prompt listlengths 1 1 | reward_model dict | data_source stringclasses 2
values | ability stringclasses 1
value |
|---|---|---|---|
[
{
"content": "The sum of four prime numbers $P,$ $Q,$ $P-Q,$ and $P+Q$ must be expressed in terms of a single letter indicating the property of the sum.",
"role": "user"
}
] | {
"ground_truth": "17",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "In a right triangle, instead of having one $90^{\\circ}$ angle and two small angles sum to $90^{\\circ}$, consider now the acute angles are $x^{\\circ}$, $y^{\\circ}$, and a smaller angle $z^{\\circ}$ where $x$, $y$, and $z$ are all prime numbers, and $x^{\\circ} + y^{\\circ} + z^{\\circ} = 90^{\\... | {
"ground_truth": "47",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given the function $f(x)=\\sin^{2}x+\\sqrt{3}\\sin x\\sin (x+\\frac{\\pi}{2})$.\n\n1. Find the value of $f(\\frac{\\pi}{12})$;\n2. Find the maximum and minimum values of the function $f(x)$ when $x\\in[0,\\frac{\\pi}{2}]$.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3}{2}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $\\triangle ABC$ be an acute scalene triangle with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ onto lines $AB$ and $AC$, respectively. Suppose $BT = CT = 16$, $BC = 22$, and $TX^2 + TY^2 + XY^2 = 1143$. Find $XY^2... | {
"ground_truth": "717",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let set $M=\\{x|-1\\leq x\\leq 5\\}$, and set $N=\\{x|x-k\\leq 0\\}$.\n1. If $M\\cap N$ has only one element, find the value of $k$.\n2. If $k=2$, find $M\\cap N$ and $M\\cup N$.",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "The smallest possible value of $m$ for which Casper can buy exactly $10$ pieces of strawberry candy, $18$ pieces of lemon candy, and $20$ pieces of cherry candy, given that each piece of orange candy costs $15$ cents.",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given vectors $\\overrightarrow{a}=(2\\cos x,1)$, $\\overrightarrow{b}=(\\sqrt{3}\\sin x+\\cos x,-1)$, and the function $f(x)=\\overrightarrow{a}\\cdot\\overrightarrow{b}$.\n\n1. Find the maximum and minimum values of $f(x)$ in the interval $[0,\\frac{\\pi}{4}]$.\n2. If $f(x_{0})=\\frac{6}{5}$, $x... | {
"ground_truth": "\\frac{1}{4}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence, and $a_2=-1$, the sequence $\\{b_n\\}$ satisfies $b_n-b_{n-1}=a_n$ ($n\\geqslant 2, n\\in \\mathbb{N}$), and $b_1=b_3=1$ \n(I) Find the value of $a_1$; \n(II) Find the general formula for the sequence $\\{b_n\\}$.",
"role": "user... | {
"ground_truth": "-3",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find the greatest common divisor of $8!$ and $(6!)^3.$",
"role": "user"
}
] | {
"ground_truth": "11520",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the largest integer that must divide the product of any 5 consecutive integers?",
"role": "user"
}
] | {
"ground_truth": "60",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "On eight cards, the numbers $1, 1, 2, 2, 3, 3, 4, 4$ are written. Is it possible to arrange these cards in a row such that there is exactly one card between the ones, two cards between the twos, three cards between the threes, and four cards between the fours?",
"role": "user"
}
] | {
"ground_truth": "41312432",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find the number of functions $f$ from $\\{0, 1, 2, 3, 4, 5, 6\\}$ to the integers such that $f(0) = 0$, $f(6) = 12$, and \\[|x - y| \\leq |f(x) - f(y)| \\leq 3|x - y|\\] for all $x$ and $y$ in $\\{0, 1, 2, 3, 4, 5, 6\\}$.",
"role": "user"
}
] | {
"ground_truth": "185",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the smallest prime factor of 1739?",
"role": "user"
}
] | {
"ground_truth": "1739",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A basketball player scored a mix of free throws, 2-pointers, and 3-pointers during a game, totaling 7 successful shots. Find the different numbers that could represent the total points scored by the player, assuming free throws are worth 1 point each.",
"role": "user"
}
] | {
"ground_truth": "15",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the minimum number of shots required in the game \"Battleship\" on a 7x7 board to definitely hit a four-cell battleship (which consists of four consecutive cells in a single row)?",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the $13$ visible numbers have the greatest possible sum. What is that sum?",
