circle of radius $2$ with center $O_2$ that lies on the circumference of circle $O_1$ , and a circle of radius $1$ with center $O_3$ that lies on the circumference of circle $O_2$ . The centers of the circle are collinear in the or... | {
"ground_truth": "\\sqrt{6}",
"style": "rule"
} | {
"index": "1802",
"split": "train"
} |
math | [
{
"content": "The solutions to the equation $x(5x+2) = 6(5x+2)$ are ___. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{2}{5}",
"style": "rule"
} | {
"index": "1803",
"split": "train"
} |
math | [
{
"content": "Calculate the value of $\\frac{2468_{10}}{111_{3}} - 3471_{9} + 1234_{7}$. Express your answer in base 10. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-1919",
"style": "rule"
} | {
"index": "1804",
"split": "train"
} |
math | [
{
"content": "A regular $n$-gon $P_{1} P_{2} \\ldots P_{n}$ satisfies $\\angle P_{1} P_{7} P_{8}=178^{\\circ}$. Compute $n$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "630",
"style": "rule"
} | {
"index": "1805",
"split": "train"
} |
math | [
{
"content": "Select 2 different numbers from 1, 3, 5, and 3 different numbers from 2, 4, 6, 8 to form a five-digit number, and determine the total number of even numbers among these five-digit numbers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "864",
"style": "rule"
} | {
"index": "1806",
"split": "train"
} |
math | [
{
"content": "The hour and minute hands on a certain 12-hour analog clock are indistinguishable. If the hands of the clock move continuously, compute the number of times strictly between noon and midnight for which the information on the clock is not sufficient to determine the time.\n\n*Proposed by Lewis Chen*... | {
"ground_truth": "132",
"style": "rule"
} | {
"index": "1807",
"split": "train"
} |
math | [
{
"content": "Find the integer $n$, $0 \\le n \\le 9$, that satisfies \\[n \\equiv -2187 \\pmod{10}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"index": "1808",
"split": "train"
} |
math | [
{
"content": "A motel bills its customers by charging a flat fee for the first night and then adding on a fixed amount for every night thereafter. If it costs George $\\$155$ to stay in the motel for 3 nights and Noah $\\$290$ to stay in the motel for 6 nights, how much is the flat fee for the first night? Plea... | {
"ground_truth": "\\$65",
"style": "rule"
} | {
"index": "1809",
"split": "train"
} |
math | [
{
"content": "On the clock tower at the train station, there is an electronic clock. Along the boundary of the circular clock face, there are small colorful lights at each minute mark. At 9:35:20 PM, there are how many small colorful lights in the acute angle formed by the minute hand and the hour hand? Please ... | {
"ground_truth": "12",
"style": "rule"
} | {
"index": "1810",
"split": "train"
} |
math | [
{
"content": "1. On a semicircle with AB as the diameter, besides points A and B, there are 6 other points. Since there are also 4 other points on AB, making a total of 12 points, how many quadrilaterals can be formed with these 12 points as vertices?\n2. On one side of angle A, there are five points (excluding... | {
"ground_truth": "200",
"style": "rule"
} | {
"index": "1811",
"split": "train"
} |
math | [
{
"content": "There are $2019$ points given in the plane. A child wants to draw $k$ (closed) discs in such a manner, that for any two distinct points there exists a disc that contains exactly one of these two points. What is the minimal $k$ , such that for any initial configuration of points it is possible... | {
"ground_truth": "1010",
"style": "rule"
} | {
"index": "1812",
"split": "train"
} |
math | [
{
"content": "There is a smallest positive real number $a$ such that there exists a positive real number $b$ such that all the roots of the polynomial $x^3-ax^2+bx-a$ are real. In fact, for this value of $a$ the value of $b$ is unique. What is the value of $b?$ Please output the final answer within \\boxed{}.",... | {
