data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given $\\sqrt[3]{2.37} \\approx 1.333$ and $\\sqrt[3]{23.7} \\approx 2.872$, determine the approximate value of $\\sqrt[3]{2370}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13.33"
} | {
"split": "train",
"index": 24049,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $z_1$ and $z_2$ be the complex roots of $z^2 + az + b = 0,$ where $a$ and $b$ are complex numbers. In the complex plane, 0, $z_1,$ and $z_2$ form the vertices of an equilateral triangle. Find $\\frac{a^2}{b}.$ Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 24050,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 24051,
"solution": "Let $a$ be the number of $2$-point shots, $b$ be the number of $3$-point shots, and $x$ be the number of free throws. We need to find $x$.\n\nGiven:\n1. The points from two-point shots equal the points from three-point shots, so $2a = 3b$.\n2. The number of free th... |
deepscaler | [
{
"role": "user",
"content": "The numbers $1,2, \\ldots, 2016$ are grouped into pairs in such a way that the product of the numbers in each pair does not exceed a certain natural number $N$. What is the smallest possible value of $N$ for which this is possible? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "1017072"
} | {
"split": "train",
"index": 24052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $x$: $\\sqrt[4]{40x + \\sqrt[4]{40x + 24}} = 24.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8293.8"
} | {
"split": "train",
"index": 24053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two lines with slopes $\\frac{1}{2}$ and $2$ intersect at $(2,2)$. What is the area of the triangle enclosed by these two lines and the line $x+y=10$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 24054,
"solution": "1. **Identify the equations of the lines**: \n - The line with slope $\\frac{1}{2}$ passing through $(2,2)$ has the equation $y - 2 = \\frac{1}{2}(x - 2)$, which simplifies to $y = \\frac{1}{2}x + 1$.\n - The line with slope $2$ passing through $(2,2)$ has the ... |
deepscaler | [
{
"role": "user",
"content": "The number of elements in a finite set $P$ is denoted as $\\text{card}(P)$. It is known that $\\text{card}(M) = 10$, $A \\subseteq M$, $B \\subseteq M$, $A \\cap B = \\emptyset$, and $\\text{card}(A) = 2$, $\\text{card}(B) = 3$. If the set $X$ satisfies $A \\subseteq X \\subset... | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 24055,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many multiples of 4 are between 70 and 300? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 24056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ has mid-segments $EF$ and $GH$ such that $EF$ goes from midpoint of $AB$ to midpoint of $CD$, and $GH$ from midpoint of $BC$ to midpoint of $AD$. Given that $EF$ and $GH$ are perpendicular, and the lengths are $EF = 18$ and $GH = 24$, find the area of $ABCD... | math | {
"style": "rule",
"ground_truth": "864"
} | {
"split": "train",
"index": 24057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag of popping corn contains $\\frac{2}{3}$ white kernels and $\\frac{1}{3}$ yellow kernels. Only $\\frac{1}{2}$ of the white kernels will pop, whereas $\\frac{2}{3}$ of the yellow ones will pop. A kernel is selected at random from the bag, and pops when placed in the popper.... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 24058,
"solution": "To solve this problem, we use the concept of conditional probability and the law of total probability. We need to find the probability that a kernel is white given that it popped, denoted as $P(\\text{white} \\mid \\text{popped})$.\n\n1. **Calculate $P(\\text{white... |
deepscaler | [
{
"role": "user",
"content": "A teacher was leading a class of four perfectly logical students. The teacher chose a set $S$ of four integers and gave a different number in $S$ to each student. Then the teacher announced to the class that the numbers in $S$ were four consecutive two-digit positive integers, ... | math | {
"style": "rule",
"ground_truth": "258"
} | {
"split": "train",
"index": 24059,
"solution": "We know right away that $42\\not\\in S$ and $84\\not\\in S$ as stated in Solution 1.\n To get a feel for the problem, let’s write out some possible values of $S$ based on the teacher’s remarks. The first multiple of 7 that is two-digit is 14. The closest multiple o... |
deepscaler | [
{
"role": "user",
"content": "What is the value of the sum\n\\[\n \\sum_z \\frac{1}{{\\left|1 - z\\right|}^2} \\, ,\n\\]where $z$ ranges over all 7 solutions (real and nonreal) of the equation $z^7 = -1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{49}{4}"