"role": "user"
}
] | {
"ground_truth": "164",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the smallest positive integer that satisfies the congruence $5x \\equiv 17 \\pmod{31}$?",
"role": "user"
}
] | {
"ground_truth": "26",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Petya approaches the entrance door with a combination lock, which has buttons numbered from 0 to 9. To open the door, three correct buttons need to be pressed simultaneously. Petya does not remember the code and tries combinations one by one. Each attempt takes Petya 2 seconds.\n\na) How much time... | {
"ground_truth": "\\frac{29}{120}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "The Annual Interplanetary Mathematics Examination (AIME) is written by a committee of five Martians, five Venusians, and five Earthlings. At meetings, committee members sit at a round table with chairs numbered from $1$ to $15$ in clockwise order. Committee rules state that a Martian must occupy c... | {
"ground_truth": "346",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A pedestrian traffic light allows pedestrians to cross the street for one minute and prohibits crossing for two minutes. Find the average waiting time for a pedestrian who approaches the intersection.",
"role": "user"
}
] | {
"ground_truth": "40",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let \\(a, b, c, d\\) be nonnegative real numbers such that \\(a + b + c + d = 1\\). Find the maximum value of\n\n\\[\n\\frac{ab}{a+b} + \\frac{ac}{a+c} + \\frac{ad}{a+d} + \\frac{bc}{b+c} + \\frac{bd}{b+d} + \\frac{cd}{c+d}.\n\\]",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{2}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A solid cube of side length 4 cm is cut into two pieces by a plane that passed through the midpoints of six edges. Find the surface area of each half cube created.",
"role": "user"
}
] | {
"ground_truth": "69",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $f(x)$ be an even function defined on $\\mathbb{R}$, which satisfies $f(x+1) = f(x-1)$ for any $x \\in \\mathbb{R}$. If $f(x) = 2^{x-1}$ for $x \\in [0,1]$, then determine the correctness of the following statements:\n\n(1) 2 is a period of the function $f(x)$.\n(2) The function $f(x)$ is incr... | {
"ground_truth": "\\frac{1}{2}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the maximum number of finite roots that the equation\n\n$$\n\\left|x - a_{1}\\right| + \\ldots + |x - a_{50}| = \\left|x - b_{1}\\right| + \\ldots + |x - b_{50}|\n$$\n\ncan have, where $a_{1}, a_{2}, \\ldots, a_{50}, b_{1}, b_{2}, \\ldots, b_{50}$ are distinct numbers?",
"role": "user"... | {
"ground_truth": "49",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the smallest positive integer $x$ that, when multiplied by $450$, results in a product that is a multiple of $800$?",
"role": "user"
}
] | {
"ground_truth": "32",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region $C$ to the area of shaded region $B$ is 11/5. Find the ratio of shaded region $D$ to the area of shaded region $A.$\n[asy] defaultpen(linewidth(0.7)+fontsize(10)); for(int i=0; i<4; i=i+1) ... | {
"ground_truth": "408",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Jo and Blair take turns counting from 1, increasing by 1 each turn. However, if the number is a multiple of 3, they skip it. Jo starts by saying \"1.\" Calculate the 53rd number said.",
"role": "user"
}
] | {
"ground_truth": "80",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "(1+11+21+31+41)+(9+19+29+39+49)=",
"role": "user"
}
] | {
"ground_truth": "200",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let \\(\\alpha\\) and \\(\\beta\\) be the two real roots of the quadratic equation \\(x^{2} - 2kx + k + 20 = 0\\). Find the minimum value of \\((\\alpha+1)^{2} + (\\beta+1)^{2}\\), and determine the value of \\(k\\) for which this minimum value is achieved.",
"role": "user"
}
] | {
"ground_truth": "18",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of $50$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?",
"role": "user"
... | {