"ground_truth": "9",
"style": "rule"
} | {
"index": "1813",
"split": "train"
} |
math | [
{
"content": "Two different natural numbers are selected from the set $\\{1, 2, 3, \\ldots, 8\\}$. What is the probability that the greatest common factor of these two numbers is one? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"index": "1814",
"split": "train"
} |
math | [
{
"content": "After a track and field event, each athlete shook hands once with every athlete from every other team, but not with their own team members. Afterwards, two coaches arrived, each only shaking hands with each athlete from their respective teams. If there were a total of 300 handshakes at the event, ... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "1815",
"split": "train"
} |
math | [
{
"content": "Find $a+b+c$ if the graph of the equation $y=ax^2+bx+c$ is a parabola with vertex $(5,3)$, vertical axis of symmetry, and contains the point $(2,0)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac73",
"style": "rule"
} | {
"index": "1816",
"split": "train"
} |
math | [
{
"content": "In triangle \\( ABC \\), \\( \\angle ABC \\) is obtuse. Point \\( D \\) lies on side \\( AC \\) such that \\( \\angle ABD \\) is right, and point \\( E \\) lies on side \\( AC \\) between \\( A \\) and \\( D \\) such that \\( BD \\) bisects \\( \\angle EBC \\). Find \\( CE \\), given that \\( AC =... | {
"ground_truth": "10",
"style": "rule"
} | {
"index": "1817",
"split": "train"
} |
math | [
{
"content": "Let $d$ and $e$ denote the solutions of $2x^{2}+3x-5=0$. What is the value of $(d-1)(e-1)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"index": "1818",
"split": "train"
} |
math | [
{
"content": "Evaluate $81^{3/4}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "27",
"style": "rule"
} | {
"index": "1819",
"split": "train"
} |
math | [
{
"content": "In the plane Cartesian coordinate system $xOy$, let two unit vectors in the directions of the $x$-axis and $y$-axis be $\\overrightarrow{i}$ and $\\overrightarrow{j}$, respectively. Given that $\\overrightarrow{OA}=2\\overrightarrow{i}+\\overrightarrow{j}$ and $\\overrightarrow{OB}=4\\overrightarr... | {
"ground_truth": "-\\frac{1}{3}",
"style": "rule"
} | {
"index": "1820",
"split": "train"
} |
math | [
{
"content": "What is the result of adding 0.45 to 52.7 and then subtracting 0.25? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "52.9",
"style": "rule"
} | {
"index": "1821",
"split": "train"
} |
math | [
{
"content": "Given that the sum of the first $n$ terms of a geometric sequence ${a_{n}}$ is $S_{n}$, if $a_{3}=4$, $S_{3}=12$, find the common ratio. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"index": "1822",
"split": "train"
} |
math | [
{
"content": "Given vectors $\\overrightarrow{a}, \\overrightarrow{b}$ satisfy $\\overrightarrow{a}=(1, \\sqrt {3}), |\\overrightarrow{b}|=1, |\\overrightarrow{a}+ \\overrightarrow{b}|= \\sqrt {3}$, then the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is ______. Please output the final answer ... | {
"ground_truth": "\\frac{2\\pi}{3}",
"style": "rule"
} | {
"index": "1823",
"split": "train"
} |
math | [
{
"content": "Triangles $\\triangle DEF$ and $\\triangle D'E'F'$ lie in the coordinate plane with vertices $D(0,0)$, $E(0,10)$, $F(15,0)$, $D'(15,25)$, $E'(25,25)$, $F'(15,10)$. A rotation of $n$ degrees clockwise around the point $(u,v)$ where $0<n<180$, will transform $\\triangle DEF$ to $\\triangle D'E'F'$. ... | {
"ground_truth": "115",
"style": "rule"
} | {
"index": "1824",
"split": "train"
} |
math | [
{
"content": "In a checkers tournament, students from 10th and 11th grades participated. Each player played against every other player exactly once. A win earned a player 2 points, a draw earned 1 point, and a loss earned 0 points. The number of 11th graders was 10 times the number of 10th graders, and together... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "1825",
"split": "train"
} |
