data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "The limiting sum of the infinite series, $\\frac{1}{10} + \\frac{2}{10^2} + \\frac{3}{10^3} + \\dots$ whose $n$th term is $\\frac{n}{10^n}$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10}{81}"
} | {
"split": "train",
"index": 33149,
"solution": "To find the sum of the series $\\frac{1}{10} + \\frac{2}{10^2} + \\frac{3}{10^3} + \\dots$, where the $n$th term is $\\frac{n}{10^n}$, we can use a technique that involves rewriting the series in a more manageable form.\n\n1. **Rewrite the series**: Notice that eac... |
deepscaler | [
{
"role": "user",
"content": "Three integers from the list $1,2,4,8,16,20$ have a product of 80. What is the sum of these three integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 33150,
"solution": "The three integers from the list whose product is 80 are 1, 4, and 20, since $1 \\times 4 \\times 20=80$. The sum of these integers is $1+4+20=25$. \n (Since 80 is a multiple of 5 and 20 is the only integer in the list that is a multiple of 5, then 20 must be inclu... |
deepscaler | [
{
"role": "user",
"content": "Convert \\(531_8\\) to base 7. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1002_7"
} | {
"split": "train",
"index": 33151,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( AB \\) as the diameter of the smallest radius circle centered at \\( C(0,1) \\) that intersects the graph of \\( y = \\frac{1}{|x|-1} \\), where \\( O \\) is the origin. Find the value of \\( \\overrightarrow{OA} \\cdot \\overrightarrow{OB} \\). Let's think step by st... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 33152,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\tan(\\alpha+ \\frac {\\pi}{4})= \\frac {3}{4}$, calculate the value of $\\cos ^{2}(\\frac {\\pi}{4}-\\alpha)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{25}"
} | {
"split": "train",
"index": 33153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The increasing sequence $3, 15, 24, 48, \\ldots$ consists of those positive multiples of 3 that are one less than a perfect square. What is the remainder when the 1994th term of the sequence is divided by 1000? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "935"
} | {
"split": "train",
"index": 33154,
"solution": "1. **Identify the form of the sequence**: The sequence consists of positive multiples of 3 that are one less than a perfect square. This can be represented as $n^2 - 1$, where $n^2 - 1$ is a multiple of 3.\n\n2. **Determine conditions for $n^2 - 1$ to be a multiple... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha$ is an angle in the third quadrant, $f\\left( \\alpha \\right)=\\dfrac{\\sin (\\alpha -\\dfrac{\\pi }{2})\\cos (\\dfrac{3\\pi }{2}+\\alpha )\\tan (\\pi -\\alpha )}{\\tan (-\\alpha -\\pi )\\sin (-\\alpha -\\pi )}$.\n\n(1) Simplify $f\\left( \\alpha \\right)$\... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{2\\sqrt{6}}{5}"
} | {
"split": "train",
"index": 33155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many values of $c$ in the interval $[0, 1000]$ does the equation \\[7 \\lfloor x \\rfloor + 2 \\lceil x \\rceil = c\\]have a solution for $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "223"
} | {
"split": "train",
"index": 33156,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a_0 = 5/2$ and $a_k = a_{k-1}^2 - 2$ for $k \\geq 1$. Compute \\[ \\prod_{k=0}^\\infty \\left(1 - \\frac{1}{a_k} \\right) \\] in closed form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{7}"
} | {
"split": "train",
"index": 33157,
"solution": "Using the identity \\[ (x + x^{-1})^2 - 2 = x^2 + x^{-2}, \\] we may check by induction on $k$ that $a_k = 2^{2^k} + 2^{-2^k}$; in particular, the product is absolutely convergent. Using the identities \\[ \\frac{x^2 + 1 + x^{-2}}{x + 1 + x^{-1}} = x - 1 + x^{-1},... |
deepscaler | [
{
"role": "user",
"content": "In a physical education class, 25 students from class 5\"B\" stood in a line. Each student is either an honor student who always tells the truth or a troublemaker who always lies.\n\nHonor student Vlad took the 13th position. All the students, except Vlad, said: \"There are exa... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 33158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The ten smallest positive odd numbers \\( 1, 3, \\cdots, 19 \\) are arranged in a circle. Let \\( m \\) be the maximum value of the sum of any one of the numbers and its two adjacent numbers. Find the minimum value of \\( m \\). Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 33159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function \\( f(x) = A \\sin (\\omega x + \\varphi) \\) where \\( A \\neq 0 \\), \\( \\omega > 0 \\), \\( 0 < \\varphi < \\frac{\\pi}{2} \\), if \\( f\\left(\\frac{5\\pi}{6}\\right) + f(0) = 0 \\), find the minimum value of \\( \\omega \\). Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{5}"
