data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "If $x$ and $y$ are positive integers with $xy = 6$, what is the sum of all possible values of $\\frac{2^{x+y}}{2^{x-y}}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4180"
} | {
"split": "train",
"index": 33749,
"solution": "Using exponent laws, the expression $\\frac{2^{x+y}}{2^{x-y}} = 2^{(x+y)-(x-y)} = 2^{2y}$. Since $x$ and $y$ are positive integers with $xy = 6$, then the possible values of $y$ are the positive divisors of 6, namely $1, 2, 3$, or 6. (These correspond to $x = 6, 3,... |
deepscaler | [
{
"role": "user",
"content": "Central High School is competing against Northern High School in a backgammon match. Each school has three players, and the contest rules require that each player play two games against each of the other school's players. The match takes place in six rounds, with three games pl... | math | {
"style": "rule",
"ground_truth": "900"
} | {
"split": "train",
"index": 33750,
"solution": "Let us label the players of the first team $A$, $B$, and $C$, and those of the second team, $X$, $Y$, and $Z$. \n\n#### Step 1: Understand the game requirements\nEach player from one team must play two games against each player from the other team. This results in ... |
deepscaler | [
{
"role": "user",
"content": "Pi Pi Lu wrote a 2020-digit number: \\( 5368 \\cdots \\cdots \\). If any four-digit number taken randomly from this multi-digit number is divisible by 11, what is the sum of the digits of this multi-digit number? Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "11110"
} | {
"split": "train",
"index": 33751,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive integer $n$ so that $n^2$ is the perfect square closest to $8 + 16 + 24 + \\cdots + 8040.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2011"
} | {
"split": "train",
"index": 33752,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 180 = 0$ has integral solutions? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 33753,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\\frac{3}{2} + \\frac{5}{4} + \\frac{9}{8} + \\frac{17}{16} + \\frac{33}{32} + \\frac{65}{64} - 7 = Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{64}"
} | {
"split": "train",
"index": 33754,
"solution": "1. **Convert each fraction to have a common denominator of 64:**\n - $\\frac{3}{2} = \\frac{3 \\times 32}{2 \\times 32} = \\frac{96}{64}$\n - $\\frac{5}{4} = \\frac{5 \\times 16}{4 \\times 16} = \\frac{80}{64}$\n - $\\frac{9}{8} = \\frac{9 \\times 8}{8 \\time... |
deepscaler | [
{
"role": "user",
"content": "Natural numbers of the form $F_n=2^{2^n} + 1 $ are called Fermat numbers. In 1640, Fermat conjectured that all numbers $F_n$, where $n\\neq 0$, are prime. (The conjecture was later shown to be false.) What is the units digit of $F_{1000}$? Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 33755,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all pairs of positive integers $m,n\\geq3$ for which there exist infinitely many positive integers $a$ such that \\[ \\frac{a^m+a-1}{a^n+a^2-1} \\] is itself an integer.\n\n[i]Laurentiu Panaitopol, Romania[/i] Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "(5, 3)"
} | {
"split": "train",
"index": 33756,
"solution": "\nWe are tasked with finding all pairs of positive integers \\( m, n \\geq 3 \\) such that there exist infinitely many positive integers \\( a \\) making the expression\n\n\\[\n\\frac{a^m + a - 1}{a^n + a^2 - 1}\n\\]\n\nan integer. To solve this problem, we aim to ... |
deepscaler | [
{
"role": "user",
"content": "Calculate $x$ such that the sum \\[1 \\cdot 1979 + 2 \\cdot 1978 + 3 \\cdot 1977 + \\dots + 1978 \\cdot 2 + 1979 \\cdot 1 = 1979 \\cdot 990 \\cdot x.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "661"
} | {
"split": "train",
"index": 33757,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $$1, \\frac{1}{2}, \\frac{2}{1}, \\frac{1}{3}, \\frac{2}{2}, \\frac{3}{1}, \\frac{1}{4}, \\frac{2}{3}, \\frac{3}{2}, \\frac{4}{1}, \\ldots$$, find the position of $$\\frac{8}{9}$$ in this sequence. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 33758,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We call a pair of natural numbers $(a, p)$ good if the number $a^{3} + p^{3}$ is divisible by $a^{2} - p^{2}$, and $a > p$.\n\n(a) (1 point) Give any possible value of $a$ for which the pair $(a, 11)$ is good.\n\n(b) (3 points) Find the number of good pairs, where $p$ is a prim... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 33759,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha \\in (-\\frac{\\pi }{2},\\frac{\\pi }{2})$, $\\beta \\in (-\\frac{\\pi }{2},\\frac{\\pi }{2})$, and $\\tan \\alpha$ and $\\tan \\beta$ are the two real roots of the equation $x^{2}+3\\sqrt{3}x+4=0$, find the value of $\\alpha + \\beta$ = \\_\\_\\_\\_\\_\\_\\... | math | {
