data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Find $\\lfloor |-4.2| \\rfloor + |\\lfloor -4.2 \\rfloor|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 32249,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The repeating decimal for $\\frac{5}{13}$ is $0.cdc\\ldots$ What is the value of the sum $c+d$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 32250,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence 1,3,1,3,3,1,3,3,3,1,3,3,3,3,1,3,... follows a certain rule. What is the sum of the first 44 terms in this sequence? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "116"
} | {
"split": "train",
"index": 32251,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The parabolas with equations \\( y = x^2 - 2x - 3 \\) and \\( y = -x^2 + 4x + c \\) intersect at points \\( A \\) and \\( B \\). Determine the value of \\( c \\) so that the sum of the \\( x \\)-coordinate and \\( y \\)-coordinate of the midpoint of \\( AB \\) is 2017. Let's th... | math | {
"style": "rule",
"ground_truth": "4031"
} | {
"split": "train",
"index": 32252,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify\n\\[\\tan x + 2 \\tan 2x + 4 \\tan 4x + 8 \\cot 8x.\\]The answer will be a trigonometric function of some simple function of $x,$ like \"$\\cos 2x$\" or \"$\\sin (x^3)$\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\cot x"
} | {
"split": "train",
"index": 32253,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Expand $(x+2)(3x-6)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3x^2-12"
} | {
"split": "train",
"index": 32254,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define a natural number to be \"super-nice\" if it is either the product of exactly three distinct prime numbers or the fourth power of a prime number. What is the sum of the first eight super-nice numbers? Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "520"
} | {
"split": "train",
"index": 32255,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n = 1990 \\), then evaluate the expression \\(\\frac{1}{2^{n}}\\left(1 - 3 C_{n}^{2} + 3^{2} C_{n}^{4} - 3^{3} C_{n}^{6} + \\cdots + 3^{994} C_{n}^{1988} - 3^{995} C_{n}^{1990}\\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": 32256,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the 200 natural numbers from 1 to 200, list the numbers that are neither multiples of 3 nor multiples of 5 in ascending order. What is the 100th number in this list? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "187"
} | {
"split": "train",
"index": 32257,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two numbers $a$ and $b$ with $0 \\leq a \\leq 1$ and $0 \\leq b \\leq 1$ are chosen at random. The number $c$ is defined by $c=2a+2b$. The numbers $a, b$ and $c$ are each rounded to the nearest integer to give $A, B$ and $C$, respectively. What is the probability that $2A+2B=C$... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{16}"
} | {
"split": "train",
"index": 32258,
"solution": "By definition, if $0 \\leq a<\\frac{1}{2}$, then $A=0$ and if $\\frac{1}{2} \\leq a \\leq 1$, then $A=1$. Similarly, if $0 \\leq b<\\frac{1}{2}$, then $B=0$ and if $\\frac{1}{2} \\leq b \\leq 1$, then $B=1$. We keep track of our information on a set of axes, labell... |
deepscaler | [
{
"role": "user",
"content": "Let S<sub>n</sub> be the sum of the first n terms of the arithmetic sequence {a<sub>n</sub>}, given that a<sub>7</sub> = 5 and S<sub>5</sub> = -55.\n\n1. Find S<sub>n</sub>.\n2. Let b<sub>n</sub> = $$\\frac {S_{n}}{n}$$, find the sum of the first 19 terms, T<sub>19</sub>, of th... | math | {
"style": "rule",
"ground_truth": "-\\frac {1}{19}"
} | {
"split": "train",
"index": 32259,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p$, $q$, and $r$ be constants, and suppose that the inequality \\[\\frac{(x-p)(x-q)}{x-r} \\le 0\\] is true if and only if $x > 2$ or $3 \\le x \\le 5$. Given that $p < q$, find the value of $p + q + 2r$. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 32260,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cone has a volume of $12288\\pi$ cubic inches and the vertex angle of the vertical cross section is 60 degrees. What is the height of the cone? Express your answer as a decimal to the nearest tenth. [asy]\n\nimport markers;\nsize(150);\nimport geometry;\ndraw(scale(1,.2)*arc(... | math | {
