data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin ^{2}x+ \\frac{ \\sqrt{3}}{2}\\sin 2x$.\n(1) Find the interval(s) where the function $f(x)$ is monotonically decreasing.\n(2) In $\\triangle ABC$, if $f(\\frac{A}{2})=1$ and the area of the triangle is $3\\sqrt{3}$, find the minimum value of side $... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 21649,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that there are 5 balls of each of the three colors: black, white, and red, each marked with the numbers 1, 2, 3, 4, 5, calculate the number of different ways to draw 5 balls such that their numbers are all different and all three colors are present. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 21650,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At the 2007 Math Olympics, Team Canada won $17$ out of a possible $100$ medals. Which one of the following is closest to the fraction of medals that they won? $$\n\\frac{1}{4} \\qquad \\frac{1}{5} \\qquad \\frac{1}{6} \\qquad \\frac{1}{7} \\qquad \\frac{1}{8}\n$$ Let's think st... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 21651,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $z$ be a complex number such that $|z| = 2.$ Find the largest possible distance between $(3 + 4i)z^3$ and $z^5$ when plotted in the complex plane. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 21652,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ ($a > b > 0$) with a vertex coordinate at $B(0,1)$, and the eccentricity of the ellipse being $\\frac{\\sqrt{3}}{2}$,\n$(I)$ find the equation of the ellipse;\n$(II)$ let point $Q$ be a point on ellipse $C$ below the... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{7}"
} | {
"split": "train",
"index": 21653,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the triangle $ABC$ it is known that $\\angle A = 75^o, \\angle C = 45^o$ . On the ray $BC$ beyond the point $C$ the point $T$ is taken so that $BC = CT$ . Let $M$ be the midpoint of the segment $AT$ . Find the measure of the $\\angle BMC$ .\n\n(Anton Trygub) Let... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 21654,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a number line, point $P$ is at 3 and $V$ is at 33. The number line between 3 and 33 is divided into six equal parts by the points $Q, R, S, T, U$. What is the sum of the lengths of $PS$ and $TV$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 21655,
"solution": "The segment of the number line between 3 and 33 has length $33 - 3 = 30$. Since this segment is divided into six equal parts, then each part has length $30 \\div 6 = 5$. The segment $PS$ is made up of 3 of these equal parts, and so has length $3 \\times 5 = 15$. Th... |
deepscaler | [
{
"role": "user",
"content": "Undecillion years ago in a galaxy far, far away, there were four space stations in the three-dimensional space, each pair spaced 1 light year away from each other. Admiral Ackbar wanted to establish a base somewhere in space such that the sum of squares of the distances from th... | math | {
"style": "rule",
"ground_truth": "\\frac{27 \\sqrt{6}}{8} \\pi"
} | {
"split": "train",
"index": 21656,
"solution": "Solution 1: Set up a coordinate system where the coordinates of the stations are $\\left(\\frac{1}{2 \\sqrt{2}}, \\frac{1}{2 \\sqrt{2}}, \\frac{1}{2 \\sqrt{2}}\\right)$, $\\left(-\\frac{1}{2 \\sqrt{2}},-\\frac{1}{2 \\sqrt{2}}, \\frac{1}{2 \\sqrt{2}}\\right),\\left(... |
deepscaler | [
{
"role": "user",
"content": "Alice and Bob live on the same road. At time $t$ , they both decide to walk to each other's houses at constant speed. However, they were busy thinking about math so that they didn't realize passing each other. Alice arrived at Bob's house at $3:19\\text{pm}$ , and Bob arrived... | math | {
"style": "rule",
"ground_truth": "179"
} | {
"split": "train",
"index": 21657,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An equilateral triangle of side length $ n$ is divided into unit triangles. Let $ f(n)$ be the number of paths from the triangle in the top row to the middle triangle in the bottom row, such that adjacent triangles in a path share a common edge and the path never travels up... | math | {
"style": "rule",
"ground_truth": "2005!"