} | {
"split": "train",
"index": 33160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Thirty-six 6-inch wide square posts are evenly spaced with 6 feet between adjacent posts to enclose a square field. What is the outer perimeter, in feet, of the fence? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "192"
} | {
"split": "train",
"index": 33161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all positive integer solutions less than or equal to $20$ to the congruence $13(3x-2)\\equiv 26\\pmod 8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 33162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that there are 16 variables $\\left\\{a_{i, j}\\right\\}_{0 \\leq i, j \\leq 3}$, each of which may be 0 or 1 . For how many settings of the variables $a_{i, j}$ do there exist positive reals $c_{i, j}$ such that the polynomial $$f(x, y)=\\sum_{0 \\leq i, j \\leq 3} a_{... | math | {
"style": "rule",
"ground_truth": "126"
} | {
"split": "train",
"index": 33163,
"solution": "For some choices of the $a_{i, j}$, let $S=\\left\\{(i, j) \\mid a_{i, j}=1\\right\\}$, and let $S^{\\prime}=S \\cup\\{(0,0)\\}$. Let $C\\left(S^{\\prime}\\right)$ denote the convex hull of $S^{\\prime}$. We claim that there exist the problem conditions are satisfi... |
deepscaler | [
{
"role": "user",
"content": "Find the $y$-intercept point of the line $3x+5y=20$. Provide your answer as an ordered pair. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(0,4)"
} | {
"split": "train",
"index": 33164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: \\\\((x+2)^{2}-4x(x+1)\\\\), where \\\\(x= \\sqrt {2}\\\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 33165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The leadership team of a sports event needs to select 4 volunteers from 5 candidates named A, B, C, D, and E to undertake four different tasks: translation, tour guiding, protocol, and driving. If A and B can only undertake the first three tasks, while the other three candidate... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 33166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the actual lighthouse's cylindrical base is 60 meters high, and the spherical top's volume is approximately 150,000 liters, and the miniature model's top holds around 0.15 liters, determine the height of Lara’s model lighthouse, in centimeters. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 33167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive value of $k$ such that the equation $4x^3 + 9x^2 + kx + 4 = 0$ has exactly one real solution in $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6.75"
} | {
"split": "train",
"index": 33168,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given plane vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\overrightarrow{c}$ satisfy $\\langle \\overrightarrow{a}, \\overrightarrow{b} \\rangle = 60^\\circ$, and $\\{|\\overrightarrow{a}|, |\\overrightarrow{b}|, |\\overrightarrow{c}|\\} = \\{1, 2, 3\\}$, calculate t... | math | {
"style": "rule",
"ground_truth": "\\sqrt{7}+3"
} | {
"split": "train",
"index": 33169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yel... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 33170,
"solution": "1. **Total number of students and pairs:**\n Given that there are $57$ students wearing blue shirts and $75$ students wearing yellow shirts, the total number of students is $57 + 75 = 132$. These students are paired into $66$ pairs.\n\n2. **Pairs with both studen... |
deepscaler | [
{
"role": "user",
"content": "In acute triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\\frac{\\sin B\\sin C}{\\sin A}=\\frac{3\\sqrt{7}}{2}$, $b=4a$, and $a+c=5$, find the area of $\\triangle ABC$. Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{7}}{4}"
} | {
"split": "train",
"index": 33171,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?\n\na square\na rectangle that is not a square\na rhombus that is not a square\na parallelogram that ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 33172,
"solution": "To solve this problem, we need to determine which of the given types of quadrilaterals have a point that is equidistant from all four vertices. This point is the circumcenter of the quadrilateral, and the quadrilateral must be cyclic (i.e., it can be inscribed in a... |
deepscaler | [
{
"role": "user",
"content": "The integers -5 and 6 are shown on a number line. What is the distance between them? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 33173,
"solution": "The distance between two numbers on the number line is equal to their positive difference. Here, this distance is $6-(-5)=11$."