} | {
"split": "train",
"index": 24060,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\{a_{n}\\}$ is a geometric sequence, $a_{2}a_{4}a_{5}=a_{3}a_{6}$, $a_{9}a_{10}=-8$, then $a_{7}=\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 24061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the angle $\\frac {19\\pi}{5}$, express it in the form of $2k\\pi+\\alpha$ ($k\\in\\mathbb{Z}$), then determine the angle $\\alpha$ that makes $|\\alpha|$ the smallest. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac {\\pi}{5}"
} | {
"split": "train",
"index": 24062,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the plane rectangular coordinate system $xOy$, the parametric equations of the line $l$ are $\\left\\{{\\begin{array}{l}{x=t}\\\\{y=-1+\\sqrt{3}t}\\end{array}}\\right.$ (where $t$ is a parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3} + 1}{3}"
} | {
"split": "train",
"index": 24063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A parabola and an ellipse share a focus, and the directrix of the parabola is the line containing the minor axis of the ellipse. The parabola and ellipse intersect at two points. Given that the equation of the ellipse is $\\frac{x^2}{25} + \\frac{y^2}{9} = 1,$ find the distance... | math | {
"style": "rule",
"ground_truth": "\\tfrac{4\\sqrt{14}}{3}"
} | {
"split": "train",
"index": 24064,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arjun and Beth play a game in which they take turns removing one brick or two adjacent bricks from one \"wall\" among a set of several walls of bricks, with gaps possibly creating new walls. The walls are one brick tall. For example, a set of walls of sizes $4$ and $2$ can be c... | math | {
"style": "rule",
"ground_truth": "(6,2,1)"
} | {
"split": "train",
"index": 24065,
"solution": "1. **Understanding the Game**: In this game, Arjun and Beth take turns removing either one brick or two adjacent bricks from a set of walls. The player who removes the last brick wins. The game can be analyzed using the concept of nim-values from combinatorial game... |
deepscaler | [
{
"role": "user",
"content": "A pyramid is constructed on a $5 \\times 12$ rectangular base. Each of the four edges joining the apex to the corners of the rectangular base has a length of $15$. Determine the volume of this pyramid. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "270"
} | {
"split": "train",
"index": 24066,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the odd function $f(x)$ is also a periodic function, and the smallest positive period of $f(x)$ is $\\pi$, when $x \\in \\left(0, \\frac{\\pi}{2}\\right)$, $f(x) = 2\\sin x$. Find the value of $f\\left(\\frac{11\\pi}{6}\\)$. Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 24067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) and \\( b \\) be positive integers such that \\( 15a + 16b \\) and \\( 16a - 15b \\) are both perfect squares. Find the smallest possible value among these squares. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "481^2"
} | {
"split": "train",
"index": 24068,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a 4-by-4 grid where each of the unit squares can be colored either purple or green. Each color choice is equally likely independent of the others. Compute the probability that the grid does not contain a 3-by-3 grid of squares all colored purple. Express your result in... | math | {
"style": "rule",
"ground_truth": "255"
} | {
"split": "train",
"index": 24069,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)$ be an odd function. Is $f(f(x))$ even, odd, or neither?\n\nEnter \"odd\", \"even\", or \"neither\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\text{odd}"
} | {
"split": "train",
"index": 24070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 5 balls of the same shape and size in a bag, including 3 red balls and 2 yellow balls. Now, balls are randomly drawn from the bag one at a time until two different colors of balls are drawn. Let the random variable $\\xi$ be the number of balls drawn at this time. Fin... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"split": "train",
"index": 24071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least common multiple of 12, 18 and 30? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 24072,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the random variable $X$ follows a normal distribution $N(1,4)$, and $P(0 \\leq X \\leq 2) = 0.68$, find $P(X > 2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.16"