} | {
"split": "train",
"index": 21658,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The isosceles trapezoid has base lengths of 24 units (bottom) and 12 units (top), and the non-parallel sides are each 12 units long. How long is the diagonal of the trapezoid? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}"
} | {
"split": "train",
"index": 21659,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 3 different pairs of shoes in a shoe cabinet. If one shoe is picked at random from the left shoe set of 6 shoes, and then another shoe is picked at random from the right shoe set of 6 shoes, calculate the probability that the two shoes form a pair. Let's think step by... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 21660,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The complete graph of $y=f(x)$, which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is $1$.)\n\nWhat is the sum of the $x$-coordinates of all points where $f(x) = x+1$? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 21661,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there was three times as many sets of twins as... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 21662,
"solution": "1. **Define Variables:**\n Let $a$ be the number of sets of twins, $b$ be the number of sets of triplets, and $c$ be the number of sets of quadruplets.\n\n2. **Set Up Equations:**\n From the problem, we have the following relationships:\n - There are four tim... |
deepscaler | [
{
"role": "user",
"content": "Find the distance between the points (0,4) and (3,0). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 21663,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the geometric sequence $\\{a_{n}\\}$, $a_{3}$ and $a_{7}$ are two distinct extreme points of the function $f\\left(x\\right)=\\frac{1}{3}x^{3}+4x^{2}+9x-1$. Find $a_{5}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 21664,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that in rhombus $ABCD$, the diagonal $AC$ is twice as long as diagonal $BD$, and point $E$ is on segment $AC$ such that line segment $BE$ bisects $\\angle ABC$, determine the ratio of the area of triangle $ABE$ to the area of rhombus $ABCD$. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 21665,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $\\log _{n}\\left(\\frac{1}{2}\\right) \\log _{n-1}\\left(\\frac{1}{3}\\right) \\cdots \\log _{2}\\left(\\frac{1}{n}\\right)$ in terms of $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-1)^{n-1}"
} | {
"split": "train",
"index": 21666,
"solution": "Using $\\log \\frac{1}{x}=-\\log x$ and $\\log _{b} a=\\frac{\\log a}{\\log b}$, we get that the product equals $\\frac{(-\\log 2)(-\\log 3) \\cdots(-\\log n)}{\\log n \\cdots \\log 3 \\log 2}=(-1)^{n-1}$."
} |
deepscaler | [
{
"role": "user",
"content": "Let $p$ , $q$ , $r$ , and $s$ be 4 distinct primes such that $p+q+r+s$ is prime, and the numbers $p^2+qr$ and $p^2+qs$ are both perfect squares. What is the value of $p+q+r+s$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 21667,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A plane is expressed parametrically by\n\\[\\mathbf{v} = \\begin{pmatrix} 1 + s - t \\\\ 2 - s \\\\ 3 - 2s + 2t \\end{pmatrix}.\\]Find the equation of the plane. Enter your answer in the form\n\\[Ax + By + Cz + D = 0,\\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ a... | math | {
"style": "rule",
"ground_truth": "2x + z - 5 = 0"
} | {
"split": "train",
"index": 21668,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\\frac{1}{2}$-mile stretch in a... | math | {
"style": "rule",
"ground_truth": "3 \\frac{3}{4}"
} | {
"split": "train",
"index": 21669,
"solution": "To determine which route is quicker and by how many minutes, we need to calculate the time taken for each route and then compare them.\n\n#### Route A:\n- **Distance:** $6$ miles\n- **Speed:** $30$ miles per hour\n\nUsing the formula for time, $t = \\frac{d}{s}$, w... |
deepscaler | [
{
"role": "user",
"content": "Positive real numbers $b \\not= 1$ and $n$ satisfy the equations \\[\\sqrt{\\log_b n} = \\log_b \\sqrt{n} \\qquad \\text{and} \\qquad b \\cdot \\log_b n = \\log_b (bn).\\] The value of $n$ is $\\frac{j}{k},$ where $j$ and $k$ are relatively prime positive integers. Find $j+k.$ ... | math | {
"style": "rule",
"ground_truth": "881"
} | {
"split": "train",
"index": 21670,