} |
deepscaler | [
{
"role": "user",
"content": "When manufacturing a steel cable, it was found that the cable has the same length as the curve given by the system of equations:\n\n$$\n\\left\\{\\begin{array}{l}\nx+y+z=10 \\\\\nx y+y z+x z=-22\n\\end{array}\\right.\n$$\n\nFind the length of the cable. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "4 \\pi \\sqrt{\\frac{83}{3}}"
} | {
"split": "train",
"index": 33174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Misha made himself a homemade dartboard at the summer house. The round board is divided into sectors by circles - it can be used to throw darts. Points are awarded according to the number written in the sector, as indicated in the diagram.\n\nMisha threw 8 darts 3 times. The se... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 33175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the total amount of money originally owned by Moe, Loki, and Nick was $72, and each of Loki, Moe, and Nick gave Ott$\\, 4, determine the fractional part of the group's money that Ott now has. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 33176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many two digit numbers have exactly $4$ positive factors? $($ Here $1$ and the number $n$ are also considered as factors of $n. )$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 33177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $F(1,0)$ is the focus of the ellipse $\\frac{x^2}{9} + \\frac{y^2}{m} = 1$, $P$ is a moving point on the ellipse, and $A(1,1)$, find the minimum value of $|PA| + |PF|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6 - \\sqrt{5}"
} | {
"split": "train",
"index": 33178,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be complex numbers such that\n\\[\\frac{x + y}{x - y} + \\frac{x - y}{x + y} = 1.\\]Find\n\\[\\frac{x^4 + y^4}{x^4 - y^4} + \\frac{x^4 - y^4}{x^4 + y^4}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{41}{20}"
} | {
"split": "train",
"index": 33179,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a moving point \\( M \\) on the base \\( A_{1}B_{1}C_{1}D_{1} \\) of the cube \\( ABCD - A_{1}B_{1}C_{1}D_{1} \\), and \\( BM \\parallel \\) plane \\( ADC \\). Find the maximum value of \\( \\tan \\angle D_{1}MD \\). Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 33180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven boys and three girls are playing basketball. I how many different ways can they make two teams of five players so that both teams have at least one girl? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 33181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There exist $s$ unique nonnegative integers $m_1 > m_2 > \\cdots > m_s$ and $s$ unique integers $b_k$ ($1\\le k\\le s$) with each $b_k$ either $1$ or $- 1$ such that\\[b_13^{m_1} + b_23^{m_2} + \\cdots + b_s3^{m_s} = 2012.\\]Find $m_1 + m_2 + \\cdots + m_s$. Let's think step by... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 33182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average of the numbers $1, 2, 3,\\dots, 49, 50,$ and $x$ is $80x$. What is $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1275}{4079}"
} | {
"split": "train",
"index": 33183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that angle $\\alpha$ is in the fourth quadrant, and the x-coordinate of the point where its terminal side intersects the unit circle is $\\frac{1}{3}$.\n(1) Find the value of $\\tan \\alpha$;\n(2) Find the value of $\\frac{\\sin^{2}\\alpha - \\sqrt{2}\\sin \\alpha\\cos \\... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{5}"
} | {
"split": "train",
"index": 33184,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a nonnegative integer less than $2023$ such that $2n^2 + 3n$ is a perfect square. What is the sum of all possible $n$ ?\n\n*Proposed by Giacomo Rizzo* Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "444"
} | {
"split": "train",
"index": 33185,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any real numbers \\( a \\) and \\( b \\), the inequality \\( \\max \\{|a+b|,|a-b|,|2006-b|\\} \\geq C \\) always holds. Find the maximum value of the constant \\( C \\). (Note: \\( \\max \\{x, y, z\\} \\) denotes the largest among \\( x, y, \\) and \\( z \\).) Let's think s... | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 33186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the least positive integer $x$ that satisfies $x+4609 \\equiv 2104 \\pmod{12}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 33187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum area of a triangle if none of its side lengths exceed 2? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 33188,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that connecting all the vertices of a polygon from a point on one of the edges results in 2022 triangles, determine the number of sides of this polygon. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2023"