} | {
"split": "train",
"index": 24073,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a luxurious ocean liner, 3000 adults consisting of men and women embark on a voyage. If 55% of the adults are men and 12% of the women as well as 15% of the men are wearing sunglasses, determine the total number of adults wearing sunglasses. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "409"
} | {
"split": "train",
"index": 24074,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$. The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.\n[asy] pointpen... | math | {
"style": "rule",
"ground_truth": "224"
} | {
"split": "train",
"index": 24075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Choose any $2$ numbers from $-5$, $-3$, $-1$, $2$, and $4$. Let the maximum product obtained be denoted as $a$, and the minimum quotient obtained be denoted as $b$. Then the value of $\\frac{a}{b}$ is ______. Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "-\\frac{15}{4}"
} | {
"split": "train",
"index": 24076,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line with slope of $-2$ intersects the positive $x$-axis at $A$ and the positive $y$-axis at $B$. A second line intersects the $x$-axis at $C(8,0)$ and the $y$-axis at $D$. The lines intersect at $E(4,4)$. What is the area of the shaded quadrilateral $OBEC$? [asy]\ndraw((0,-1... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 24077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(ABCD\\) be a quadrilateral circumscribed about a circle with center \\(O\\). Let \\(O_1, O_2, O_3,\\) and \\(O_4\\) denote the circumcenters of \\(\\triangle AOB, \\triangle BOC, \\triangle COD,\\) and \\(\\triangle DOA\\). If \\(\\angle A = 120^\\circ\\), \\(\\angle B =... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 24078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $PQR$ has sides $\\overline{PQ}$, $\\overline{QR}$, and $\\overline{RP}$ of length 47, 14, and 50, respectively. Let $\\omega$ be the circle circumscribed around $\\triangle PQR$ and let $S$ be the intersection of $\\omega$ and the perpendicular bisector of $\\overline... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 24079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x) = e^x - ax + 3$ where $a \\in \\mathbb{R}$.\n1. Discuss the monotonicity of the function $f(x)$.\n2. If the minimum value of the function $f(x)$ on the interval $[1,2]$ is $4$, find the value of $a$. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "e - 1"
} | {
"split": "train",
"index": 24080,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbb{R}$ denote the set of real numbers. Find all functions $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ such that \n\\[f(xf(y)+y)+f(-f(x))=f(yf(x)-y)+y\\]\nfor all $x,y\\in\\mathbb{R}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "f(x) = x + 1"
} | {
"split": "train",
"index": 24081,
"solution": "\nWe are tasked with finding all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the functional equation:\n\n\\[\nf(xf(y)+y)+f(-f(x))=f(yf(x)-y)+y\n\\]\n\nfor all \\( x, y \\in \\mathbb{R} \\).\n\n### Step 1: Explore the Equation by Substitut... |
deepscaler | [
{
"role": "user",
"content": "Let \\( ABCDEF \\) be a regular hexagon, and let \\( J, K, L \\) be the midpoints of sides \\( AB, CD, EF \\) respectively. If the area of \\( \\triangle JKL \\) is \\( 144 \\), what is the area of hexagon \\( ABCDEF \\)? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "384"
} | {
"split": "train",
"index": 24082,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The minimum distance from a point on the parabola $y=x^2$ to the line $2x-y-10=0$ is what? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 24083,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The longer leg of a right triangle is $1$ foot shorter than twice the length of the shorter leg. The area of the triangle is $60$ square feet. What is the length of the hypotenuse, in feet? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 24084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of the region in the coordinate plane where the discriminant of the quadratic $ax^2 + bxy + cy^2 = 0$ is not positive. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49 \\pi"
} | {
"split": "train",
"index": 24085,
"solution": "To find the region in question, we want to find $(a, b)$ such that the discriminant of the quadratic is not positive. In other words, we want $$4(a+b-7)^{2}-4(a)(2b) \\leq 0 \\Leftrightarrow a^{2}+b^{2}-7a-7b+49 \\leq 0 \\Leftrightarrow(a-7)^{2}+(b-7)^{2} \\leq 49$... |