"solution": "Denote $x = \\log_b n$. Hence, the system of equations given in the problem can be rewritten as \\begin{align*} \\sqrt{x} & = \\frac{1}{2} x , \\\\ bx & = 1 + x . \\end{align*} Solving the system gives $x = 4$ and $b = \\frac{5}{4}$. Therefore, \\[n = b^x = \\frac{... |
deepscaler | [
{
"role": "user",
"content": "In the plane rectangular coordinate system $(xOy)$, establish a polar coordinate system $(.$ with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. If the polar coordinate equation of the line $l$ is $\\sqrt {2}ρ\\cos (θ- \\dfrac {π}{4})-2=0$, and the polar c... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt {6}"
} | {
"split": "train",
"index": 21671,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cinema is showing four animated movies: Toy Story, Ice Age, Shrek, and Monkey King. The ticket prices are 50 yuan, 55 yuan, 60 yuan, and 65 yuan, respectively. Each viewer watches at least one movie and at most two movies. However, due to time constraints, viewers cannot watc... | math | {
"style": "rule",
"ground_truth": "1792"
} | {
"split": "train",
"index": 21672,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A builder has two identical bricks. She places them side by side in three different ways, resulting in shapes with surface areas of 72, 96, and 102. What is the surface area of one original brick?\nA) 36\nB) 48\nC) 52\nD) 54\nE) 60 Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 21673,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind vel... | math | {
"style": "rule",
"ground_truth": "12.8"
} | {
"split": "train",
"index": 21674,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the greatest real number $ C $, such that for every positive integer $ n\\ge 2 $, there exists $ x_1, x_2,..., x_n \\in [-1,1]$, so that\n$$\\prod_{1\\le i<j\\le n}(x_i-x_j) \\ge C^{\\frac{n(n-1)}{2}}$$. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 21675,
"solution": "\nTo determine the greatest real number \\( C \\) such that for every positive integer \\( n \\geq 2 \\), there exist \\( x_1, x_2, \\ldots, x_n \\in [-1, 1] \\) satisfying\n\\[\n\\prod_{1 \\le i < j \\le n} (x_i - x_j) \\geq C^{\\frac{n(n-1)}{2}},\n\\]\nwe conside... |
deepscaler | [
{
"role": "user",
"content": "If the arithmetic sequence $\\{a_n\\}$ satisfies $a_{17} + a_{18} + a_{19} > 0$ and $a_{17} + a_{20} < 0$, then the sum of the first $n$ terms of $\\{a_n\\}$ is maximized when $n =$ ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 21676,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a positive integer $n$ , let $f_n(x)=\\cos (x) \\cos (2 x) \\cos (3 x) \\cdots \\cos (n x)$ . Find the smallest $n$ such that $\\left|f_n^{\\prime \\prime}(0)\\right|>2023$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 21677,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a set of sample data with $8$ numbers, the average is $8$, and the variance is $12$. Two unknown numbers are added to this set of sample data to form a new set of sample data. It is known that the average of the new sample data is $9$. Find the minimum value of the varian... | math | {
"style": "rule",
"ground_truth": "13.6"
} | {
"split": "train",
"index": 21678,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the vectors $\\overrightarrow{m}=(\\cos x,\\sin x)$ and $\\overrightarrow{n}=(2 \\sqrt {2}+\\sin x,2 \\sqrt {2}-\\cos x)$, and the function $f(x)= \\overrightarrow{m}\\cdot \\overrightarrow{n}$, where $x\\in R$.\n(I) Find the maximum value of the function $f(x)$;\n(II) If... | math | {
"style": "rule",
"ground_truth": "-\\frac {3 \\sqrt {5}+1}{8}"
} | {
"split": "train",
"index": 21679,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $(2 \\times 10^9) - (6 \\times 10^7) \\div (2 \\times 10^2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1999700000"
} | {
"split": "train",
"index": 21680,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\{a_n\\}$ be a geometric sequence, $\\{b_n\\}$ be an arithmetic sequence, and $b_1=0$, $c_n=a_n+b_n$. If $\\{c_n\\}$ is $1$, $1$, $2$, $\\ldots$, find the sum of the first $10$ terms of the sequence $\\{c_n\\}$. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "978"
} | {
"split": "train",