math | [
{
"content": "Find the value of $k$ for which $kx^2 -5x-12 = 0$ has solutions $x=3$ and $ x = -\\frac{4}{3}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"index": "1826",
"split": "train"
} |
math | [
{
"content": "For positive integers $a, b, a \\uparrow \\uparrow b$ is defined as follows: $a \\uparrow \\uparrow 1=a$, and $a \\uparrow \\uparrow b=a^{a \\uparrow \\uparrow(b-1)}$ if $b>1$. Find the smallest positive integer $n$ for which there exists a positive integer $a$ such that $a \\uparrow \\uparrow 6 \... | {
"ground_truth": "283",
"style": "rule"
} | {
"index": "1827",
"split": "train"
} |
math | [
{
"content": "How many positive factors of 96 are also multiples of 12? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "1828",
"split": "train"
} |
math | [
{
"content": "Given the function $f(x) = x^2 - (2t + 1)x + t \\ln x$ where $t \\in \\mathbb{R}$,\n\n(1) If $t = 1$, find the extreme values of $f(x)$.\n\n(2) Let $g(x) = (1 - t)x$, and suppose there exists an $x_0 \\in [1, e]$ such that $f(x_0) \\geq g(x_0)$ holds. Find the maximum value of the real number $t$.... | {
"ground_truth": "\\frac{e(e - 2)}{e - 1}",
"style": "rule"
} | {
"index": "1829",
"split": "train"
} |
math | [
{
"content": "In a 5 by 5 grid, each of the 25 small squares measures 2 cm by 2 cm and is shaded. Five unshaded circles are then placed on top of the grid as shown. The area of the visible shaded region can be written in the form $A-B\\pi$ square cm. What is the value $A+B$?\n\n[asy]\nfor(int i = 0; i < 5; ++i)... | {
"ground_truth": "113",
"style": "rule"
} | {
"index": "1830",
"split": "train"
} |
math | [
{
"content": "On Arbor Day, 20 students in a class planted trees along one side of a straight road, with each person planting one tree, and the distance between two adjacent trees being 10 meters. Initially, it is required to place all the saplings next to one of the tree pits so that the total distance travele... | {
"ground_truth": "2000",
"style": "rule"
} | {
"index": "1831",
"split": "train"
} |
math | [
{
"content": "There are five people in a room. They each simultaneously pick two of the other people in the room independently and uniformly at random and point at them. Compute the probability that there exists a group of three people such that each of them is pointing at the other two in the group. Please out... | {
"ground_truth": "\\frac{5}{108}",
"style": "rule"
} | {
"index": "1832",
"split": "train"
} |
math | [
{
"content": "Compute $\\sqrt[3]{466560000}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "360",
"style": "rule"
} | {
"index": "1833",
"split": "train"
} |
math | [
{
"content": "Six chairs are evenly spaced around a circular table. One person is seated in each chair. Each person gets up and sits down in a chair that is not the same and is not adjacent to the chair he or she originally occupied, so that again one person is seated in each chair. In how many ways can this be... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "1834",
"split": "train"
} |
math | [
{
"content": "A circle is divided into six equal sections. Each section is to be coloured with a single colour so that three sections are red, one is blue, one is green, and one is yellow. Two circles have the same colouring if one can be rotated to match the other. How many different colourings are there for t... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "1835",
"split": "train"
} |
math | [
{
"content": "Two positive integers $m$ and $n$ are chosen such that $m$ is the smallest positive integer with only two positive divisors and $n$ is the largest integer less than $100$ with exactly three positive divisors. What is $m+n$? Please output the final answer within \\boxed{}.",
"role": "user"
}
... | {
"ground_truth": "51",
"style": "rule"
} | {
"index": "1836",
"split": "train"
} |
math | [
{