"style": "rule",
"ground_truth": "- \\frac{2\\pi}{3}"
} | {
"split": "train",
"index": 33760,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given any positive integer, we can write the integer in base 12 and add together the digits of its base 12 representation. We perform this operation on the number $7^{6^{5^{3^{2^{1}}}}}$ repeatedly until a single base 12 digit remains. Find this digit. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 33761,
"solution": "For a positive integer $n$, let $s(n)$ be the sum of digits when $n$ is expressed in base 12. We claim that $s(n) \\equiv n(\\bmod 11)$ for all positive integers $n$. Indeed, if $n=d_{k} 12^{k}+d_{k-1} 12^{k-1}+\\cdots+d_{0}$ with each $d_{i}$ an integer between 0 ... |
deepscaler | [
{
"role": "user",
"content": "Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 33762,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A truck travels due west at $\\frac{3}{4}$ mile per minute on a straight road. At the same time, a circular storm, whose radius is $60$ miles, moves southwest at $\\frac{1}{2}\\sqrt{2}$ mile per minute. At time $t=0$, the center of the storm is $130$ miles due north of the truc... | math | {
"style": "rule",
"ground_truth": "208"
} | {
"split": "train",
"index": 33763,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum total number of boxes that Carley could have bought if each treat bag contains exactly 1 chocolate, 1 mint, and 1 caramel, and chocolates come in boxes of 50, mints in boxes of 40, and caramels in boxes of 25? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 33764,
"solution": "Suppose that Carley buys $x$ boxes of chocolates, $y$ boxes of mints, and $z$ boxes of caramels. In total, Carley will then have $50x$ chocolates, $40y$ mints, and $25z$ caramels. Since $50x=40y=25z$, dividing by 5 gives $10x=8y=5z$. The smallest possible value of ... |
deepscaler | [
{
"role": "user",
"content": "Given tetrahedron $P-ABC$, if one line is randomly selected from the lines connecting the midpoints of each edge, calculate the probability that this line intersects plane $ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 33765,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that α and β are acute angles, and $\\tan \\alpha = \\frac{2}{t}$, $\\tan \\beta = \\frac{t}{15}$. When $10\\tan \\alpha + 3\\tan \\beta$ reaches its minimum value, the value of $\\alpha + \\beta$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 33766,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of solutions to:\n\\[\\sin x = \\left(\\frac{1}{3}\\right)^x\\]\non the interval $(0, 50\\pi)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 33767,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, if $\\angle PQR = 48^\\circ$, what is the measure of $\\angle PMN$? [asy]\n\nsize(6cm);\n\npair p = (0, 0); pair m = dir(180 - 24); pair n = dir(180 + 24); pair r = 1.3 * dir(24); pair q = 2 * 1.3 * Cos(48) * dir(-24);\n\nlabel(\"$M$\", m, N); label(\"$R$\", r, ... | math | {
"style": "rule",
"ground_truth": "66^\\circ"
} | {
"split": "train",
"index": 33768,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For Beatrix's latest art installation, she has fixed a $2 \\times 2$ square sheet of steel to a wall. She has two $1 \\times 2$ magnetic tiles, both of which she attaches to the steel sheet, in any orientation, so that none of the sheet is visible and the line separating the tw... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 33769,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Boys and girls are standing in a circle (there are both), a total of 20 children. It is known that each boy's neighbor in the clockwise direction is a child in a blue T-shirt, and each girl's neighbor in the counterclockwise direction is a child in a red T-shirt. Can you unique... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 33770,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A tetrahedron $ABCD$ satisfies the following conditions: the edges $AB,AC$ and $AD$ are pairwise orthogonal, $AB=3$ and $CD=\\sqrt2$ . Find the minimum possible value of $$ BC^6+BD^6-AC^6-AD^6. $$ Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "1998"
} | {
"split": "train",
"index": 33771,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A \"stair-step\" figure is made of alternating black and white squares in each row. Rows $1$ through $4$ are shown. All rows begin and end with a white square. The number of black squares in the $37\\text{th}$ row is\n[asy]\ndraw((0,0)--(7,0)--(7,1)--(0,1)--cycle);\ndraw((1,0)-... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 33772,