} | {
"split": "train",
"index": 33189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The positive integer $i$ is chosen at random such that the probability of a positive integer $k$ being chosen is $\\frac{3}{2}$ times the probability of $k+1$ being chosen. What is the probability that the $i^{\\text {th }}$ digit after the decimal point of the decimal expansio... | math | {
"style": "rule",
"ground_truth": "\\frac{108}{665}"
} | {
"split": "train",
"index": 33190,
"solution": "First we note that the probability that $n$ is picked is $\\frac{1}{2} \\times\\left(\\frac{2}{3}\\right)^{n}$, because this is the sequence whose terms decrease by a factor of $\\frac{2}{3}$ each time and whose sum is 1 (recall that probabilities must sum to 1 ). ... |
deepscaler | [
{
"role": "user",
"content": "If $x@y=xy-2x$, what is the value of $(5@3)-(3@5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 33191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $\\triangle PQR$ is right-angled at $P$ and has $PQ=2$ and $PR=2\\sqrt{3}$. Altitude $PL$ intersects median $RM$ at $F$. What is the length of $PF$? [asy]\ndraw((0,0)--(10,0)--(0,10*sqrt(3))--cycle);\ndraw((0,0)--(7.5,4.33)); draw((0,10*sqrt(3))--(5,0));\ndraw... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{3}}{7}"
} | {
"split": "train",
"index": 33192,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If a natural number \\(N\\) can be expressed as the sum of 3 consecutive natural numbers, the sum of 11 consecutive natural numbers, and the sum of 12 consecutive natural numbers, then the smallest value of \\(N\\) is \\(\\qquad\\). (Note: The smallest natural number is 0.) Let... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 33193,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the parabola defined by $y = ax^2 + 6$ is tangent to the line $y = x,$ then calculate the constant $a.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{24}"
} | {
"split": "train",
"index": 33194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that two children, A and B, and three adults, 甲, 乙, and 丙, are standing in a line, A is not at either end, and exactly two of the three adults are standing next to each other. The number of different arrangements is $\\boxed{\\text{answer}}$. Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 33195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The decimal representation of a fraction ends in $0.\\overline{3}$. When the decimal is changed to a common fraction and reduced to lowest terms, what is the denominator of the fraction? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 33196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an isosceles triangle \\( ABC \\), the bisectors \\( AD, BE, CF \\) are drawn.\n\nFind \\( BC \\), given that \\( AB = AC = 1 \\), and the vertex \\( A \\) lies on the circle passing through the points \\( D, E, \\) and \\( F \\). Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{17} - 1}{2}"
} | {
"split": "train",
"index": 33197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "All triangles have the same value, and all circles have the same value. What is the sum of three circles? \\begin{align*}\n\\Delta + \\bigcirc + \\Delta + \\bigcirc + \\Delta&= 21\\\\\n\\bigcirc + \\Delta+\\bigcirc+\\Delta+\\bigcirc &= 19\\\\\n\\bigcirc + \\bigcirc + \\bigcirc ... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 33198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $a$, $b,$ and $c$ are positive numbers satisfying: \\begin{align*}\na^2/b &= 1, \\\\\nb^2/c &= 2, \\text{ and}\\\\\nc^2/a &= 3.\n\\end{align*} Find $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12^{1/7}"
} | {
"split": "train",
"index": 33199,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A four-digit integer $m$ and the four-digit integer obtained by reversing the order of the digits of $m$ are both divisible by 63. If $m$ is also divisible by 11, what is the greatest possible value of $m$? Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "9702"
} | {
"split": "train",
"index": 33200,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a connected simple graph \\( G \\) with a known number of edges \\( e \\), where each vertex has some number of pieces placed on it (each piece can only be placed on one vertex of \\( G \\)). The only operation allowed is when a vertex \\( v \\) has a number of pieces not... | math | {