deepscaler | [
{
"role": "user",
"content": "The graph of the function $f(x)=\\sin (2x+\\varphi )$ $(|\\varphi| < \\frac{\\pi}{2})$ is shifted to the left by $\\frac{\\pi}{6}$ units, and the resulting graph corresponds to an even function. Find the minimum value of $m$ such that there exists $x \\in \\left[ 0,\\frac{\\pi}... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 24086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\\\(\\alpha\\\\) and \\\\(\\beta\\\\) are acute angles, and \\\\(\\cos \\alpha= \\frac{\\sqrt{5}}{5}\\\\), \\\\(\\sin (\\alpha+\\beta)= \\frac{3}{5}\\\\), find the value of \\\\(\\cos \\beta\\\\. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{5}}{25}"
} | {
"split": "train",
"index": 24087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the polynomial \\(x^2 - kx + 24\\) has only positive integer roots, find the average of all distinct possibilities for \\(k\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 24088,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the remainder when the sum $100001 + 100002 + \\cdots + 100010$ is divided by 11. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 24089,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( F_1 \\) and \\( F_2 \\) are the left and right foci of the ellipse \\( C: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1 \\) where \\( a > b > 0 \\), and \\( P \\) is a point on the ellipse \\( C \\). The incenter of triangle \\( \\triangle F_{1}PF_{2} \\) is \\( I ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 24090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To transmit a positive integer less than 1000, the Networked Number Node offers two options.\n\nOption 1. Pay $\\$$d to send each digit d. Therefore, 987 would cost $\\$$9 + $\\$$8 + $\\$$7 = $\\$$24 to transmit.\n\nOption 2. Encode integer into binary (base 2) first, and then ... | math | {
"style": "rule",
"ground_truth": "503"
} | {
"split": "train",
"index": 24091,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive real number $c,$ such that for all nonnegative real numbers $x$ and $y,$\n\\[\\sqrt{xy} + c |x - y| \\ge \\frac{x + y}{2}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 24092,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\dbinom{14}{11}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "364"
} | {
"split": "train",
"index": 24093,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $1.45$ expressed as a fraction? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{29}{20}"
} | {
"split": "train",
"index": 24094,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the median of the following list of numbers that includes integers from $1$ to $2020$, their squares, and their cubes? \\[1, 2, 3, \\ldots, 2020, 1^2, 2^2, \\ldots, 2020^2, 1^3, 2^3, \\ldots, 2020^3\\]\nA) $2040200$ \nB) $2040201$\nC) $2040202$\nD) $2040203$\nE) $204020... | math | {
"style": "rule",
"ground_truth": "2040201"
} | {
"split": "train",
"index": 24095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the grid shown, Jane starts at dot $A$. She tosses a fair coin to determine which way to move. If she tosses a head, she moves up one dot. If she tosses a tail, she moves right one dot. After four tosses of the coin, Jane will be at one of the dots $P, Q, R, S$, or $T$. What... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"split": "train",
"index": 24096,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when $5^{5^{5^5}}$ is divided by 500. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 24097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ and $BCFG$ be two faces of a cube with $AB=12$. A beam of light emanates from vertex $A$ and reflects off face $BCFG$ at point $P$, which is 7 units from $\\overline{BG}$ and 5 units from $\\overline{BC}$. The beam continues to be reflected off the faces of the cube.... | math | {
"style": "rule",
"ground_truth": "230"
} | {
"split": "train",
"index": 24098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\frac{1}{2}{f'}(1){x^2}+lnx+\\frac{{f(1)}}{{3x}}$, find the value of ${f'}\\left(2\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{33}{4}"
} | {
"split": "train",
"index": 24099,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two individuals, A and B, travel from point $A$ to point $B$. A departs 48 minutes before B. When A has traveled $\\frac{2}{3}$ of the total distance, B catches up to A. If B immediately returns to point $A$ after arriving at point $B$ at the same speed, B meets A 6 minutes aft... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 24100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Take one point $M$ on the curve $y=\\ln x$ and another point $N$ on the line $y=2x+6$, respectively. The minimum value of $|MN|$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {(7+\\ln 2) \\sqrt {5}}{5}"