"index": 21681,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The equation of the line joining the complex numbers $-2 + 3i$ and $1 + i$ can be expressed in the form\n\\[az + b \\overline{z} = 10\\]for some complex numbers $a$ and $b$. Find the product $ab$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 21682,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the first fifty positive odd integers subtracted from the sum of the first fifty positive even integers, each decreased by 3, calculate the result. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-100"
} | {
"split": "train",
"index": 21683,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When two standard dice and one 8-sided die (with faces showing numbers from 1 to 8) are tossed, the numbers \\(a, b, c\\) are obtained respectively where \\(a\\) and \\(b\\) are from the standard dice and \\(c\\) is from the 8-sided die. Find the probability that \\((a-1)(b-1)(... | math | {
"style": "rule",
"ground_truth": "\\frac{175}{288}"
} | {
"split": "train",
"index": 21684,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The rules for a race require that all runners start at $A$, touch any part of the 1500-meter wall, touch any part of the opposite 1500-meter wall, and stop at $B$. What is the minimum distance a participant must run? Assume that $A$ is 400 meters directly south of the first wal... | math | {
"style": "rule",
"ground_truth": "2915"
} | {
"split": "train",
"index": 21685,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We denote by gcd (...) the greatest common divisor of the numbers in (...). (For example, gcd $(4, 6, 8)=2$ and gcd $(12, 15)=3$ .) Suppose that positive integers $a, b, c$ satisfy the following four conditions: $\\bullet$ gcd $(a, b, c)=1$ , $\\bullet$ gcd $(a, b + c)... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 21686,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse with foci at $(1,0)$ and $(-1,0)$, it intersects with the line $y=x-2$. Determine the maximum value of the eccentricity of this ellipse. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{5}"
} | {
"split": "train",
"index": 21687,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\left|\\frac{12}{x}+3\\right|=2$, find the product of all possible values of $x$. Express your answer as an improper fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{144}{5}"
} | {
"split": "train",
"index": 21688,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given point $A(0,2)$, and $P$ is any point on the ellipse $\\frac{x^2}{4}+y^2=1$, then the maximum value of $|PA|$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{21}}{3}"
} | {
"split": "train",
"index": 21689,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the dot product of $\\begin{pmatrix} 3 \\\\ -4 \\\\ -3 \\end{pmatrix}$ and $\\begin{pmatrix} -5 \\\\ 2 \\\\ 1 \\end{pmatrix}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-26"
} | {
"split": "train",
"index": 21690,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The roots of the equation $2x^2 - 5x - 4 = 0$ can be written in the form $x = \\frac{m \\pm \\sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of 1. What is the value of $n$? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 21691,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A quadrilateral pyramid \\(SABCD\\) is given, with a base that is a trapezoid \\(ABCD\\). The ratio of the bases \\(AD\\) and \\(BC\\) of this trapezoid is 2. Construct the cross-section of the pyramid with a plane passing through point \\(D\\) and the midpoints of the edges \\... | math | {
"style": "rule",
"ground_truth": "2:1"
} | {
"split": "train",
"index": 21692,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Augustin has six $1 \\times 2 \\times \\pi$ bricks. He stacks them, one on top of another, to form a tower six bricks high. Each brick can be in any orientation so long as it rests flat on top of the next brick below it (or on the floor). How many distinct heights of towers can... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 21693,
"solution": "If there are $k$ bricks which are placed so that they contribute either 1 or 2 height, then the height of these $k$ bricks can be any integer from $k$ to $2 k$. Furthermore, towers with different values of $k$ cannot have the same height. Thus, for each $k$ there a... |
deepscaler | [
{
"role": "user",
"content": "Let \\( f(x) = \\frac{1}{x^3 + 3x^2 + 2x} \\). Determine the smallest positive integer \\( n \\) such that \n\\[ f(1) + f(2) + f(3) + \\cdots + f(n) > \\frac{503}{2014}. \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "44"