"style": "rule",
"ground_truth": "e"
} | {
"split": "train",
"index": 33201,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has vertices $A(0, 8)$, $B(2, 0)$, $C(8, 0)$. A horizontal line with equation $y=t$ intersects line segment $ \\overline{AB} $ at $T$ and line segment $ \\overline{AC} $ at $U$, forming $\\triangle ATU$ with area 13.5. Compute $t$. Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 33202,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The cost of 60 copies of the first volume and 75 copies of the second volume is 2700 rubles. In reality, the total payment for all these books was only 2370 rubles because a discount was applied: 15% off the first volume and 10% off the second volume. Find the original price of... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 33203,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The 31st World University Summer Games will be held in Chengdu, Sichuan from July 28th to August 8th, 2023. A company decided to evaluate a certain product under its umbrella for bidding for related endorsement activities. The original selling price of the product was $25 per u... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 33204,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given in the Cartesian coordinate system $xOy$, the parametric equation of curve $C$ is $\\begin{cases} x=3+5\\cos \\alpha \\\\ y=4+5\\sin \\alpha \\end{cases}$, ($\\alpha$ is the parameter), points $A$ and $B$ are on curve $C$. With the origin $O$ as the pole and the positive ... | math | {
"style": "rule",
"ground_truth": "\\frac{25\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 33205,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each term of a sequence, after the first term, is inversely proportional to the term preceding it, and the constant of proportionality stays the same. If the first term is 2 and the second term is 5, what is the 12th term? Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 33206,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$AM$ is the angle bisector of triangle $ABC$. $BM = 2$, $CM = 3$, and $D$ is the point where the extension of $AM$ intersects the circumcircle of the triangle. If $MD = 2$, find $AB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}"
} | {
"split": "train",
"index": 33207,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is given by $ \\begin{cases} x=-\\frac{1}{2}t \\\\ y=2+\\frac{\\sqrt{3}}{2}t \\end{cases} (t\\text{ is the parameter})$, and a circle $C$ with polar coordinate equation $\\rho=4\\cos\\theta$ is es... | math | {
"style": "rule",
"ground_truth": "4+2\\sqrt{3}"
} | {
"split": "train",
"index": 33208,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Regular octagon $A_1A_2A_3A_4A_5A_6A_7A_8$ is inscribed in a circle of area $1.$ Point $P$ lies inside the circle so that the region bounded by $\\overline{PA_1},\\overline{PA_2},$ and the minor arc $\\widehat{A_1A_2}$ of the circle has area $\\tfrac{1}{7},$ while the region bo... | math | {
"style": "rule",
"ground_truth": "504"
} | {
"split": "train",
"index": 33209,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Last month, Xiao Ming's household expenses were 500 yuan for food, 200 yuan for education, and 300 yuan for other expenses. This month, the costs of these three categories increased by 6%, 20%, and 10%, respectively. What is the percentage increase in Xiao Ming's household expe... | math | {
"style": "rule",
"ground_truth": "10\\%"
} | {
"split": "train",
"index": 33210,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C D$ be a cyclic quadrilateral, and let segments $A C$ and $B D$ intersect at $E$. Let $W$ and $Y$ be the feet of the altitudes from $E$ to sides $D A$ and $B C$, respectively, and let $X$ and $Z$ be the midpoints of sides $A B$ and $C D$, respectively. Given that the ... | math | {
"style": "rule",
"ground_truth": "17+\\frac{15}{2} \\sqrt{3}"
} | {
"split": "train",
"index": 33211,
"solution": "Reflect $E$ across $D A$ to $E_{W}$, and across $B C$ to $E_{Y}$. As $A B C D$ is cyclic, $\\triangle A E D$ and $\\triangle B E C$ are similar. Thus $E_{W} A E D$ and $E B E_{Y} C$ are similar too. Now since $W$ is the midpoint of $E_{W} E, X$ is the midpoint of $... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive real $\\alpha$, such that $$\\frac{x+y} {2}\\geq \\alpha\\sqrt{xy}+(1 - \\alpha)\\sqrt{\\frac{x^2+y^2}{2}}$$ for all positive reals $x, y$. 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": 33212,