} | {
"split": "train",
"index": 24101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the arc lengths of the curves given by the equations in the rectangular coordinate system.\n\n$$\ny=2-e^{x}, \\ln \\sqrt{3} \\leq x \\leq \\ln \\sqrt{8}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1 + \\frac{1}{2} \\ln \\frac{3}{2}"
} | {
"split": "train",
"index": 24102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha$ and $\\beta$ be complex numbers such that $|\\beta| = 1$ and $\\overline{\\alpha} \\beta \\neq 1.$ Find the maximum value of\n\\[\\left| \\frac{\\beta - \\alpha}{1 - \\overline{\\alpha} \\beta} \\right|.\\] Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 24103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, with $c=2$ and $b=\\sqrt{2}a$. Find the maximum value of the area of $\\triangle ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 24104,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A permutation of a finite set $S$ is a one-to-one function from $S$ to $S$ . A permutation $P$ of the set $\\{ 1, 2, 3, 4, 5 \\}$ is called a W-permutation if $P(1) > P(2) < P(3) > P(4) < P(5)$ . A permutation of the set $\\{1, 2, 3, 4, 5 \\}$ is selected at rando... | math | {
"style": "rule",
"ground_truth": "2/15"
} | {
"split": "train",
"index": 24105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $n \\in \\mathbb{N}^*$, in the expansion of $(x+2)^n$, the coefficient of the second term is $\\frac{1}{5}$ of the coefficient of the third term. \n(1) Find the value of $n$; \n(2) Find the term with the maximum binomial coefficient in the expansion; \n(3) If $(x+2)^n=... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 24106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider an $m$-by-$n$ grid of unit squares, indexed by $(i,j)$ with $1 \\leq i \\leq m$ and $1 \\leq j \\leq n$. There are $(m-1)(n-1)$ coins, which are initially placed in the squares $(i,j)$ with $1 \\leq i \\leq m-1$ and $1 \\leq j \\leq n-1$. If a coin occupies the square ... | math | {
"style": "rule",
"ground_truth": "\\binom{m+n-2}{m-1}"
} | {
"split": "train",
"index": 24107,
"solution": "The number of such configurations is $\\binom{m+n-2}{m-1}$. Initially the unoccupied squares form a path from $(1,n)$ to $(m,1)$ consisting of $m-1$ horizontal steps and $n-1$ vertical steps, and every move preserves this property. This yields an injective map from... |
deepscaler | [
{
"role": "user",
"content": "Find the value of $k$ for which $kx^2 -5x-12 = 0$ has solutions $x=3$ and $ x = -\\frac{4}{3}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 24108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest prime factor of $1337$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "191"
} | {
"split": "train",
"index": 24109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiao Zhang departs from point A to point B at 8:00 AM, traveling at a speed of 60 km/h. At 9:00 AM, Xiao Wang departs from point B to point A. After arriving at point B, Xiao Zhang immediately returns along the same route and arrives at point A at 12:00 PM, at the same time as ... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 24110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can 13 bishops be placed on an $8 \\times 8$ chessboard such that:\n(i) a bishop is placed on the second square in the second row,\n(ii) at most one bishop is placed on each square,\n(iii) no bishop is placed on the same diagonal as another bishop,\n(iv) every ... | math | {
"style": "rule",
"ground_truth": "1152"
} | {
"split": "train",
"index": 24111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sets \\( A = \\{(x, y) \\mid ax + y = 1, x, y \\in \\mathbb{Z}\\} \\), \\( B = \\{(x, y) \\mid x + ay = 1, x, y \\in \\mathbb{Z}\\} \\), and \\( C = \\{(x, y) \\mid x^2 + y^2 = 1\\} \\), find the value of \\( a \\) when \\( (A \\cup B) \\cap C \\) is a set with four e... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 24112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each integer $n\\geq 2$, let $S_n$ be the sum of all products $jk$, where $j$ and $k$ are integers and $1\\leq j<k\\leq n$. What is the sum of the 10 least values of $n$ such that $S_n$ is divisible by $3$? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "197"
} | {
"split": "train",