"content": "Calculate the amount of personal income tax (НДФЛ) paid by Sergey over the past year if he is a resident of the Russian Federation and had a stable income of 30,000 rubles per month and a one-time vacation bonus of 20,000 rubles during this period. Last year, Sergey sold his car, which he inherite... | {
"ground_truth": "10400",
"style": "rule"
} | {
"index": "1837",
"split": "train"
} |
math | [
{
"content": "Two fair 6-sided dice are rolled. What is the probability at least one of the dice shows a 1? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{11}{36}",
"style": "rule"
} | {
"index": "1838",
"split": "train"
} |
math | [
{
"content": "Let the following system of equations hold for positive numbers \\(x, y, z\\):\n\n\\[ \\left\\{\\begin{array}{l}\nx^{2}+x y+y^{2}=48 \\\\\ny^{2}+y z+z^{2}=25 \\\\\nz^{2}+x z+x^{2}=73\n\\end{array}\\right. \\]\n\nFind the value of the expression \\(x y + y z + x z\\). Please output the final answer... | {
"ground_truth": "40",
"style": "rule"
} | {
"index": "1839",
"split": "train"
} |
math | [
{
"content": "Given the function $f(x) = x + \\sin(\\pi x) - 3$, study its symmetry center $(a, b)$ and find the value of $f\\left( \\frac {1}{2016} \\right) + f\\left( \\frac {2}{2016} \\right) + f\\left( \\frac {3}{2016} \\right) + \\ldots + f\\left( \\frac {4030}{2016} \\right) + f\\left( \\frac {4031}{2016}... | {
"ground_truth": "-8062",
"style": "rule"
} | {
"index": "1840",
"split": "train"
} |
math | [
{
"content": "Given that $m$ is a positive integer, and given that $\\mathop{\\text{lcm}}[40,m]=120$ and $\\mathop{\\text{lcm}}[m,45]=180$, what is $m$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"index": "1841",
"split": "train"
} |
math | [
{
"content": "If $S=1!+2!+3!+\\cdots +99!$, then the units' digit in the value of S is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"index": "1842",
"split": "train"
} |
math | [
{
"content": "Suppose $a, b$, and $c$ are distinct positive integers such that $\\sqrt{a \\sqrt{b \\sqrt{c}}}$ is an integer. Compute the least possible value of $a+b+c$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7",
"style": "rule"
} | {
"index": "1843",
"split": "train"
} |
math | [
{
"content": "A right triangular prism $ABC-A_{1}B_{1}C_{1}$ has all its vertices on the surface of a sphere. Given that $AB=3$, $AC=5$, $BC=7$, and $AA_{1}=2$, find the surface area of the sphere. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{208\\pi}{3}",
"style": "rule"
} | {
"index": "1844",
"split": "train"
} |
math | [
{
"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 solution $(x,y,z,u)$ of the system, with $x \\geq y$. Please output the final answer within \\boxed{}.",
"role": "us... | {
"ground_truth": "3 + 2\\sqrt{2}",
"style": "rule"
} | {
"index": "1845",
"split": "train"
} |
math | [
{
"content": "Given that the line $l$ passes through the point $P(3,4)$<br/>(1) Its intercept on the $y$-axis is twice the intercept on the $x$-axis, find the equation of the line $l$.<br/>(2) If the line $l$ intersects the positive $x$-axis and positive $y$-axis at points $A$ and $B$ respectively, find the min... | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "1846",
"split": "train"
} |
math | [
{
"content": "If $3 \times n=6 \times 2$, what is the value of $n$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "1847",
"split": "train"
} |
math | [
{
"content": "Let $a_{n}(n\\geqslant 2, n\\in N^{*})$ be the coefficient of the linear term of $x$ in the expansion of ${({3-\\sqrt{x}})^n}$. Find the value of $\\frac{3^2}{a_2}+\\frac{3^3}{a_3}+…+\\frac{{{3^{18}}}}{{{a_{18}}}}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "17",
"style": "rule"
} | {
"index": "1848",
"split": "train"
} |
math | [
{
"content": "How many two-digit prime numbers have a units digit of 7? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"index": "1849",
"split": "train"
} |
math | [
{