"solution": "1. **Identify the pattern in the number of squares per row**: \n - Observing the given diagram, each row starts and ends with a white square and has alternating black and white squares in between.\n - From row 1 to row 2, we notice that two squares are added (o... |
deepscaler | [
{
"role": "user",
"content": "$ABC$ is a triangle: $A=(0,0), B=(36,15)$ and both the coordinates of $C$ are integers. What is the minimum area $\\triangle ABC$ can have?\n$\\textbf{(A)}\\ \\frac{1}{2} \\qquad \\textbf{(B)}\\ 1 \\qquad \\textbf{(C)}\\ \\frac{3}{2} \\qquad \\textbf{(D)}\\ \\frac{13}{2}\\qquad... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 33773,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $AB$ is parallel to $DC,$ and $ACE$ is a straight line. What is the value of $x?$ [asy]\ndraw((0,0)--(-.5,5)--(8,5)--(6.5,0)--cycle);\ndraw((-.5,5)--(8.5,-10/7));\nlabel(\"$A$\",(-.5,5),W);\nlabel(\"$B$\",(8,5),E);\nlabel(\"$C$\",(6.5,0),S);\nlabel(\"$D$\",(0,0)... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 33774,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point \\(A\\) lies on the line \\(y=\\frac{12}{5} x-9\\), and point \\(B\\) lies on the parabola \\(y=x^{2}\\). What is the minimum length of segment \\(AB\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "189/65"
} | {
"split": "train",
"index": 33775,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. For example, $\\clubsuit(8)=8$ and $\\clubsuit(123)=1+2+3=6$. For how many two-digit values of $x$ is $\\clubsuit(\\clubsuit(x))=3$? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 33776,
"solution": "1. **Define the function and its application**: Let $\\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. For example, $\\clubsuit(8) = 8$ and $\\clubsuit(123) = 1 + 2 + 3 = 6$.\n\n2. **Determine possible values of $y = \\clubsuit(x)$ for two-di... |
deepscaler | [
{
"role": "user",
"content": "A certain fruit store deals with two types of fruits, A and B. The situation of purchasing fruits twice is shown in the table below:\n\n| Purchase Batch | Quantity of Type A Fruit ($\\text{kg}$) | Quantity of Type B Fruit ($\\text{kg}$) | Total Cost ($\\text{元}$) |\n|----------... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 33777,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of distinct even numbers that can be formed using the digits 0, 1, 2, and 3. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 33778,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of numbers is arranged in the following pattern: \\(1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, \\cdots\\). Starting from the first number on the left, find the sum of the first 99 numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1782"
} | {
"split": "train",
"index": 33779,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The administrator accidentally mixed up the keys for 10 rooms. If each key can only open one room, what is the maximum number of attempts needed to match all keys to their corresponding rooms? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 33780,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ordered pairs of integers $(a, b)$ such that $a, b$ are divisors of 720 but $a b$ is not. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2520"
} | {
"split": "train",
"index": 33781,
"solution": "First consider the case $a, b>0$. We have $720=2^{4} \\cdot 3^{2} \\cdot 5$, so the number of divisors of 720 is $5 * 3 * 2=30$. We consider the number of ways to select an ordered pair $(a, b)$ such that $a, b, a b$ all divide 720. Using the balls and urns method ... |
deepscaler | [
{
"role": "user",
"content": "What is the lowest prime number that is thirteen more than a cube? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "229"
} | {
"split": "train",
"index": 33782,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the domain of the function\n\\[f(x) = \\sqrt{1 - \\sqrt{2 - \\sqrt{3 - x}}}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[-1,2]"
} | {
"split": "train",
"index": 33783,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a board, the following two sums are written:\n\n$$\n\\begin{array}{r}\n1+22+333+4444+55555+666666+7777777+ \\\\\n+88888888+999999999\n\\end{array}\n$$\n\n$9+98+987+9876+98765+987654+9876543+$\n\n$+98765432+987654321$\n\nDetermine which of them is greater (or if they are equa... | math | {
"style": "rule",
"ground_truth": "1097393685"
} | {
"split": "train",