"index": 24113,
"solution": "1. **Define the sets and express $S_n$:**\n Let $A_{n, <} = \\{(j, k) : 1 \\leq j < k \\leq n\\}$ and $A_{n, >} = \\{(j, k) : 1 \\leq k < j \\leq n\\}$. Note that $A_{n, <}$ and $A_{n, >}$ are symmetric, and each product $jk$ where $j < k$ has a corresponding pro... |
deepscaler | [
{
"role": "user",
"content": "How many integers between 0 and 8 inclusive have an inverse modulo 9? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 24114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of\n\\[\n\\frac{3x + 4y + 6}{\\sqrt{x^2 + 4y^2 + 4}}\n\\]\nover all real numbers \\(x\\) and \\(y\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{61}"
} | {
"split": "train",
"index": 24115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Denote by \\( f(n) \\) the integer obtained by reversing the digits of a positive integer \\( n \\). Find the greatest integer that is certain to divide \\( n^{4} - f(n)^{4} \\) regardless of the choice of \\( n \\). Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "99"
} | {
"split": "train",
"index": 24116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How can 50 cities be connected with the smallest number of airline routes so that it is possible to travel from any city to any other city with no more than two layovers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 24117,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that when $(a+b+c+d+e+1)^N$ is expanded and like terms are combined, the resulting expression contains exactly 2002 terms that include all five variables $a, b, c, d, e$, each to some positive power, find the value of $N$. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 24118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The integers 195 and 61 are expressed in base 4 and added. What is the resulting sum, expressed in base 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10000"
} | {
"split": "train",
"index": 24119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the set $\\{10, 11, 12, \\ldots, 19\\}$, 5 different numbers were chosen, and from the set $\\{90, 91, 92, \\ldots, 99\\}$, 5 different numbers were also chosen. It turned out that the difference of any two numbers from the ten chosen numbers is not divisible by 10. Find t... | math | {
"style": "rule",
"ground_truth": "545"
} | {
"split": "train",
"index": 24120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( x \\) is a real number and \\( y = \\sqrt{x^2 - 2x + 2} + \\sqrt{x^2 - 10x + 34} \\). Find the minimum value of \\( y \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{2}"
} | {
"split": "train",
"index": 24121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a right-angled triangle $ABC$, where $AB = AC = 1$, an ellipse is constructed with point $C$ as one of its foci. The other focus of the ellipse lies on side $AB$, and the ellipse passes through points $A$ and $B$. Determine the focal length of the ellipse. Let's think step b... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 24122,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $$E: \\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1 (a > b > 0)$$ has an eccentricity of $$\\frac{\\sqrt{2}}{2}$$, and the point $$A(1, \\sqrt{2})$$ is on the ellipse. \n(1) Find the equation of ellipse E; \n(2) If a line $l$ with a slope of $$\\sqrt{2}$$ i... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 24123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $\\prod_{n=2}^{\\infty}\\left(1-\\frac{1}{n^{2}}\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 24124,
"solution": "$\\prod_{n=2}^{\\infty}\\left(1-\\frac{1}{n^{2}}\\right)=\\prod_{n=2}^{\\infty} \\frac{n^{2}-1}{n^{2}}=\\prod_{n=2}^{\\infty} \\frac{(n-1)(n+1)}{n \\cdot n}=\\frac{1 \\cdot 3}{2 \\cdot 2} \\frac{2 \\cdot 4}{3 \\cdot 3} \\frac{3 \\cdot 5}{4 \\cdot 4} \\frac{4 \\cdot... |
deepscaler | [
{
"role": "user",
"content": "The average of the seven numbers in a list is 62. The average of the first four numbers is 58. What is the average of the last three numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "67.\\overline{3}"
} | {
"split": "train",
"index": 24125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ways to arrange the letters of the word \"SUCCESS\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "420"
} | {
"split": "train",
"index": 24126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mattis is hosting a badminton tournament for $40$ players on $20$ courts numbered from $1$ to $20$. The players are distributed with $2$ players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court $1$, and the player who w... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 24127,