"content": "Given a hyperbola $F$ with the equation $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$, let $F$ be its left focus. Draw a line perpendicular to one asymptote of the hyperbola passing through $F$, and denote the foot of the perpendicular as $A$ and the intersection with the other ... | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": "1850",
"split": "train"
} |
math | [
{
"content": "In right triangle $DEF$, $DE=15$, $DF=9$ and $EF=12$ units. What is the distance from $F$ to the midpoint of segment $DE$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7.5",
"style": "rule"
} | {
"index": "1851",
"split": "train"
} |
math | [
{
"content": "Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \\frac {1}{z} = 5,$ and $y + \\frac {1}{x} = 29.$ Find $z + \\frac {1}{y}.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": "1852",
"split": "train"
} |
math | [
{
"content": "If $x - 2x + 3x = 100$, what is the value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "50",
"style": "rule"
} | {
"index": "1853",
"split": "train"
} |
math | [
{
"content": "Find the discriminant of $3x^2 + \\left(3 + \\frac 13\\right)x + \\frac 13$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{64}{9}",
"style": "rule"
} | {
"index": "1854",
"split": "train"
} |
math | [
{
"content": "For $n$ measured in degrees, let $T(n) = \\cos^2(30^\\circ -n) - \\cos(30^\\circ -n)\\cos(30^\\circ +n) +\\cos^2(30^\\circ +n)$ . Evaluate $$ 4\\sum^{30}_{n=1} n \\cdot T(n). $$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1395",
"style": "rule"
} | {
"index": "1855",
"split": "train"
} |
math | [
{
"content": "There are three pairs of real numbers $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ that satisfy both $x^3 - 3xy^2 = 2017$ and $y^3 - 3x^2y = 2016$. Compute $\\left(2 - \\frac{x_1}{y_1}\\right)\\left(2 - \\frac{x_2}{y_2}\\right)\\left(2 - \\frac{x_3}{y_3}\\right)$. Please output the final answer withi... | {
"ground_truth": "\\frac{26219}{2016}",
"style": "rule"
} | {
"index": "1856",
"split": "train"
} |
math | [
{
"content": "For the \"Skillful Hands\" club, Anton needs to cut several identical pieces of wire (the length of each piece is an integer number of centimeters). Initially, Anton took a piece of wire 10 meters long and was able to cut only 9 required pieces from it. Then Anton took a piece 11 meters long, but ... | {
"ground_truth": "111",
"style": "rule"
} | {
"index": "1857",
"split": "train"
} |
math | [
{
"content": "Let $A=\\{a_{1}, a_{2}, \\ldots, a_{7}\\}$ be a set of distinct positive integers such that the mean of the elements of any nonempty subset of $A$ is an integer. Find the smallest possible value of the sum of the elements in $A$. Please output the final answer within \\boxed{}.",
"role": "user... | {
"ground_truth": "1267",
"style": "rule"
} | {
"index": "1858",
"split": "train"
} |
math | [
{
"content": "If \\(100^a = 4\\) and \\(100^b = 5\\), then find \\(20^{(1 - a - b)/(2(1 - b))}\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"index": "1859",
"split": "train"
} |
math | [
{
"content": "Find the value of $x$ such that $\\sqrt{3x + 7} = 10$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "31",
"style": "rule"
} | {
"index": "1860",
"split": "train"
} |
math | [
{
"content": "The function $f_n (x)\\ (n=1,2,\\cdots)$ is defined as follows.\r\n\r\n\\[f_1 (x)=x,\\ f_{n+1}(x)=2x^{n+1}-x^n+\\frac{1}{2}\\int_0^1 f_n(t)\\ dt\\ \\ (n=1,2,\\cdots)\\]\r\n\r\nEvaluate \r\n\r\n\\[\\lim_{n\\to\\infty} f_n \\left(1+\\frac{1}{2n}\\right)\\] Please output the final answer within \\... | {
"ground_truth": "e^{1/2}",
"style": "rule"
} | {
"index": "1861",
"split": "train"
} |
math | [
{
"content": "The target below is made up of concentric circles with diameters $4$ , $8$ , $12$ , $16$ , and $20$ . The area of the dark region is $n\\pi$ . Find $n$ .\n\n[asy]\nsize(150);\ndefaultpen(linewidth(0.8));\nint i;\nfor(i=5;i>=1;i=i-1)\n{\nif (floor(i/2)==i/2)\n{\nfilldraw(circle(origin,4*i),w... | {
"ground_truth": "60",
"style": "rule"
} | {
"index": "1862",
"split": "train"