"index": 33784,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $G$ be the centroid of triangle $PQR.$ If $GP^2 + GQ^2 + GR^2 = 22,$ then find $PQ^2 + PR^2 + QR^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 33785,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$100$ children stand in a line each having $100$ candies. In one move, one of them may take some of their candies and distribute them to a non-empty set of the remaining children. After what least number of moves can it happen that no two children have the same number of candie... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 33786,
"solution": "\nTo solve the problem, we consider the process of redistributing candies among $100$ children such that no two children have the same number of candies. Initially, each child has $100$ candies.\n\nThe goal is to reach a state where all $100$ values are distinct. L... |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression $\\sqrt{13+\\sqrt{7+\\sqrt{4}}}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 33787,
"solution": "We evaluate from the inside towards the outside: $\\sqrt{13+\\sqrt{7+\\sqrt{4}}}=\\sqrt{13+\\sqrt{7+2}}=\\sqrt{13+\\sqrt{9}}=\\sqrt{13+3}=\\sqrt{16}=4$."
} |
deepscaler | [
{
"role": "user",
"content": "A bookstore has a sale on days of the month that are multiples of 5 (such as June 5, June 10...). A shoe store has a sale every 6 days. The shoe store has a sale on July 3. How many times in July do the two stores have sales on the same date? Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 33788,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Diana is three years younger than Eduardo. Eduardo is four years older than Chad. Faye is three years older than Chad. Diana is 14 years old. How many years old is Faye? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 33789,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has $AB=25$ , $AC=29$ , and $BC=36$ . Additionally, $\\Omega$ and $\\omega$ are the circumcircle and incircle of $\\triangle ABC$ . Point $D$ is situated on $\\Omega$ such that $AD$ is a diameter of $\\Omega$ , and line $AD$ intersects $\\om... | math | {
"style": "rule",
"ground_truth": "252"
} | {
"split": "train",
"index": 33790,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine if there exists a positive integer \\( m \\) such that the equation\n\\[\n\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c}+\\frac{1}{abc}=\\frac{m}{a+b+c}\n\\]\nhas infinitely many solutions in positive integers \\( (a, b, c) \\). Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 33791,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of the equation $x + 2y + 3 = 0$ is perpendicular to the graph of the equation $ax + 2y + 3 = 0$. What is the value of $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 33792,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that construction teams A and B each have a certain number of workers. If team A transfers 90 workers to team B, the total number of workers in team B will be twice that of team A. If team B transfers a certain number of workers to team A, then the total number of workers... | math | {
"style": "rule",
"ground_truth": "153"
} | {
"split": "train",
"index": 33793,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular 12-sided polygon is inscribed in a circle of radius 1. How many chords of the circle that join two of the vertices of the 12-gon have lengths whose squares are rational? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 33794,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a modified octahedron with an additional ring of vertices. There are 4 vertices on the top ring, 8 on the middle ring, and 4 on the bottom ring. An ant starts at the highest top vertex and walks down to one of four vertices on the next level down (the middle ring). Fro... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 33795,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S = \\{5^k | k \\in \\mathbb{Z}, 0 \\le k \\le 2004 \\}$. Given that $5^{2004} = 5443 \\cdots 0625$ has $1401$ digits, how many elements of $S$ begin with the digit $1$?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "604"
} | {
"split": "train",
"index": 33796,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a New Year's cultural evening of a senior high school class, there was a game involving a box containing 6 cards of the same size, each with a different idiom written on it. The idioms were: 意气风发 (full of vigor), 风平浪静 (calm and peaceful), 心猿意马 (restless), 信马由缰 (let things ta... | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{5}"
} | {
"split": "train",