"solution": "\nTo solve the problem of finding the smallest positive real \\(\\alpha\\) such that \n\n\\[\n\\frac{x+y}{2} \\geq \\alpha\\sqrt{xy} + (1 - \\alpha)\\sqrt{\\frac{x^2 + y^2}{2}}\n\\]\n\nfor all positive reals \\(x\\) and \\(y\\), we proceed as follows:\n\n### Step 1... |
deepscaler | [
{
"role": "user",
"content": "What is $2453_6 + 16432_6$? Express your answer in both base 6 and base 10. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3881"
} | {
"split": "train",
"index": 33213,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(a_n)$ and $(b_n)$ be the sequences of real numbers such that\n\\[ (2 + i)^n = a_n + b_ni \\]for all integers $n\\geq 0$, where $i = \\sqrt{-1}$. What is\n\\[\\sum_{n=0}^\\infty\\frac{a_nb_n}{7^n}\\,?\\] Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{16}"
} | {
"split": "train",
"index": 33214,
"solution": "1. **Express $(2+i)$ in polar form**: \n We start by expressing the complex number $2+i$ in polar form. We calculate the modulus and the argument of $2+i$:\n \\[ |2+i| = \\sqrt{2^2 + 1^2} = \\sqrt{5}, \\]\n \\[ \\theta = \\arctan\\left(\\frac{1}{2}\\right). \... |
deepscaler | [
{
"role": "user",
"content": "What is the 100th digit to the right of the decimal point in the decimal representation of $\\frac{13}{90}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 33215,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the figure, $\\triangle ABC$ has $\\angle A =45^{\\circ}$ and $\\angle B =30^{\\circ}$. A line $DE$, with $D$ on $AB$ \nand $\\angle ADE =60^{\\circ}$, divides $\\triangle ABC$ into two pieces of equal area.\n(Note: the figure may not be accurate; perhaps $E$ is on $CB$ inst... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt[4]{12}}"
} | {
"split": "train",
"index": 33216,
"solution": "1. **Identify the position of $E$**: We start by assuming $E = C$ and analyze the consequences. Drop an altitude from $C$ to $AB$, meeting $AB$ at $F$. Assume $CF = 1$ for simplicity. \n\n2. **Calculate the ratio of areas assuming $E = C$**: The area of $\\triangle... |
deepscaler | [
{
"role": "user",
"content": "How many students are there in our city? The number expressing the quantity of students is the largest of all numbers where any two adjacent digits form a number that is divisible by 23. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "46923"
} | {
"split": "train",
"index": 33217,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x^5 - x^4 + x^3 - px^2 + qx + 4$ is divisible by $(x + 2)(x - 1),$ find the ordered pair $(p,q).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-7,-12)"
} | {
"split": "train",
"index": 33218,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a four-digit number that is a perfect square, knowing that the first two digits, as well as the last two digits, are each equal to each other. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7744"
} | {
"split": "train",
"index": 33219,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each edge of a regular tetrahedron is divided into three equal parts. Through each resulting division point, two planes are drawn, parallel to the two faces of the tetrahedron that do not pass through that point. Into how many parts do the constructed planes divide the tetrahed... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 33220,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and they satisfy the equation $$\\frac {2c-b}{a} = \\frac {\\cos{B}}{\\cos{A}}$$. If $a = 2\\sqrt {5}$, find the maximum value of $b + c$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "4\\sqrt{5}"
} | {
"split": "train",
"index": 33221,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the base 4 representation of the base 2 number $101010101_2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11111_4"
} | {
"split": "train",
"index": 33222,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a similar mistake during multiplication, Tom reversed the digits of the two-digit number c and mistakenly multiplied the reversed number with d, resulting in the erroneous product of 143. Determine the correct product of c and d. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "341"
} | {
"split": "train",
"index": 33223,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $ABC$ is a scalene right triangle, and $P$ is the point on hypotenuse $\\overline{AC}$ such that $\\angle{ABP} = 30^{\\circ}$. Given that $AP = 3$ and $CP = 1$, compute the area of triangle $ABC$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "\\frac{12}{5}"
} | {
"split": "train",