} |
math | [
{
"content": "A high school basketball team has 12 players, including a set of twins, John and James. In how many ways can we choose a starting lineup of 5 players if exactly one of the twins must be in the lineup? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "660",
"style": "rule"
} | {
"index": "1863",
"split": "train"
} |
math | [
{
"content": "How many integer values of $x$ satisfy $|x|<3\\pi$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "19",
"style": "rule"
} | {
"index": "1864",
"split": "train"
} |
math | [
{
"content": "A natural number $n$ is said to be $good$ if $n$ is the sum or $r$ consecutive positive integers, for some $r \\geq 2 $ . Find the number of good numbers in the set $\\{1,2 \\dots , 100\\}$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "93",
"style": "rule"
} | {
"index": "1865",
"split": "train"
} |
math | [
{
"content": "Let $\\triangle XYZ$ be a right triangle with $Y$ as the right angle. A circle with diameter $YZ$ intersects side $XZ$ at point $W$. Given that $XW = 2$ and $YW = 3$, find the length of $ZW$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{2}",
"style": "rule"
} | {
"index": "1866",
"split": "train"
} |
math | [
{
"content": "Let $P(x)$ be a polynomial such that\n\\[P(x) = P(0) + P(1) x + P(2) x^2\\]and $P(-1) = 1.$ Find $P(x).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "x^2 - x - 1",
"style": "rule"
} | {
"index": "1867",
"split": "train"
} |
math | [
{
"content": "The equation \\( x y z 1 = 4 \\) can be rewritten as \\( x y z = 4 \\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "48",
"style": "rule"
} | {
"index": "1868",
"split": "train"
} |
math | [
{
"content": "Let $P$ be a point chosen on the interior of side $\\overline{BC}$ of triangle $\\triangle ABC$ with side lengths $\\overline{AB} = 10, \\overline{BC} = 10, \\overline{AC} = 12$ . If $X$ and $Y$ are the feet of the perpendiculars from $P$ to the sides $AB$ and $AC$ , then the minim... | {
"ground_truth": "1936",
"style": "rule"
} | {
"index": "1869",
"split": "train"
} |
math | [
{
"content": "When three standard dice are tossed, the numbers $a, b, c$ are obtained. Find the probability that $abc = 216$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{216}",
"style": "rule"
} | {
"index": "1870",
"split": "train"
} |
math | [
{
"content": "Given the parabola $C: x^{2}=2py\\left(p \\gt 0\\right)$ with focus $F$, and the minimum distance between $F$ and a point on the circle $M: x^{2}+\\left(y+4\\right)^{2}=1$ is $4$.<br/>$(1)$ Find $p$;<br/>$(2)$ If point $P$ lies on $M$, $PA$ and $PB$ are two tangents to $C$ with points $A$ and $B$ ... | {
"ground_truth": "20\\sqrt{5}",
"style": "rule"
} | {
"index": "1871",
"split": "train"
} |
math | [
{
"content": "The larger of two consecutive odd integers is three times the smaller. What is their sum? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "1872",
"split": "train"
} |
math | [
{
"content": "Charlie and Dana play a game where they take turns rolling a standard die. If a player rolls $n$, she is awarded $g(n)$ points, where \n\\[g(n) = \\left\\{\n\\begin{array}{cl} \n7 & \\text{if } n \\text{ is a multiple of 3 and 5}, \\\\\n3 & \\text{if } n \\text{ is only a multiple of 3}, \\\\\n0 ... | {
"ground_truth": "36",
"style": "rule"
} | {
"index": "1873",
"split": "train"
} |
math | [
{
"content": "One base of a trapezoid is $100$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $2: 3$. Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel to the bases and t... | {
"ground_truth": "181",
"style": "rule"
} | {
"index": "1874",
"split": "train"
} |
math | [
{
"content": "How many positive integer multiples of $1001$ can be expressed in the form $10^{j} - 10^{i}$, where $i$ and $j$ are integers and $0\\leq i < j \\leq 99$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "784",
"style": "rule"
} | {
"index": "1875",
"split": "train"
} |
math | [
{