"style": "rule",
"ground_truth": "48.0"
} | {
"split": "train",
"index": 32261,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sides opposite to the internal angles $A$, $B$, and $C$ of triangle $\\triangle ABC$ be $a$, $b$, and $c$ respectively. Given that $\\sin B - \\sin C = \\sin (A-C)$. \n$(1)$ Find the value of $A$. \n$(2)$ If $AB=2$, $AC=5$, and the medians $AM$ and $BN$ on sides $BC$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{91}}{91}"
} | {
"split": "train",
"index": 32262,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The side \\( AD \\) of the rectangle \\( ABCD \\) is equal to 2. On the extension of the side \\( AD \\) beyond point \\( A \\), a point \\( E \\) is taken such that \\( EA = 1 \\), and \\( \\angle BEC = 30^\\circ \\). Find \\( BE \\). Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 32263,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A watch loses $2\\frac{1}{2}$ minutes per day. It is set right at $1$ P.M. on March 15. Let $n$ be the positive correction, in minutes, to be added to the time shown by the watch at a given time. When the watch shows $9$ A.M. on March 21, $n$ equals: Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "14\\frac{14}{23}"
} | {
"split": "train",
"index": 32264,
"solution": "1. **Calculate the total time passed on the watch**: \n The watch is set at 1 P.M. on March 15 and shows 9 A.M. on March 21. To find the total time passed according to the watch:\n - From 1 P.M. on March 15 to 1 P.M. on March 21 is 6 days.\n - From 1 P.M. to ... |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers not exceeding 500 are not divisible by 2, 3, or 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "134"
} | {
"split": "train",
"index": 32265,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A quadrilateral is inscribed in a circle of radius $250$. Three sides of this quadrilateral have lengths of $250$, $250$, and $100$ respectively. What is the length of the fourth side? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 32266,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At lunch, Abby, Bart, Carl, Dana, and Evan share a pizza divided radially into 16 slices. Each one takes takes one slice of pizza uniformly at random, leaving 11 slices. The remaining slices of pizza form \"sectors\" broken up by the taken slices, e.g. if they take five consecu... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{3}"
} | {
"split": "train",
"index": 32267,
"solution": "Consider the more general case where there are $N$ slices and $M>0$ slices are taken. Let $S$ denote the number of adjacent pairs of slices of pizza which still remain. There are $N-M$ slices and a sector of $k$ slices contributes $k-1$ pairs to $S$. Hence the numb... |
deepscaler | [
{
"role": "user",
"content": "What is the probability, expressed as a decimal, of drawing one marble which is either green or white from a bag containing 4 green, 3 white, and 8 black marbles? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.4667"
} | {
"split": "train",
"index": 32268,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum value of $\\frac{(3^t - 2t)t}{9^t}$ for integer values of $t$?\n**A)** $\\frac{1}{8}$ \n**B)** $\\frac{1}{10}$ \n**C)** $\\frac{1}{12}$ \n**D)** $\\frac{1}{16}$ \n**E)** $\\frac{1}{18}$ Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 32269,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find, with proof, all positive integers $n$ for which $2^n + 12^n + 2011^n$ is a perfect square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "n = 1"
} | {
"split": "train",
"index": 32270,
"solution": "The answer is $n=1$ , which is easily verified to be a valid integer $n$ .\nNotice that \\[2^n+12^n+2011^n\\equiv 2^n+7^n \\pmod{12}.\\] Then for $n\\geq 2$ , we have $2^n+7^n\\equiv 3,5 \\pmod{12}$ depending on the parity of $n$ . But perfect squares can only be $... |