"index": 33797,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three volleyballs with a radius of 18 lie on a horizontal floor, each pair touching one another. A tennis ball with a radius of 6 is placed on top of them, touching all three volleyballs. Find the distance from the top of the tennis ball to the floor. (All balls are spherical i... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 33798,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $\\triangle ABC$ is isosceles with $AB = AC$ and $BC = 30 \\mathrm{~cm}$. Square $EFGH$, which has a side length of $12 \\mathrm{~cm}$, is inscribed in $\\triangle ABC$, as shown. The area of $\\triangle AEF$, in $\\mathrm{cm}^{2}$, is Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 33799,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that ${(1-2x)^{2016}}=a_{0}+a_{1}(x-2)+a_{2}(x-2)^{2}+\\cdots+a_{2015}(x-2)^{2015}+a_{2016}(x-2)^{2016}$ $(x\\in\\mathbb{R})$, find the value of $a_{1}-2a_{2}+3a_{3}-4a_{4}+\\cdots+2015a_{2015}-2016a_{2016}$. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "4032"
} | {
"split": "train",
"index": 33800,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, let vector $\\vec{a} = (1, \\cos B)$ and vector $\\vec{b} = (\\sin B, 1)$, and suppose $\\vec{a}$ is perpendicular to $\\vec{b}$. Find the magnitude of angle $B$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{4}"
} | {
"split": "train",
"index": 33801,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base $ABCD$ of a tetrahedron $P-ABCD$ is a convex quadrilateral with diagonals $AC$ and $BD$ intersecting at $O$. If the area of $\\triangle AOB$ is 36, the area of $\\triangle COD$ is 64, and the height of the tetrahedron is 9, what is the minimum volume of such a tetrahed... | math | {
"style": "rule",
"ground_truth": "588"
} | {
"split": "train",
"index": 33802,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of two whole numbers is 24. Calculate the smallest possible sum of these two numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 33803,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "As shown in the diagram, four small plates \\( A, B, C, D \\) are arranged in a circular shape, with an unspecified number of candies placed on each plate. In each move, it is allowed to take all candies from 1, 3, or 4 plates, or from 2 adjacent plates. What is the maximum num... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 33804,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the pattern and fill in the blanks:\n\n1. 12, 16, 20, \\_\\_\\_\\_\\_\\_, \\_\\_\\_\\_\\_\\_\n2. 2, 4, 8, \\_\\_\\_\\_\\_\\_, \\_\\_\\_\\_\\_\\_ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 33805,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\[f(x) =\n\\begin{cases}\n9x+16 &\\text{if }x<2, \\\\\n2x-14&\\text{if }x\\ge2.\n\\end{cases}\n\\]If $f(x)=-2$, find the sum 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": "4"
} | {
"split": "train",
"index": 33806,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For positive integer $k>1$, let $f(k)$ be the number of ways of factoring $k$ into product of positive integers greater than $1$ (The order of factors are not countered, for example $f(12)=4$, as $12$ can be factored in these $4$ ways: $12,2\\cdot 6,3\\cdot 4, 2\\cdot 2\\cdot 3... | math | {
"style": "rule",
"ground_truth": "\\frac{n}{p}"
} | {
"split": "train",
"index": 33807,
"solution": "\nFor a positive integer \\( k > 1 \\), let \\( f(k) \\) represent the number of ways to factor \\( k \\) into a product of positive integers greater than 1. For example, \\( f(12) = 4 \\) because 12 can be factored in these 4 ways: \\( 12 \\), \\( 2 \\cdot 6 \\), ... |
deepscaler | [
{
"role": "user",
"content": "Santa Claus has 36 identical gifts distributed among 8 bags. Each bag contains at least 1 gift, and the number of gifts in each of the 8 bags is unique. From these bags, select some bags such that the total number of gifts in the selected bags can be evenly divided among 8 chil... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 33808,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $S_{n}$ is the sum of the first $n$ terms of the sequence $\\{a_{n}\\}$, with $a_{1}=1$, $a_{2}=2$, $a_{3}=3$, and the sequence $\\{a_{n}+a_{n+1}+a_{n+2}\\}$ is an arithmetic sequence with a common difference of $2$, calculate the value of $S_{25}$. Let's think step ... | math | {
"style": "rule",
"ground_truth": "269"
} | {
"split": "train",