"content": "An inscribed dodecagon. A convex dodecagon is inscribed in a circle. The lengths of some six sides of the dodecagon are $\\sqrt{2}$, and the lengths of the remaining six sides are $\\sqrt{24}$. What is the radius of the circle? Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "\\sqrt{38}",
"style": "rule"
} | {
"index": "1876",
"split": "train"
} |
math | [
{
"content": "I won a VIP trip for five to a music festival. I can bring four of my friends. I have 10 friends to choose from: 4 are musicians, and 6 are non-musicians. In how many ways can I form my music festival group so that at least one musician is in the group? Please output the final answer within \\boxe... | {
"ground_truth": "195",
"style": "rule"
} | {
"index": "1877",
"split": "train"
} |
math | [
{
"content": "Given vectors \\( \\boldsymbol{a} \\), \\( \\boldsymbol{b} \\), and \\( \\boldsymbol{c} \\) satisfying\n$$\n|\\boldsymbol{a}|:|\\boldsymbol{b}|:|\\boldsymbol{c}|=1: k: 3 \\quad \\left(k \\in \\mathbf{Z}_{+}\\right),\n$$\nand \\( \\boldsymbol{b} - \\boldsymbol{a} = 2(\\boldsymbol{c} - \\boldsymbol{... | {
"ground_truth": "-\\frac{1}{12}",
"style": "rule"
} | {
"index": "1878",
"split": "train"
} |
math | [
{
"content": "Given that $a$, $b$, $c$, $d$ are the thousands, hundreds, tens, and units digits of a four-digit number, respectively, and the digits in lower positions are not less than those in higher positions. When $|a-b|+|b-c|+|c-d|+|d-a|$ reaches its maximum value, the minimum value of this four-digit numb... | {
"ground_truth": "1119",
"style": "rule"
} | {
"index": "1879",
"split": "train"
} |
math | [
{
"content": "Given a hyperbola $C$ that shares the same foci with the ellipse $\\frac{x^{2}}{27}+ \\frac{y^{2}}{36}=1$ and passes through the point $(\\sqrt{15},4)$.\n\n(I) Find the equation of the hyperbola $C$.\n\n(II) If $F\\_1$ and $F\\_2$ are the two foci of the hyperbola $C$, and point $P$ is on the hype... | {
"ground_truth": "\\frac{5\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": "1880",
"split": "train"
} |
math | [
{
"content": "Given that $\\tan{\\alpha} = 3$, calculate:\n\n1. $$\\frac{4\\sin{\\alpha} - \\cos{\\alpha}}{3\\sin{\\alpha} + 5\\cos{\\alpha}}$$\n2. $$\\sin{\\alpha} \\cdot \\cos{\\alpha}$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3}{10}",
"style": "rule"
} | {
"index": "1881",
"split": "train"
} |
math | [
{
"content": "( Ricky Liu ) For what values of $k > 0$ is it possible to dissect a $1 \\times k$ rectangle into two similar, but incongruent, polygons? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\[ k \\neq 1 \\]",
"style": "rule"
} | {
"index": "1882",
"split": "train"
} |
math | [
{
"content": "Find the quadratic function $f(x) = x^2 + ax + b$ such that\n\\[\\frac{f(f(x) + x)}{f(x)} = x^2 + 1776x + 2010.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "x^2 + 1774x + 235",
"style": "rule"
} | {
"index": "1883",
"split": "train"
} |
math | [
{
"content": "A collection $\\mathcal{S}$ of 10000 points is formed by picking each point uniformly at random inside a circle of radius 1. Let $N$ be the expected number of points of $\\mathcal{S}$ which are vertices of the convex hull of the $\\mathcal{S}$. (The convex hull is the smallest convex polygon conta... | {
"ground_truth": "72.8",
"style": "rule"
} | {
"index": "1884",
"split": "train"
} |
math | [
{
"content": "Add $256_{7} + 463_{7} + 132_7$. Express your answer in base $7$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1214_{7}",
"style": "rule"
} | {
"index": "1885",
"split": "train"
} |
math | [
{
"content": "Does there exist a six-digit number that increases by 6 times if its first three digits, without changing their order, are moved to the end of the number? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "142857",
"style": "rule"
} | {
"index": "1886",
"split": "train"
} |
math | [
{
"content": "If the minute hand is moved back by 5 minutes, the number of radians it has turned is __________. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\pi}{6}",