"ground_truth": "128",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given a point $P$ on a triangular piece of paper $ABC,\\,$ consider the creases that are formed in the paper when $A, B,\\,$ and $C\\,$ are folded onto $P.\\,$ Let us call $P$ a fold point of $\\triangle ABC\\,$ if these creases, which number three unless $P$ is one of the vertices, do not interse... | {
"ground_truth": "597",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "In isosceles triangle $\\triangle ABC$, $A$ is located at the origin and $B$ is located at $(20,0)$. Point $C$ is in the first quadrant with $AC = BC$ and angle $BAC = 75^{\\circ}$. If triangle $ABC$ is rotated counterclockwise about point $A$ until the image of $C$ lies on the positive $y$-axis, ... | {
"ground_truth": "875",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given that Lucas makes a batch of lemonade using 200 grams of lemon juice, 100 grams of sugar, and 300 grams of water. If there are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar, and water has no calories, determine the total number of calories in 200 grams of this... | {
"ground_truth": "145",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Compute $\\binom{12}{9}$ and then find the factorial of the result.",
"role": "user"
}
] | {
"ground_truth": "220",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Several points were marked on a line, and then two additional points were placed between each pair of neighboring points. This procedure was repeated once more with the entire set of points. Could there have been 82 points on the line as a result?",
"role": "user"
}
] | {
"ground_truth": "10",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find the smallest four-digit number that satisfies the following system of congruences:\n\\begin{align*}\n3x &\\equiv 6 \\pmod{12} \\\\\n5x + 20 &\\equiv 25 \\pmod{15} \\\\\n3x - 2 &\\equiv 2x \\pmod{35}\n\\end{align*}",
"role": "user"
}
] | {
"ground_truth": "1274",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "If \\(\\log_{2} a + \\log_{2} b \\geq \\gamma\\), determine the smallest positive value \\(\\delta\\) for \\(a+b\\).",
"role": "user"
}
] | {
"ground_truth": "16",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A given sequence $r_1, r_2, \\dots, r_n$ of distinct real numbers can be put in ascending order by means of one or more \"bubble passes\". A bubble pass through a given sequence consists of comparing the second term with the first term, and exchanging them if and only if the second term is smaller... | {
"ground_truth": "931",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "If $x$ is the cube of a positive integer and $d$ is the number of positive integers that are divisors of $x$, then $d$ could be",
"role": "user"
}
] | {
"ground_truth": "202",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find a whole number, $M$, such that $\\frac{M}{5}$ is strictly between 9.5 and 10.5.",
"role": "user"
}
] | {
"ground_truth": "51",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Remove all perfect squares from the sequence of positive integers \\(1, 2, 3, \\cdots\\) to get a new sequence, and calculate the 2003rd term of this new sequence.",
"role": "user"
}
] | {
"ground_truth": "2047",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "The average weight of 8 boys is 160 pounds, and the average weight of 6 girls is 130 pounds. Calculate the average weight of these 14 children.",
"role": "user"
}
] | {
"ground_truth": "147",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "In a hypothetical math competition, contestants are given the problem to find three distinct positive integers $X$, $Y$, and $Z$ such that their product $X \\cdot Y \\cdot Z = 399$. What is the largest possible value of the sum $X+Y+Z$?",
"role": "user"
}
] | {
"ground_truth": "29",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A park is in the shape of a regular hexagon $2$ km on a side. Starting at a corner, Alice walks along the perimeter of the park for a distance of $5$ km. How many kilometers is she from her starting point?\n$\\textbf{(A)}\\ \\sqrt{13}\\qquad \\textbf{(B)}\\ \\sqrt{14}\\qquad \\textbf{(C)}\\ \\sqrt... | {
"ground_truth": "\\sqrt{13}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "If $x$ and $y$ are positive integers such that $xy - 8x + 9y = 632$, what is the minimal possible value of $|x - y|$?",
"role": "user"
}
] | {