} | {
"split": "train",
"index": 21694,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a\\_n\\}$, it is known that $a\\_1 - a\\_4 - a\\_8 - a\\_{12} + a\\_{15} = 2$. Find the value of $S\\_{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-30"
} | {
"split": "train",
"index": 21695,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the second smallest integer that can be written as the sum of two positive cubes in two different ways. Compute $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4104"
} | {
"split": "train",
"index": 21696,
"solution": "A computer search yields that the second smallest number is 4104 . Indeed, $4104=9^{3}+15^{3}=2^{3}+16^{3}$"
} |
deepscaler | [
{
"role": "user",
"content": "This century will mark the 200th anniversary of the birth of the famous Russian mathematician Pafnuty Lvovich Chebyshev, a native of Kaluga province. The sum of the digits in the hundreds and thousands places of the year he was born is 3 times the sum of the digits in the units... | math | {
"style": "rule",
"ground_truth": "1821"
} | {
"split": "train",
"index": 21697,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Shuai Shuai memorized more than one hundred words in seven days. The number of words memorized in the first three days is $20\\%$ less than the number of words memorized in the last four days, and the number of words memorized in the first four days is $20\\%$ more than the num... | math | {
"style": "rule",
"ground_truth": "198"
} | {
"split": "train",
"index": 21698,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be a point on the line\n\\[\\begin{pmatrix} 3 \\\\ -1 \\\\ 2 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ -2 \\\\ 1 \\end{pmatrix}\\]and let $Q$ be a point on the line\n\\[\\begin{pmatrix} 0 \\\\ 0 \\\\ 4 \\end{pmatrix} + s \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 21699,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A ball inside a rectangular container of width 7 and height 12 is launched from the lower-left vertex of the container. It first strikes the right side of the container after traveling a distance of $\\sqrt{53}$ (and strikes no other sides between its launch and its impact with... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 21700,
"solution": "Let $h$ be this height. Then, using the Pythagorean theorem, we see that $h^{2} + 7^{2} = 53$, so $h = 2$."
} |
deepscaler | [
{
"role": "user",
"content": "Given a quadratic polynomial $q(x) = x^2 - px + q$ known to be \"mischievous\" if the equation $q(q(x)) = 0$ is satisfied by exactly three different real numbers, determine the value of $q(2)$ for the unique polynomial $q(x)$ for which the product of its roots is minimized. Let... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 21701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a given arithmetic series the sum of the first $50$ terms is $200$, and the sum of the next $50$ terms is $2700$. The first term in the series is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-20.5"
} | {
"split": "train",
"index": 21702,
"solution": "1. **Define the terms and expressions for the sums:**\n Let the first term of the arithmetic sequence be $a$ and the common difference be $d$. The $n$-th term of an arithmetic sequence can be expressed as $a + (n-1)d$.\n\n2. **Expression for the sum of the first ... |
deepscaler | [
{
"role": "user",
"content": "Fill in the table with the numbers $0, 1, 2, \\cdots, 14, 15$ so that for each row and each column, the remainders when divided by 4 are exactly $0, 1, 2, 3$ each, and the quotients when divided by 4 are also exactly $0, 1, 2, 3$ each, and determine the product of the four numb... | math | {
"style": "rule",
"ground_truth": "32760"
} | {
"split": "train",
"index": 21703,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among all integers that alternate between 1 and 0, starting and ending with 1 (e.g., 101, 10101, 10101…), how many are prime numbers? Why? And list all the prime numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 21704,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct arrangements of the letters in the word \"balloon\" are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"split": "train",