"style": "rule"
} | {
"index": "1887",
"split": "train"
} |
math | [
{
"content": "Given vectors $\\overrightarrow{a}=(\\sin (\\frac{\\omega}{2}x+\\varphi), 1)$ and $\\overrightarrow{b}=(1, \\cos (\\frac{\\omega}{2}x+\\varphi))$, where $\\omega > 0$ and $0 < \\varphi < \\frac{\\pi}{4}$, define the function $f(x)=(\\overrightarrow{a}+\\overrightarrow{b})\\cdot(\\overrightarrow{a}... | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": "1888",
"split": "train"
} |
math | [
{
"content": "The function $g : \\mathbb{R} \\to \\mathbb{R}$ satisfies\n\\[g(x) + 3g(1 - x) = 2x^2 + 1\\]for all $x.$ Find $g(5).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-9",
"style": "rule"
} | {
"index": "1889",
"split": "train"
} |
math | [
{
"content": "Given $\\sin 2\\alpha = 3\\sin 2\\beta$, calculate the value of $\\frac {\\tan(\\alpha-\\beta)}{\\tan(\\alpha +\\beta )}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": "1890",
"split": "train"
} |
math | [
{
"content": "In quadrilateral ABCD, m∠B = m∠C = 120°, AB = 4, BC = 6, and CD = 7. Diagonal BD = 8. Calculate the area of ABCD. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "16.5\\sqrt{3}",
"style": "rule"
} | {
"index": "1891",
"split": "train"
} |
math | [
{
"content": "Let \\( ABC \\) be a triangle in which \\( \\angle ABC = 60^\\circ \\). Let \\( I \\) and \\( O \\) be the incentre and circumcentre of \\( ABC \\), respectively. Let \\( M \\) be the midpoint of the arc \\( BC \\) of the circumcircle of \\( ABC \\), which does not contain the point \\( A \\). Det... | {
"ground_truth": "30",
"style": "rule"
} | {
"index": "1892",
"split": "train"
} |
math | [
{
"content": "When arranging the performance order of 5 singers, it is required that a certain singer does not perform first, and another singer performs last. The number of different arrangements is ______. (Answer with a number) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18",
"style": "rule"
} | {
"index": "1893",
"split": "train"
} |
math | [
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted as $S_n$, and it is known that $a_1 > 0$, $a_3 + a_{10} > 0$, $a_6a_7 < 0$, determine the maximum natural number $n$ that satisfies $S_n > 0$. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "12",
"style": "rule"
} | {
"index": "1894",
"split": "train"
} |
math | [
{
"content": "Find all functions $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ such that $$f(x^2y)=f(xy)+yf(f(x)+y)$$ for all real numbers $x$ and $y$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "f(x) = 0",
"style": "rule"
} | {
"index": "1895",
"split": "train"
} |
math | [
{
"content": "A tetrahedron $PQRS$ has edges of lengths $8, 14, 19, 28, 37,$ and $42$ units. If the length of edge $PQ$ is $42$, determine the length of edge $RS$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "14",
"style": "rule"
} | {
"index": "1896",
"split": "train"
} |
math | [
{
"content": "A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players $A$, $B$, and $C$ start with $15$, ... | {
"ground_truth": "37",
"style": "rule"
} | {
"index": "1897",
"split": "train"
} |
math | [
{
"content": "Given that in the expansion of $(1-2x)^{n} (n \\in \\mathbb{N^*})$, the coefficient of $x^{3}$ is $-80$, find the sum of all the binomial coefficients in the expansion. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "32",
"style": "rule"
} | {
"index": "1898",
"split": "train"
} |
math | [
{
"content": "Let $f(n)$ and $g(n)$ be functions satisfying \\[f(n) = \\begin{cases}\\sqrt{n} & \\text{ if } \\sqrt{n} \\text{ is an integer}\\\\ 1 + f(n+1) & \\text{ otherwise} \\end{cases}\\]and \\[g(n) = \\begin{cases}\\sqrt{n} & \\text{ if } \\sqrt{n} \\text{ is an integer}\\\\ 2 + g(n+2) & \\text{ otherwis... | {
"ground_truth": "258",
"style": "rule"
} | {
"index": "1899",
"split": "train"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.