"ground_truth": "27",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A square sheet of paper has area $6 \\text{ cm}^2$. The front is white and the back is black. When the sheet is folded so that point $A$ rests on the diagonal as shown, the visible black area is equal to the visible white area. How many centimeters is $A$ from its original position? Express your a... | {
"ground_truth": "2\\sqrt{2}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "The sum of an infinite geometric series is \\( 16 \\) times the series that results if the first two terms of the original series are removed. What is the value of the series' common ratio?",
"role": "user"
}
] | {
"ground_truth": "-\\frac{1}{4}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Given that $y$ is a multiple of $45678$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(14y+9)(y+14)$ and $y$?",
"role": "user"
}
] | {
"ground_truth": "1512",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the greatest integer less than 150 for which the greatest common divisor of that integer and 18 is 6?",
"role": "user"
}
] | {
"ground_truth": "144",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let \\( x = 19.\\overline{87} \\). If \\( 19.\\overline{87} = \\frac{a}{99} \\), find \\( a \\).\n\nIf \\( \\frac{\\sqrt{3}}{b \\sqrt{7} - \\sqrt{3}} = \\frac{2 \\sqrt{21} + 3}{c} \\), find \\( c \\).\n\nIf \\( f(y) = 4 \\sin y^{\\circ} \\) and \\( f(a - 18) = b \\), find \\( b \\).",
"role": ... | {
"ground_truth": "25",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Determine the smallest positive integer $m$ such that $11m-3$ and $8m + 5$ have a common factor greater than $1$.",
"role": "user"
}
] | {
"ground_truth": "108",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Determine the smallest positive integer \\( m \\) for which \\( m^3 - 90 \\) is divisible by \\( m + 9 \\).",
"role": "user"
}
] | {
"ground_truth": "12",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, what number of words would be an appropriate length for her speech?",
"role": "user"
}
... | {
"ground_truth": "5650",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\). Additionally, find its height dropped from vertex \\( A_{4} \\) onto the face \\( A_{1} A_{2} A_{3} \\).\n\nVertices:\n- \\( A_{1}(-1, 2, 4) \\)\n- \\( A_{2}(-1, -2, -4) \\)\n- \\( A_{3}(3, 0, -1) \... | {
"ground_truth": "24",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "In a certain school, there are $3$ times as many boys as girls and $9$ times as many girls as teachers. Using the letters $b, g, t$ to represent the number of boys, girls, and teachers, respectively, then the total number of boys, girls, and teachers can be represented by the expression",
"rol... | {
"ground_truth": "\\frac{37b}{27}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Borya and Vova play the following game on an initially white $8 \\times 8$ board. Borya goes first and, on each of his turns, colors any four white cells black. After each of his turns, Vova colors an entire row or column white. Borya aims to color as many cells black as possible, while Vova tries... | {
"ground_truth": "25",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find a factor of 100140001 which lies between 8000 and 9000.",
"role": "user"
}
] | {
"ground_truth": "8221",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Find the largest prime divisor of \\( 16^2 + 81^2 \\).",
"role": "user"
}
] | {
"ground_truth": "53",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let \\(a_{1}, a_{2}, \\cdots, a_{10}\\) be any 10 distinct positive integers such that \\(a_{1} + a_{2} + \\cdots + a_{10} = 1995\\). Find the minimum value of \\(a_{1} a_{2} + a_{2} a_{3} + \\cdots + a_{10} a_{1}\\).",
"role": "user"
}
] | {
"ground_truth": "6044",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "(a) The natural number \\( n \\) is less than 150. What is the largest remainder that the number 269 can give when divided by \\( n \\)?\n\n(b) The natural number \\( n \\) is less than 110. What is the largest remainder that the number 269 can give when divided by \\( n \\)?",
"role": "user"
... | {
"ground_truth": "109",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Solve the equation: $4x^2 - (x^2 - 2x + 1) = 0$.",
"role": "user"
}
] | {