"index": 33224,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sheila has been invited to a picnic tomorrow. The picnic will occur, rain or shine. If it rains, there is a $20\\%$ probability that Sheila will decide to go, but if it is sunny, there is an $80\\%$ probability that Sheila will decide to go. The forecast for tomorrow states ... | math | {
"style": "rule",
"ground_truth": "0.56 = 56\\%"
} | {
"split": "train",
"index": 33225,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Place 6 balls, labeled from 1 to 6, into 3 different boxes. If each box is to contain 2 balls, and the balls labeled 1 and 2 are to be placed in the same box, calculate the total number of different ways to do this. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 33226,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest positive integer $m$ which makes it possible to color several cells of a $70\\times 70$ table red such that [list] [*] There are no two red cells satisfying: the two rows in which they are have the same number of red cells, while the two columns in which they a... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 33227,
"solution": "\nTo find the largest positive integer \\( m \\) that allows coloring several cells of a \\( 70 \\times 70 \\) table red such that:\n1. There are no two red cells satisfying: the two rows in which they are have the same number of red cells, while the two columns in... |
deepscaler | [
{
"role": "user",
"content": "Meredith drives 5 miles to the northeast, then 15 miles to the southeast, then 25 miles to the southwest, then 35 miles to the northwest, and finally 20 miles to the northeast. How many miles is Meredith from where she started? Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 33228,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Pick a random digit in the decimal expansion of $\\frac{1}{99999}$. What is the probability that it is 0? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 33229,
"solution": "The decimal expansion of $\\frac{1}{99999}$ is $0.\\overline{00001}$. Therefore, the probability that a random digit is 0 is $\\frac{4}{5}$."
} |
deepscaler | [
{
"role": "user",
"content": "Find the last two digits of the sum\n\n$$\n1^{2}+2^{2}+\\ldots+50^{2}-51^{2}-\\ldots-100^{2}+101^{2}+\\ldots 150^{2}-151^{2}-\\ldots 200^{2}+\\ldots-2000^{2}+2001^{2}+\\ldots+2017^{2}\n$$\n\n(i.e., 50 numbers with a \"plus\" sign, 50 with a \"minus\" sign, and so on.) Let's thi... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 33230,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Right triangle $ACD$ with right angle at $C$ is constructed outwards on the hypotenuse $\\overline{AC}$ of isosceles right triangle $ABC$ with leg length $1$, as shown, so that the two triangles have equal perimeters. What is $\\sin(2\\angle BAD)$? Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{9}"
} | {
"split": "train",
"index": 33231,
"solution": "\n1. **Identify the length of hypotenuse $AC$ in $\\triangle ABC$:**\n Since $\\triangle ABC$ is an isosceles right triangle with leg length $1$, by the Pythagorean Theorem, we have:\n \\[\n AC = \\sqrt{AB^2 + BC^2} = \\sqrt{1^2 + 1^2} = \\sqrt{2}\n \\]\n\n... |
deepscaler | [
{
"role": "user",
"content": "Each block on the grid shown in the Figure is 1 unit by 1 unit. Suppose we wish to walk from $A$ to $B$ via a 7 unit path, but we have to stay on the grid -- no cutting across blocks. How many different paths can we take?[asy]size(3cm,3cm);int w=5;int h=4;int i;for (i=0; i<h;... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 33232,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A local community group sells 180 event tickets for a total of $2652. Some tickets are sold at full price, while others are sold at a discounted rate of half price. Determine the total revenue generated from the full-price tickets.\nA) $960\nB) $984\nC) $1008\nD) $1032 Let's th... | math | {
"style": "rule",
"ground_truth": "984"
} | {
"split": "train",
"index": 33233,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In rectangle $ABCD$, $AB=100$. Let $E$ be the midpoint of $\\overline{AD}$. Given that line $AC$ and line $BE$ are perpendicular, find the greatest integer less than $AD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "141"
} | {
"split": "train",
"index": 33234,
"solution": "Let $x$ be the ratio of $BC$ to $AB$. On the coordinate plane, plot $A=(0,0)$, $B=(100,0)$, $C=(100,100x)$, and $D=(0,100x)$. Then $E=(0,50x)$. Furthermore, the slope of $\\overline{AC}$ is $x$ and the slope of $\\overline{BE}$ is $-x/2$. They are perpendicular, so... |
deepscaler | [
{
"role": "user",
"content": "The function $f(x)=\\frac{1}{3}x^{3}-ax^{2}+4$, and $x=2$ is a local minimum point of the function $f(x)$.\n\n(1) Find the value of the real number $a$;\n\n(2) Find the maximum and minimum values of $f(x)$ on the interval $[-1,3]$. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{3}"