"index": 21705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Henry walked on a flat field 9 meters due north from a tree. He then turned due east and walked 24 feet. He then turned due south and walked 9 meters plus 32 feet. How many feet away from his original starting point is Henry? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "40\\text{ feet}"
} | {
"split": "train",
"index": 21706,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given three forces in space, $\\overrightarrow {F_{1}}$, $\\overrightarrow {F_{2}}$, and $\\overrightarrow {F_{3}}$, each with a magnitude of 2, and the angle between any two of them is 60°, the magnitude of their resultant force $\\overrightarrow {F}$ is ______. Let's think st... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt {6}"
} | {
"split": "train",
"index": 21707,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest negative root \\( x_{0} \\) of the equation \\( \\frac{\\sin x}{1+\\cos x} = 2 - \\operatorname{ctg} x \\). Write the answer as \\( x_{0} \\cdot \\frac{3}{\\pi} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3.5"
} | {
"split": "train",
"index": 21708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given vectors $\\overrightarrow{m} = (\\cos B, \\cos C)$ and $\\overrightarrow{n} = (2a + c, b)$, and $\\overrightarrow{m} \\perp \\overrightarrow{n}$.\n\n(I) Find the measure ... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 21709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The matrix\n\\[\\begin{pmatrix} a & \\frac{15}{34} \\\\ c & \\frac{25}{34} \\end{pmatrix}\\]corresponds to a projection. Enter the ordered pair $(a,c).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left( \\frac{9}{34}, \\frac{15}{34} \\right)"
} | {
"split": "train",
"index": 21710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For polynomial $P(x)=1-\\dfrac{1}{3}x+\\dfrac{1}{6}x^{2}$, define\n\\[Q(x)=P(x)P(x^{3})P(x^{5})P(x^{7})P(x^{9})=\\sum_{i=0}^{50} a_ix^{i}.\\]Find $\\sum_{i=0}^{50} |a_i|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{243}{32}"
} | {
"split": "train",
"index": 21711,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic-geometric sequence $\\{a\\_n\\}$, where $a\\_1 + a\\_3 = 10$ and $a\\_4 + a\\_6 = \\frac{5}{4}$, find its fourth term and the sum of the first five terms. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{31}{2}"
} | {
"split": "train",
"index": 21712,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\(\\frac{\\cos 100^\\circ}{1-4 \\sin 25^\\circ \\cos 25^\\circ \\cos 50^\\circ}=\\tan x^\\circ\\), find \\(x\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "95"
} | {
"split": "train",
"index": 21713,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ways to arrange the letters of the word MOREMOM. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "420"
} | {
"split": "train",
"index": 21714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the number of geometric sequences of length $3$ where each number is a positive integer no larger than $10$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 21715,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the function \\( f(x) = x^3 + 3x^2 + 6x + 14 \\), and \\( f(a) = 1 \\), \\( f(b) = 19 \\). Then \\( a + b = \\quad \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 21716,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Binbin's height is 1.46 meters, his father is 0.32 meters taller than Binbin, and his mother's height is 1.5 meters. \n(1) How tall is Binbin's father? \n(2) How much shorter is Binbin's mother than his father? Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "0.28"
} | {
"split": "train",
"index": 21717,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, \\(C\\) lies on \\(AE\\) and \\(AB=BC=CD\\). If \\(\\angle CDE=t^{\\circ}, \\angle DEC=(2t)^{\\circ}\\), and \\(\\angle BCA=\\angle BCD=x^{\\circ}\\), determine the measure of \\(\\angle ABC\\). Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 21718,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Spencer is making burritos, each of which consists of one wrap and one filling. He has enough filling for up to four beef burritos and three chicken burritos. However, he only has five wraps for the burritos; in how many orders can he make exactly five burritos? Let's think ste... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 21719,
"solution": "Spencer's burrito-making can include either 3, 2, or 1 chicken burrito; consequently, he has $\\binom{5}{3}+\\binom{5}{2}+\\binom{5}{1}=25$ orders in which he can make burritos."