"ground_truth": "-1",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $m \\ge 3$ be an integer and let $S = \\{3,4,5,\\ldots,m\\}$. Find the smallest value of $m$ such that for every partition of $S$ into two subsets, at least one of the subsets contains integers $a$, $b$, and $c$ (not necessarily distinct) such that $ab = c$.\n",
"role": "user"
}
] | {
"ground_truth": "243",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "In any isosceles triangle $PQR$ with $PQ = PR$, the altitude $PS$ bisects the base $QR$ so that $QS = RS$. Given that the triangle sides are $PQ = PR = 15$ and the entire base length $QR = 20$.\n\n[asy]\ndraw((0,0)--(20,0)--(10,36)--cycle,black+linewidth(1));\ndraw((10,36)--(10,0),black+linewidth(... | {
"ground_truth": "50\\sqrt{5}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let a $9$ -digit number be balanced if it has all numerals $1$ to $9$ . Let $S$ be the sequence of the numerals which is constructed by writing all balanced numbers in increasing order consecutively. Find the least possible value of $k$ such that any two subsequences of $S$ which has con... | {
"ground_truth": "17",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Distinct planes $p_1, p_2, \\dots, p_k$ intersect the interior of a cube $Q$. Let $S$ be the union of the faces of $Q$ and let $P = \\bigcup_{j=1}^{k} p_j$. The intersection of $P$ and $S$ consists of the union of all segments joining the midpoints of every pair of edges belonging to the same face... | {
"ground_truth": "20",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "A cylindrical barrel with radius $4$ feet and height $10$ feet is full of water. A solid cube with side length $8$ feet is set into the barrel so that the diagonal of the cube is vertical. The volume of water thus displaced is $v$ cubic feet. Find $v^2$.\n[asy] import three; import solids; size(5c... | {
"ground_truth": "384",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $f(x) = \\frac{x+1}{x-1}$. Then for $x^2 \\neq 1$, $f(-x)$ is",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{f(x)}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Is it possible to divide an equilateral triangle into 1,000,000 convex polygons such that any straight line intersects no more than 40 of them?",
"role": "user"
}
] | {
"ground_truth": "1707",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "An eight-sided die (numbered 1 through 8) is rolled, and $Q$ is the product of the seven numbers that are visible. What is the largest number that is certain to divide $Q$?",
"role": "user"
}
] | {
"ground_truth": "960",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Six distinct integers are picked at random from $\\{1,2,3,\\ldots,10\\}$. What is the probability that, among those selected, the second smallest is $3$?\n$\\textbf{(A)}\\ \\frac{1}{60}\\qquad \\textbf{(B)}\\ \\frac{1}{6}\\qquad \\textbf{(C)}\\ \\frac{1}{3}\\qquad \\textbf{(D)}\\ \\frac{1}{2}\\qqu... | {
"ground_truth": "\\frac{1}{3}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "1. Calculate the value of the following expression:\n$(1)(2\\frac{7}{9})^{\\frac{1}{2}} - (2\\sqrt{3} - \\pi)^{0} - (2\\frac{10}{27})^{-\\frac{2}{3}} + 0.25^{-\\frac{3}{2}}$\n2. Given that $x + x^{-1} = 4 (0 < x < 1)$, find the value of ${x^{\\frac{1}{2}}} + {x^{-\\frac{1}{2}}}$.",
"role": "us... | {
"ground_truth": "\\frac{389}{48}",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the least possible positive four-digit palindrome that is divisible by 4?",
"role": "user"
}
] | {
"ground_truth": "1881",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Mutually prime positive integers $p_n, q_n$ satisfy $\\\\frac{P_n}{q_n}=1+\\\\frac12+\\\\frac13+\\\\cdots+\\\\frac1n$. The sum of all positive integers $n$ such that $3|p_n$ is \\\\underline{\\\\hspace{2cm}}.",
"role": "user"
}
] | {
"ground_truth": "31",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Players $A$ and $B$ play a game on a blackboard that initially contains 2020 copies of the number 1. In every round, player $A$ erases two numbers $x$ and $y$ from the blackboard, and then player $B$ writes one of the numbers $x+y$ and $|x-y|$ on the blackboard. The game terminates as soon as, at ... | {
"ground_truth": "7",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "What is the sum of the digits of the integer equal to $\\left(10^{3}+1\\right)^{2}$ ?",