"index": 33809,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The integers \\( r \\) and \\( k \\) are randomly selected, where \\(-5 < r < 10\\) and \\(0 < k < 10\\). What is the probability that the division \\( r \\div k \\) results in \\( r \\) being a square number? Express your answer as a common fraction. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{63}"
} | {
"split": "train",
"index": 33810,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha$ and $\\beta$ be the roots of $x^2 + px + 1 = 0,$ and let $\\gamma$ and $\\delta$ are the roots of $x^2 + qx + 1 = 0.$ Express\n\\[(\\alpha - \\gamma)(\\beta - \\gamma)(\\alpha + \\delta)(\\beta + \\delta)\\]in terms of $p$ and $q.$ Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "q^2 - p^2"
} | {
"split": "train",
"index": 33811,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cat and Claire are having a conversation about Cat's favorite number. Cat says, \"My favorite number is a two-digit positive prime integer whose first digit is less than its second, and when you reverse its digits, it's still a prime number!\" \n\nClaire asks, \"If you picked a... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 33812,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two dice are differently designed. The first die has faces numbered $1$, $1$, $2$, $2$, $3$, and $5$. The second die has faces numbered $2$, $3$, $4$, $5$, $6$, and $7$. What is the probability that the sum of the numbers on the top faces of the two dice is $3$, $7$, or $8$?\nA... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{36}"
} | {
"split": "train",
"index": 33813,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of the expression \\((\\sqrt{36-4 \\sqrt{5}} \\sin x-\\sqrt{2(1+\\cos 2 x)}-2) \\cdot (3+2 \\sqrt{10-\\sqrt{5}} \\cos y-\\cos 2 y)\\). If the answer is not an integer, round it to the nearest whole number. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 33814,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a > 0$, $b > 0$, and $2a+b=1$, find the maximum value of $2 \\sqrt {ab}-4a^{2}-b^{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac { \\sqrt {2}-1}{2}"
} | {
"split": "train",
"index": 33815,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the infinite series $1-\\frac{1}{2}-\\frac{1}{4}+\\frac{1}{8}-\\frac{1}{16}-\\frac{1}{32}+\\frac{1}{64}-\\frac{1}{128}-\\cdots$, find the limiting sum of the series. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{7}"
} | {
"split": "train",
"index": 33816,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the function $f\\left( x \\right)=\\sin \\left( wx-\\frac{\\pi }{6} \\right)+\\sin \\left( wx-\\frac{\\pi }{2} \\right)$, where $0 < w < 3$, and it is known that $f\\left( \\frac{\\pi }{6} \\right)=0$,\n\n$(I)$ Find $w$\n\n$(II)$ Stretch the x-coordinates of the points on t... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"split": "train",
"index": 33817,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, $c$ be the three sides of a triangle, and let $\\alpha$, $\\beta$, $\\gamma$ be the angles opposite them. If $a^2 + b^2 = 2020c^2$, determine the value of\n\\[\\frac{\\cot \\gamma}{\\cot \\alpha + \\cot \\beta}.\\] Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "1009.5"
} | {
"split": "train",
"index": 33818,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an arithmetic sequence \\(\\left\\{a_{n}\\right\\}\\), if \\(\\frac{a_{11}}{a_{10}} < -1\\), and the sum of its first \\(n\\) terms \\(S_{n}\\) has a maximum value. Then, when \\(S_{n}\\) attains its smallest positive value, \\(n =\\) ______ . Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 33819,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A straight river that is $264$ meters wide flows from west to east at a rate of $14$ meters per minute. Melanie and Sherry sit on the south bank of the river with Melanie a distance of $D$ meters downstream from Sherry. Relative to the water, Melanie swims at $80$ meters per mi... | math | {
"style": "rule",
"ground_truth": "550"
} | {
"split": "train",
"index": 33820,
"solution": "Claim\n Median $AM$ and altitude $AH$ are drawn in triangle $ABC$. $AB = c, AC = b < c, BC = a$ are known. Let's denote $MH = x$.\n Prove that \\begin{align*}2ax = c^{2} – b^{2}\\end{align*}\nProof \\[BH + CH = a,\\] \\begin{align*} BH^{2} – CH^{2} = c^{2} – b^{2}\... |
deepscaler | [
{
"role": "user",
"content": "An integer between $1000$ and $9999$, inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{56}{225}"
} | {
"split": "train",
"index": 33821,
"solution": "To solve this problem, we need to calculate the total number of integers between $1000$ and $9999$ and then find how many of these integers meet the given conditions (odd and all digits distinct).\n\n1. **Total number of integers between $1000$ and $9999$:**\n - ... |