} |
deepscaler | [
{
"role": "user",
"content": "Compute $1-2+3-4+\\dots+100-101$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-151"
} | {
"split": "train",
"index": 21720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In acute triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, with $a=2$ and $2\\sin A=\\sin C$. \n$(1)$ Find the length of $c$; \n$(2)$ If $\\cos C=\\frac{1}{4}$, find the area of $\\triangle ABC$. Let's think ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{15}"
} | {
"split": "train",
"index": 21721,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In isosceles right-angled triangle $ABC$ , $CA = CB = 1$ . $P$ is an arbitrary point on the sides of $ABC$ . Find the maximum of $PA \\cdot PB \\cdot PC$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 21722,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have? Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 21723,
"solution": "1. **Define Variables:**\n Let $x$ be the number of 5-cent coins Claudia has, and let $y$ be the number of 10-cent coins. Since Claudia has 12 coins in total, we have:\n \\[\n x + y = 12\n \\]\n\n2. **Express Total Value Range:**\n The smallest value Clau... |
deepscaler | [
{
"role": "user",
"content": "Factor the following expression: $45x+30$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15(3x+2)"
} | {
"split": "train",
"index": 21724,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all prime numbers $p$ which satisfy \\[p = a^4 + b^4 + c^4 - 3\\] for some primes (not necessarily distinct) $a$ , $b$ and $c$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "719"
} | {
"split": "train",
"index": 21725,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(Geometry Proof Exercise) From a point A outside a circle ⊙O with radius 2, draw a line intersecting ⊙O at points C and D. A line segment AB is tangent to ⊙O at B. Given that AC=4 and AB=$4 \\sqrt {2}$, find $tan∠DAB$. Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {2}}{4}"
} | {
"split": "train",
"index": 21726,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the least common multiple of $A$ and $B$ is $120$, and the ratio of $A$ to $B$ is $3:4$, then what is their greatest common divisor? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 21727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the expansion of \\((-xy + 2x + 3y - 6)^6\\), what is the coefficient of \\(x^4 y^3\\)? (Answer with a specific number) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-21600"
} | {
"split": "train",
"index": 21728,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that point $A(-2,3)$ lies on the axis of parabola $C$: $y^{2}=2px$, and the line passing through point $A$ is tangent to $C$ at point $B$ in the first quadrant. Let $F$ be the focus of $C$. Then, $|BF|=$ _____ . Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 21729,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, and $c$ be the roots of the equation $x^3 - 2x - 5 = 0$. Find $\\frac{1}{a-2} + \\frac{1}{b-2} + \\frac{1}{c-2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 21730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $C$: $y^{2}=2px$ with the focus at $F(2,0)$, and points $P(m,0)$ and $Q(-m,n)$, a line $l$ passing through $P$ with a slope of $k$ (where $k\\neq 0$) intersects the parabola $C$ at points $A$ and $B$.\n(Ⅰ) For $m=k=2$, if $\\vec{QA} \\cdot \\vec{QB} = 0$, fin... | math | {
"style": "rule",
"ground_truth": "\\frac{32\\sqrt{3}}{9}"
} | {
"split": "train",
"index": 21731,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To set up for a Fourth of July party, David is making a string of red, white, and blue balloons. He places them according to the following rules: - No red balloon is adjacent to another red balloon. - White balloons appear in groups of exactly two, and groups of white balloons ... | math | {
"style": "rule",
"ground_truth": "99"
} | {
"split": "train",
"index": 21732,
"solution": "It is possible to achieve 99 red balloons with the arrangement $$\\text { WWBBBWW } \\underbrace{\\text { RBBBWWRBBBWW ...RBBBWW, }}_{99 \\text { RBBBWW's }}$$ which contains $99 \\cdot 6+7=601$ balloons. Now assume that one can construct a chain with 98 or fewer r... |
deepscaler | [
{
"role": "user",
"content": "Three equilateral triangles $ABC$, $BCD$, and $CDE$ are positioned such that $B$, $C$, and $D$ are collinear, and $C$ is the midpoint of $BD$. Triangle $CDE$ is positioned such that $E$ is on the same side of line $BD$ as $A$. What is the value of $AE \\div BC$ when expressed i... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 21733,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the array of 13 squares shown below, 8 squares are colored red, and the remaining 5 squares are colored blue. If one of all possible such colorings is chosen at random, the probability that the chosen colored array appears the same when rotated 90 degrees around the central ... | math | {
"style": "rule",
"ground_truth": "429"
} | {
"split": "train",
"index": 21734,
"solution": "When the array appears the same after a 90-degree rotation, the top formation must look the same as the right formation, which looks the same as the bottom one, which looks the same as the right one. There are four of the same configuration. There are not enough re... |
deepscaler | [
{
"role": "user",