"role": "user"
}
] | {
"ground_truth": "1002001",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $W=(0,0), A=(7,0), S=(7,1)$, and $H=(0,1)$. Compute the number of ways to tile rectangle $W A S H$ with triangles of area $1 / 2$ and vertices at lattice points on the boundary of WASH.",
"role": "user"
}
] | {
"ground_truth": "3432",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Let $S=\\{1,2, \\ldots, 20\\}$, and let $f$ be a function from $S$ to $S$; that is, for all $s \\in S, f(s) \\in S$. Define the sequence $s_{1}, s_{2}, s_{3}, \\ldots$ by setting $s_{n}=\\sum_{k=1}^{20} \\underbrace{(f \\circ \\cdots \\circ f)}_{n}(k)$. That is, $s_{1}=f(1)+$ $\\cdots+f(20), s_{2}... | {
"ground_truth": "140",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Derek starts at the point $(0,0)$, facing the point $(0,1)$, and he wants to get to the point $(1,1)$. He takes unit steps parallel to the coordinate axes. A move consists of either a step forward, or a $90^{\\circ}$ right (clockwise) turn followed by a step forward, so that his path does not cont... | {
"ground_truth": "529",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Players $1,2,3,\\ldots,n$ are seated around a table, and each has a single penny. Player 1 passes a penny to player 2, who then passes two pennies to player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two ... | {
"ground_truth": "3098",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "Define a \\textit{growing spiral} in the plane to be a sequence of points with integer coordinates $P_0 = (0,0), P_1, \\dots, P_n$ such that $n \\geq 2$ and: \\begin{itemize} \\item the directed line segments $P_0 P_1, P_1 P_2, \\dots, P_{n-1} P_n$ are in the successive coordinate directions east ... | {
"ground_truth": "10053",
"mean_reward": 0
} | dishsoap | reasoning |
[
{
"content": "105 A cube of wood with an edge length of 3 meters, has a square hole with a side length of 1 meter drilled through the center of each face, all the way through, with the edges of the hole parallel to the corresponding edges of the cube. The total surface area (including the inside) of this object... | {
"ground_truth": "72",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The calculator's keyboard has digits from 0 to 9 and symbols of two operations. Initially, the display shows the number 0. Any keys can be pressed. The calculator performs operations in the sequence of key presses. If an operation symbol is pressed several times in a row, the calculator will remem... | {
"ground_truth": "1/3",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Three, let $M$ be a set of $n$ points in the plane, satisfying:\n(1) There exist 7 points in $M$ that are the 7 vertices of a convex heptagon;\n(2) For any 5 points in $M$, if these 5 points are the 5 vertices of a convex pentagon, then this convex pentagon contains at least one point from $M$ ins... | {
"ground_truth": "11",
"mean_reward": 0.015625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "# 8. Problem 8.1\n\nPentagon $A B C D E$ is circumscribed around a circle.\n\nAngles $\\angle A B C, \\angle B A E, \\angle C D E$ are each $104^{\\circ}$. Find $\\angle A D B$. Write the answer in degrees (the number only, without specifying the unit of measurement).\n\n#",
"role": "user"
}... | {
"ground_truth": "38",
"mean_reward": 0.03125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The points $(6,12)$ and $(0,-6)$ are connected by a straight line. Another point on this line is:",
"role": "user"
}
] | {
"ground_truth": "(3,3)",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is [asy] unitsize(36); draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5... | {
"ground_truth": "20",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "In a certain high school physical examination for seniors, the heights (in centimeters) of 12 students are $173$, $174$, $166$, $172$, $170$, $165$, $165$, $168$, $164$, $173$, $175$, $178$. Find the upper quartile of this data set.",
"role": "user"
}
] | {
"ground_truth": "173.5",
"mean_reward": 0.328125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Nationality, Movie-Genre, Sport, Transport.\nThe attributes have the following possible values:\n- Nationality: british, chinese, japanese, nigerian, spanish\n- Movie-Ge... | {