deepscaler | [
{
"role": "user",
"content": "If $a$, $b$, and $c$ are positive integers such that $\\gcd(a,b) = 168$ and $\\gcd(a,c) = 693$, then what is the smallest possible value of $\\gcd(b,c)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 33822,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each positive integer $n$, let $S(n)$ denote the sum of the digits of $n$. For how many values of $n$ is $n+S(n)+S(S(n))=2007$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 33823,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A_{1} A_{2} \\ldots A_{6}$ be a regular hexagon with side length $11 \\sqrt{3}$, and let $B_{1} B_{2} \\ldots B_{6}$ be another regular hexagon completely inside $A_{1} A_{2} \\ldots A_{6}$ such that for all $i \\in\\{1,2, \\ldots, 5\\}, A_{i} A_{i+1}$ is parallel to $B_{i... | math | {
"style": "rule",
"ground_truth": "3 \\sqrt{3}"
} | {
"split": "train",
"index": 33824,
"solution": "Let $X=A_{1} A_{2} \\cap A_{3} A_{4}$, and let $O$ be the center of $B_{1} B_{2} \\ldots B_{6}$. Let $p$ be the apothem of hexagon $B$. Since $O A_{2} X A_{3}$ is a convex quadrilateral, we have $$\\begin{aligned} {\\left[A_{2} A_{3} X\\right] } & =\\left[A_{2} X O... |
deepscaler | [
{
"role": "user",
"content": "Given that the central angle of a sector is $\\frac{3}{2}$ radians, and its radius is 6 cm, then the arc length of the sector is \\_\\_\\_\\_\\_\\_ cm, and the area of the sector is \\_\\_\\_\\_\\_\\_ cm<sup>2</sup>. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 33825,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least positive integer with exactly $12$ positive factors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 33826,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Phil rolls 5 fair 10-sided dice. What is the probability that at least two dice show the same number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1744}{2500}"
} | {
"split": "train",
"index": 33827,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the cube $ABCDEFGH$, find $\\sin \\angle BAC$ ensuring that the angle is uniquely determined and forms a right angle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 33828,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A basketball is dropped from 150 feet and rebounds two-fifths of the distance it falls each time it bounces. How many feet will the basketball have traveled when it hits the ground the sixth time? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "347.952"
} | {
"split": "train",
"index": 33829,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $(xOy)$, the polar coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of circle $C$ is $ρ=2 \\sqrt{2}\\cos \\left(θ+\\frac{π}{4} \\right)$, and the paramet... | math | {
"style": "rule",
"ground_truth": "\\frac{10 \\sqrt{5}}{9}"
} | {
"split": "train",
"index": 33830,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, and it is given that $a\\sin B=-b\\sin \\left(A+ \\frac {\\pi}{3}\\right)$. \n$(1)$ Find $A$; \n$(2)$ If the area of $\\triangle ABC$, $S= \\frac { \\sqrt {3}}{4}c^{2}$, fi... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {7}}{14}"
} | {
"split": "train",
"index": 33831,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\cos(\\pi+\\theta) = -\\frac{1}{2}$, find the value of $\\tan(\\theta - 9\\pi)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 33832,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A roll of quarters contains $40$ quarters and a roll of dimes contains $50$ dimes. James has a jar that contains $83$ quarters and $159$ dimes. Lindsay has a jar that contains $129$ quarters and $266$ dimes. James and Lindsay pool these quarters and dimes and make complete rol... | math | {
"style": "rule",
"ground_truth": "\\$5.50"
} | {
"split": "train",
"index": 33833,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Identical red balls and three identical black balls are arranged in a row, numbered from left to right as 1, 2, 3, 4, 5, 6. Calculate the number of arrangements where the sum of the numbers of the red balls is less than the sum of the numbers of the black balls. Let's think ste... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 33834,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x$ is doubled, increased by $3$, and then divided by $5$, the result is $11$. What is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 33835,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin (\\omega x+\\varphi)$ $(0 < \\omega < 3,0 < \\varphi < \\pi)$, if $x=-\\frac{\\pi}{4}$ is a zero of the function $f(x)$, and $x=\\frac{\\pi}{3}$ is an axis of symmetry for the graph of the function $f(x)$, then the value of $\\omega$ is \\_\\_\\_\... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{7}"