"content": "In a modified version of a walking game, I play by different rules. On the first move, I stand still, but for each subsequent move $n$ where $2 \\le n \\le 25$, I take two steps forward if $n$ is prime and three steps backward if $n$ is composite. After completing all 25 moves,... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 21735,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the largest real solution to the equation\n\\[\\dfrac{4}{x-2} + \\dfrac{6}{x-6} + \\dfrac{13}{x-13} + \\dfrac{15}{x-15} = x^2 - 7x - 6\\]\nThere are positive integers $p, q,$ and $r$ such that $n = p + \\sqrt{q + \\sqrt{r}}$. Find $p+q+r$. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "103"
} | {
"split": "train",
"index": 21736,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of all positive integers $n<2048$ such that $n$ has an even number of 1's in its binary representation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1048064"
} | {
"split": "train",
"index": 21737,
"solution": "Note that the positive integers less than 2047 are those with at most 11 binary digits. Consider the contribution from any one of those digits. If we set that digit to 1, then the remaining 10 digits can be set in $2^{9}=512$ ways so that the number of 1's is even.... |
deepscaler | [
{
"role": "user",
"content": "What is the largest difference that can be formed by subtracting two numbers chosen from the set $\\{ -16,-4,0,2,4,12 \\}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 21738,
"solution": "To find the largest difference that can be formed by subtracting two numbers chosen from the set $\\{ -16,-4,0,2,4,12 \\}$, we need to consider the subtraction $a - b$, where $a$ and $b$ are elements of the set. The goal is to maximize this expression.\n\n1. **Maxi... |
deepscaler | [
{
"role": "user",
"content": "What percent of the prime numbers less than 12 are divisible by 2? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"split": "train",
"index": 21739,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The reciprocal of $-2024$ is ______; $7.8963\\approx$ ______ (rounded to the nearest hundredth). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7.90"
} | {
"split": "train",
"index": 21740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $ABCD$ is a rectangle. $E$ is a point on $AB$ between $A$ and $B$ , and $F$ is a point on $AD$ between $A$ and $D$ . The area of the triangle $EBC$ is $16$ , the area of the triangle $EAF$ is $12$ and the area of the triangle $FDC$ is 30. Find the area ... | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 21741,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square $WXYZ$ with side length 8 units is divided into four smaller squares by drawing lines from the midpoints of one side to the midpoints of the opposite sides. The top right square of each iteration is shaded. If this dividing and shading process is done 100 times, what i... | math | {
"style": "rule",
"ground_truth": "\\frac{64}{3}"
} | {
"split": "train",
"index": 21742,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "During the Spring Festival, a supermarket holds a promotional lottery event. When the amount spent by a customer reaches a certain threshold, they can participate in a lottery. The rules of the event are: from a box containing 3 black balls, 2 red balls, and 1 white ball (ident... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{9}"
} | {
"split": "train",
"index": 21743,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let set $A=\\{-1, 2, 3\\}$, and set $B=\\{a+2, a^2+2\\}$. If $A \\cap B = \\{3\\}$, then the real number $a=$ ___. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 21744,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the set $\\{1,2,3, \\cdots, 20\\}$, choose 4 different numbers such that these 4 numbers form an arithmetic sequence. Determine the number of such arithmetic sequences. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "114"
} | {
"split": "train",
"index": 21745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In two places, A and B, the monthly telephone rental fee is $18. The monthly telephone fee $y (in dollars)$ varies with time $x (in minutes)$. Based on the data in the table below, answer the following questions:\n\n| Talk Time $x (minutes)$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 21746,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For integers $a,b,$ and $c$ define $\\fbox{a,b,c}$ to mean $a^b-b^c+c^a$. Then $\\fbox{1,-1,2}$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 21747,
"solution": "1. **Substitute the values of $a$, $b$, and $c$ into the expression $\\fbox{a,b,c} = a^b - b^c + c^a$:**\n - Here, $a = 1$, $b = -1$, and $c = 2$.\n - Thus, $\\fbox{1,-1,2} = 1^{-1} - (-1)^2 + 2^1$.\n\n2. **Calculate each term in the expression:**\n - $1^{-1}... |
deepscaler | [
{
"role": "user",
"content": "\nEvery Sunday, a married couple has breakfast with their mothers. Unfortunately, the relationships each spouse has with the other's mother are quite strained: both know that there is a two-thirds chance of getting into an argument with the mother-in-law. In the event of a conf... | math | {
"style": "rule",
"ground_truth": "4/9"
} | {
"split": "train",
"index": 21748,
"solution": ""
} |
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