} | {
"split": "train",
"index": 33235,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From 3 male students and 2 female students, calculate the number of different election results in which at least one female student is elected. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 33236,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify \\[\\frac{1}{\\dfrac{3}{\\sqrt{5}+2} + \\dfrac{4}{\\sqrt{7}-2}}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{5} + 4\\sqrt{7} + 10}{(9\\sqrt{5} + 4\\sqrt{7})^2 - 100}"
} | {
"split": "train",
"index": 33237,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $A=\\{a^{2},a+1,-3\\}$ and $B=\\{a-3,3a-1,a^{2}+1\\}$, if $A∩B=\\{-3\\}$, find the value of the real number $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac {2}{3}"
} | {
"split": "train",
"index": 33238,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base of an inclined parallelepiped is a rhombus with a side length of 60. A diagonal section plane passing through the longer diagonal of the base is perpendicular to the base's plane. The area of this section is 7200. Find the shorter diagonal of the base if the lateral ed... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 33239,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define a \"hook\" to be a figure made up of six unit squares as shown below in the picture, or any of the figures obtained by applying rotations and reflections to this figure. \n\n[asy]\nunitsize(0.5 cm);\n\ndraw((0,0)--(1,0));\ndraw((0,1)--(1,1));\ndraw((2,1)--(3,1));\ndraw((... | math | {
"style": "rule",
"ground_truth": "\\{1, 2, 5\\} \\not\\subseteq \\{m, n\\},\n\\]\n\\[\n3 \\mid m \\text{ or } 3 \\mid n,\n\\]\n\\[\n4 \\mid m \\text{ or } 4 \\mid n"
} | {
"split": "train",
"index": 33240,
"solution": "\nTo solve this problem, we need to understand the structure and properties of the \"hook\" figure. The hook consists of six unit squares arranged in a specific pattern. We are tasked with determining which \\( m \\times n \\) rectangles can be completely covered u... |
deepscaler | [
{
"role": "user",
"content": "Vasya loves picking mushrooms. He calculated that during the autumn, he collected a three-digit number of mushrooms with the sum of its digits equal to 14. Then Vasya calculated that 8% of the mushrooms were white, and 14% were boletus. How many mushrooms did Vasya collect? Let... | math | {
"style": "rule",
"ground_truth": "950"
} | {
"split": "train",
"index": 33241,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The parabola with the equation \\( y = 25 - x^2 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( B \\).\n\n(a) Determine the length of \\( AB \\).\n\n(b) Rectangle \\( ABCD \\) is formed such that \\( C \\) and \\( D \\) are below the \\( x \\)-axis and \\( BD = 26... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 33242,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the integers between 1 and 1500, inclusive, can be expressed as the difference of the squares of two positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1125"
} | {
"split": "train",
"index": 33243,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How can 13 rectangles of sizes $1 \\times 1, 2 \\times 1, 3 \\times 1, \\ldots, 13 \\times 1$ be combined to form a rectangle, where all sides are greater than 1? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13 \\times 7"
} | {
"split": "train",
"index": 33244,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At each vertex of a cube with an edge length of 1, there is the center of a sphere. All the spheres are identical, and each touches three neighboring spheres. Find the length of the part of the space diagonal of the cube that lies outside the spheres. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} - 1"
} | {
"split": "train",
"index": 33245,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least five-digit positive integer which is congruent to 5 (mod 15)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10,\\!010"
} | {
"split": "train",
"index": 33246,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\frac{(2200 - 2096)^2}{121}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "89"
} | {
"split": "train",
"index": 33247,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the digits in the product of $\\overline{A A A A A A A A A} \\times \\overline{B B B B B B B B B}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 33248,
"solution": ""
} |
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