"solution": "\nMattis is organizing a badminton tournament with the following setup: there are \\(40\\) players distributed evenly across \\(20\\) courts, with \\(2\\) players on each court. In each round of the tournament, a match is played on each court, and a winner and a lo... |
deepscaler | [
{
"role": "user",
"content": "Fran writes the numbers \\(1,2,3, \\ldots, 20\\) on a chalkboard. Then she erases all the numbers by making a series of moves; in each move, she chooses a number \\(n\\) uniformly at random from the set of all numbers still on the chalkboard, and then erases all of the divisors... | math | {
"style": "rule",
"ground_truth": "\\frac{131}{10}"
} | {
"split": "train",
"index": 24128,
"solution": "For each \\(n, 1 \\leq n \\leq 20\\), consider the first time that Fran chooses one of the multiples of \\(n\\). It is in this move that \\(n\\) is erased, and all the multiples of \\(n\\) at most 20 are equally likely to be chosen for this move. Hence this is the ... |
deepscaler | [
{
"role": "user",
"content": "Let \\( x \\) be a non-zero real number such that \n\n\\[ \\sqrt[5]{x^{3}+20 x}=\\sqrt[3]{x^{5}-20 x} \\]. \n\nFind the product of all possible values of \\( x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-5"
} | {
"split": "train",
"index": 24129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fenced area of a yard is an 18.5-foot by 14-foot rectangular region with a 3.5-foot by 3.5-foot square cutout. Calculate the area of the region within the fence, in square feet. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "246.75"
} | {
"split": "train",
"index": 24130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Herbert rolls 6 fair standard dice and computes the product of all of his rolls. If the probability that the product is prime can be expressed as $\\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100 a+b$. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "2692"
} | {
"split": "train",
"index": 24131,
"solution": "The only way this can happen is if 5 of the dice roll 1 and the last die rolls a prime number (2, 3, or 5). There are 6 ways to choose the die that rolls the prime, and 3 ways to choose the prime. Thus, the probability is $\\frac{3 \\cdot 6}{6^{6}}=\\frac{1}{2592}$... |
deepscaler | [
{
"role": "user",
"content": "Let $w$ and $z$ be complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18$. Find the smallest possible value of $|w^3+z^3|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 24132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fract... | math | {
"style": "rule",
"ground_truth": "\\frac{47}{72}"
} | {
"split": "train",
"index": 24133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius $20$ feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point $10$ vertical feet ab... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 24134,
"solution": "1. **Understanding the problem**: We need to find the time it takes for a rider to move from the bottom of a Ferris wheel to a point 10 feet above the bottom. The Ferris wheel has a radius of 20 feet and completes one revolution per minute.\n\n2. **Setting up the e... |
deepscaler | [
{
"role": "user",
"content": "In the following diagram (not to scale), $A$ , $B$ , $C$ , $D$ are four consecutive vertices of an 18-sided regular polygon with center $O$ . Let $P$ be the midpoint of $AC$ and $Q$ be the midpoint of $DO$ . Find $\\angle OPQ$ in degrees.\n[asy]\npathpen = rgb(0,... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 24135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In racing over a distance $d$ at uniform speed, $A$ can beat $B$ by $20$ yards, $B$ can beat $C$ by $10$ yards, and $A$ can beat $C$ by $28$ yards. Then $d$, in yards, equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 24136,
"solution": "1. **Define Variables:**\n Let $a$, $b$, and $c$ be the speeds of $A$, $B$, and $C$ respectively.\n\n2. **Set Up Equations:**\n - When $A$ finishes the race, $B$ is 20 yards behind. Thus, in the time $\\frac{d}{a}$ it takes for $A$ to finish, $B$ covers $d - 20... |
deepscaler | [
{
"role": "user",
"content": "$ABCD$ is a trapezoid with the measure of base $\\overline{AB}$ twice the measure of the base $\\overline{CD}$. Point $E$ is the point of intersection of the diagonals. The measure of diagonal $\\overline{AC}$ is 11. Find the length of segment $\\overline{EC}$. Express your ans... | math | {
"style": "rule",
"ground_truth": "\\dfrac{11}{3}"