} | {
"split": "train",
"index": 33836,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$ passes through the point $(1, \\frac{2\\sqrt{3}}{3})$, with its left and right foci being $F_1$ and $F_2$ respectively. The chord formed by the intersection of the circle $x^2 + y^2 = 2$ and the line $x... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 33837,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\cos(\\alpha + \\frac{\\pi}{4}) = \\frac{\\sqrt{2}}{4}$, find the value of $\\sin(2\\alpha)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 33838,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a two-day problem-solving competition, Gamma and Delta participated and attempted questions worth a total of 500 points. On the first day, Gamma scored 180 points out of 280 points attempted, and on the second day, he scored 120 points out of 220 points attempted. Delta, who... | math | {
"style": "rule",
"ground_truth": "\\frac{409}{500}"
} | {
"split": "train",
"index": 33839,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A recipe calls for $5 \\frac{3}{4}$ cups of flour and $2 \\frac{1}{2}$ cups of sugar. If you make one-third of the recipe, how many cups of flour and sugar do you need? Express your answers as mixed numbers. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 33840,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\theta$ is an angle in the third quadrant, and $sin^{4}\\theta+cos^{4}\\theta= \\frac {5}{9}$, then $sin2\\theta= \\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {2 \\sqrt {2}}{3}"
} | {
"split": "train",
"index": 33841,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{Q} \\rightarrow \\{-1, 1\\} \\) such that for all distinct \\( x, y \\in \\mathbb{Q} \\) satisfying \\( xy = 1 \\) or \\( x + y \\in \\{0, 1\\} \\), we have \\( f(x) f(y) = -1 \\).\n\nIntermediate question: Let \\( f \\) be a function having t... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 33842,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A solid cube of side length $4$ has $12$ edges, and a solid cube of side length $2$ has $12$ edges. The remaining solid is created by removing $8$ solid cubes of side length $2$ from the corners of the solid cube of side length $4$. Calculate the total number of edges of the re... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 33843,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The inverse of $f(x) = \\frac{3x - 2}{x + 4}$ may be written in the form $f^{-1}(x)=\\frac{ax+b}{cx+d}$, where $a$, $b$, $c$, and $d$ are real numbers. Find $a/c$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 33844,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "<u>Set 1</u>**p1.** Assume the speed of sound is $343$ m/s. Anastasia and Bananastasia are standing in a field in front of you. When they both yell at the same time, you hear Anastasia’s yell $5$ seconds before Bananastasia’s yell. If Bananastasia yells first, and then Anas... | math | {
"style": "rule",
"ground_truth": "1715"
} | {
"split": "train",
"index": 33845,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $C$ be the circle with equation $x^2+12y+57=-y^2-10x$. If $(a,b)$ is the center of $C$ and $r$ is its radius, what is the value of $a+b+r$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-9"
} | {
"split": "train",
"index": 33846,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $EFGH$, $EFDC$, and $EHBC$ be three adjacent square faces of a cube, for which $EC = 8$, and let $A$ be the eighth vertex of the cube. Let $I$, $J$, and $K$, be the points on $\\overline{EF}$, $\\overline{EH}$, and $\\overline{EC}$, respectively, so that $EI = EJ = EK = 2$.... | math | {
"style": "rule",
"ground_truth": "417"
} | {
"split": "train",
"index": 33847,
"solution": "[asy] import three; currentprojection = orthographic(camera=(1/4,2,3/4)); defaultpen(linewidth(0.7)); pen l = linewidth(0.5) + linetype(\"10 2\"); triple S=(1,0,0), T=(2,0,2), U=(8,6,8), V=(8,8,6), W=(2,2,0), X=(6,8,8); draw((1,0,0)--(8,0,0)--(8,0,8)--(0,0,8)--(0,0... |
deepscaler | [
{
"role": "user",
"content": "In a school's mentoring program, several first-grade students can befriend one sixth-grade student, while one sixth-grade student cannot befriend multiple first-grade students. It is known that $\\frac{1}{3}$ of the sixth-grade students and $\\frac{2}{5}$ of the first-grade stu... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{11}"
} | {
"split": "train",
"index": 33848,
"solution": ""
} |
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