"ground_truth": "thriller",
"mean_reward": 0.171875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A circle of radius 7 is inscribed in a rectangle. The ratio of the length of the rectangle to its width is 3:1. Calculate the area of the rectangle.",
"role": "user"
}
] | {
"ground_truth": "588",
"mean_reward": 0.3125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "60. Some locks' keys have been mixed up, and it would take at most 28 tries to match each lock with its own key. There are $\\qquad$ locks.",
"role": "user"
}
] | {
"ground_truth": "8",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Alex is a perfectionist when it comes to coding, and he spends a lot of time ensuring every detail is correct. One night, Alex is debugging a piece of code and notices that for every misplaced variable he finds, it takes him 15 minutes to fix it. In the first hour, he finds 3 misplaced variables. ... | {
"ground_truth": "10",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Authors: Dumanov I., Krumovsky R.\n\nDiscussing winter holidays in class, Sasha said: \"Now, after I flew to Addis Ababa, I have celebrated New Year's in all possible hemispheres of the Earth, except one!\n\nWhat is the minimum number of places where Sasha has celebrated New Year's?\n\nConsider th... | {
"ground_truth": "4",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "If the bisector of the acute angle $B$ in the right triangle $ABC$ divides the leg $AC$ in such a way that the segments are in the ratio $2:\\sqrt{3}$, then the angle $C$ of the triangle is $60^{\\circ}$.",
"role": "user"
}
] | {
"ground_truth": "60^\\circ",
"mean_reward": 0.21875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "The diagram shows three squares, \\( PQRS \\), \\( TUVW \\), and \\( WXYZ \\). Angles \\( PU V \\) and \\( QYX \\) are \\( 62^{\\circ} \\) and \\( 74^{\\circ} \\) respectively. Find the measure of angle \\( VWX \\) in degrees.",
"role": "user"
}
] | {
"ground_truth": "44^{\\circ}",
"mean_reward": 0.390625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Two cyclists, $C$ and $D$, start at the same time to ride from town X to town Y and town Z respectively, where town Y is $90$ miles away from X and town Z is $120$ miles away. Cyclist $C$ travels $6$ mph slower than cyclist $D$, who reaches town Y and then travels $30$ miles further before meeting... | {
"ground_truth": "6",
"mean_reward": 0.078125
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "4. [4] For $0 \\leq y \\leq 2$, let $D_{y}$ be the half-disk of diameter 2 with one vertex at $(0, y)$, the other vertex on the positive $x$-axis, and the curved boundary further from the origin than the straight boundary. Find the area of the union of $D_{y}$ for all $0 \\leq y \\leq 2$.",
"r... | {
"ground_truth": "\\pi",
"mean_reward": 0.265625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Among the 12 lines where the edges of a hexagonal pyramid are located, how many pairs of skew lines exist? Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "24",
"mean_reward": 0.0625
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "A certain middle school holds a math problem-solving competition. The scores of 5 participants are $70$, $85$, $90$, $75$, $95$. Find the upper quartile of these 5 scores. Express your answer as a whole number.",
"role": "user"
}
] | {
"ground_truth": "90",
"mean_reward": 0
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Problem 4. We say a 2023-tuple of nonnegative integers $\\left(a_{1}, a_{2}, \\ldots a_{2023}\\right)$ is sweet if the following conditions hold:\n\n- $a_{1}+a_{2}+\\ldots+a_{2023}=2023$,\n- $\\frac{a_{1}}{2^{1}}+\\frac{a_{2}}{2^{2}}+\\ldots+\\frac{a_{2023}}{2^{2023}} \\leqslant 1$.\n\nDetermine t... | {
"ground_truth": "22228",
"mean_reward": 0.296875
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
[
{
"content": "Find the value of $m + n$ where $m$ and $n$ are integers such that the positive difference between the roots of the equation $4x^2 - 12x - 9 = 0$ can be expressed as $\\frac{\\sqrt{m}}{n}$, with $m$ not divisible by the square of any prime number.",
"role": "user"
}
] | {
"ground_truth": "19",
"mean_reward": 0.375
} | AceReason-Math-Qwen3-4B-Instruct-eval-32k-64_partial | reasoning |
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