} | {
"split": "train",
"index": 24137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB = 11$, $AC = 13$, and $BC = 20$. The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$. Let $P$ be the foot of the altitude from $G$ to $BC$. Find $GP$.\n\n[asy]\nunitsize(0.3 cm);\n\npair A, B, C, D, E, F, G, P;\n\nA = (44/5... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{5}"
} | {
"split": "train",
"index": 24138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The vertices of a regular nonagon are colored such that 1) adjacent vertices are different colors and 2) if 3 vertices form an equilateral triangle, they are all different colors. Let m be the minimum number of colors needed for a valid coloring, and n be the total number of co... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 24139,
"solution": "It's clear that m is more than 2 since it's impossible to alternate the color of the vertices without having two of the same color adjacent (since the graph is not bipartite). However, it's possible to use 3 colors. Number the vertices 1 through 9 in order and let ... |
deepscaler | [
{
"role": "user",
"content": "The diagram shows five circles of the same radius touching each other. A square is drawn so that its vertices are at the centres of the four outer circles. What is the ratio of the area of the shaded parts of the circles to the area of the unshaded parts of the circles? Let's t... | math | {
"style": "rule",
"ground_truth": "2:3"
} | {
"split": "train",
"index": 24140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A four-digit number with digits in the thousands, hundreds, tens, and units places respectively denoted as \\(a, b, c, d\\) is formed by \\(10 \\cdot 23\\). The sum of these digits is 26. The tens digit of the product of \\(b\\) and \\(d\\) equals \\((a+c)\\). Additionally, \\(... | math | {
"style": "rule",
"ground_truth": "1979"
} | {
"split": "train",
"index": 24141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A semicircle has diameter $XY$ . A square $PQRS$ with side length 12 is inscribed in the semicircle with $P$ and $S$ on the diameter. Square $STUV$ has $T$ on $RS$ , $U$ on the semicircle, and $V$ on $XY$ . What is the area of $STUV$ ? Let's think step by step... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 24142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Construct the cross-section of a triangular pyramid \\( A B C D \\) with a plane passing through the midpoints \\( M \\) and \\( N \\) of edges \\( A C \\) and \\( B D \\) and the point \\( K \\) on edge \\( C D \\), for which \\( C K: K D = 1: 2 \\). In what ratio does this pl... | math | {
"style": "rule",
"ground_truth": "1:2"
} | {
"split": "train",
"index": 24143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the random variable $X$ follows a normal distribution $N(0,\\sigma^{2})$, if $P(X > 2) = 0.023$, determine the probability $P(-2 \\leqslant X \\leqslant 2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.954"
} | {
"split": "train",
"index": 24144,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangular region is bounded by the two coordinate axes and the line given by the equation $3x + y = 9$. Check if the point (1,1) lies inside this triangular region and find the region's area in square units. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{2}"
} | {
"split": "train",
"index": 24145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "[asy] draw((0,0)--(2,2)--(5/2,1/2)--(2,0)--cycle,dot); MP(\"A\",(0,0),W);MP(\"B\",(2,2),N);MP(\"C\",(5/2,1/2),SE);MP(\"D\",(2,0),S); MP(\"a\",(1,0),N);MP(\"b\",(17/8,1/8),N); [/asy]\nIn the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is tw... | math | {
"style": "rule",
"ground_truth": "a+b"
} | {
"split": "train",
"index": 24146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the planar vectors $\\overrightarrow{a}, \\overrightarrow{b}$, with $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b}=1$, let $\\overrightarrow{e}$ be a unit vector in the plane. Find the maximum value of $y=\\overri... | math | {
"style": "rule",
"ground_truth": "\\sqrt{7}"
} | {
"split": "train",
"index": 24147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathcal{T}$ be the set of real numbers that can be represented as repeating decimals of the form $0.\\overline{abcd}$ where $a, b, c, d$ are distinct digits. Find the sum of the elements of $\\mathcal{T}.$ Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "2520"
} | {
"split": "train",
"index": 24148,
"solution": ""
} |
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