deepscaler | [
{
"role": "user",
"content": "Let \\( S = \\{1, 2, 3, 4, \\ldots, 16\\} \\). Each of the following subsets of \\( S \\):\n\\[ \\{6\\},\\{1, 2, 3\\}, \\{5, 7, 9, 10, 11, 12\\}, \\{1, 2, 3, 4, 5, 6, 7, 8, 9\\} \\]\nhas the property that the sum of all its elements is a multiple of 3. Find the total number of ... | math | {
"style": "rule",
"ground_truth": "21855"
} | {
"split": "train",
"index": 32271,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the smallest positive integer with exactly 2015 positive factors. What is the sum of the (not necessarily distinct) prime factors of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "116"
} | {
"split": "train",
"index": 32272,
"solution": "Note that $2015=5 \\times 13 \\times 31$ and that $N=2^{30} \\cdot 3^{12} \\cdot 5^{4}$ has exactly 2015 positive factors. We claim this is the smallest such integer. Note that $N<2^{66}$. If $n$ has 3 distinct prime factors, it must be of the form $p^{30} q^{12} r... |
deepscaler | [
{
"role": "user",
"content": "Given the sequences $\\{a_{n}\\}$ and $\\{b_{n}\\}$, where $a_{n}$ represents the $n$-th digit after the decimal point of $\\sqrt{2}=1.41421356237⋯$ (for example, $a_{1}=4$, $a_{6}=3)$, and $b_{1}=a_{1}$, with ${b_{n+1}}={a_{{b_n}}}$ for all $n\\in N^{*}$, find all values of $n... | math | {
"style": "rule",
"ground_truth": "675"
} | {
"split": "train",
"index": 32273,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Enter all the solutions to\n\\[ \\sqrt{4x-3}+\\frac{10}{\\sqrt{4x-3}}=7,\\]separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac 74,7"
} | {
"split": "train",
"index": 32274,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let\n\\[ f(x) = \\left\\{ \n\\begin{array}{cl} \n2ax + 4, & \\text{if } x > 2, \\\\\nx^2-2 & \\text{if } -2 \\le x \\le 2, \\\\\n3x - c, & \\text{if } x < -2. \n\\end{array} \n\\right. \\]\nFind $a+c$ if the piecewise function is continuous. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "-\\frac{17}{2}"
} | {
"split": "train",
"index": 32275,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$, $y$, and $z$ be distinct real numbers that sum to $0$. Compute \\[ \\dfrac {xy+yz+zx}{x^2+y^2+z^2}. \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac12"
} | {
"split": "train",
"index": 32276,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For his birthday, Piglet baked a big cake weighing 10 kg and invited 100 guests. Among them was Winnie-the-Pooh, who has a weakness for sweets. The birthday celebrant announced the cake-cutting rule: the first guest cuts themselves a piece of cake equal to \\(1\\%\\) of the rem... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 32277,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and $\\cos A= \\frac{ \\sqrt{6}}{3}$.\n(1) Find $\\tan 2A$;\n(2) If $\\cos B= \\frac{ 2\\sqrt{2}}{3}, c=2\\sqrt{2}$, find the area of $\\triangle ABC$. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 32278,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a number line, there are three points A, B, and C which represent the numbers -24, -10, and 10, respectively. Two electronic ants, named Alpha and Beta, start moving towards each other from points A and C, respectively. Alpha moves at a speed of 4 units per second, while Bet... | math | {
"style": "rule",
"ground_truth": "-44"
} | {
"split": "train",
"index": 32279,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T = TNFTPP$ . As $n$ ranges over the integers, the expression $n^4 - 898n^2 + T - 2160$ evaluates to just one prime number. Find this prime.\n\n[b]Note: This is part of the Ultimate Problem, where each question depended on the previous questi... | math | {
"style": "rule",
"ground_truth": "1801"
} | {
"split": "train",
"index": 32280,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the share of the Japanese yen in the currency structure of the NWF funds as of 01.07.2021 using one of the following methods:\n\nFirst method:\n\na) Find the total amount of NWF funds placed in Japanese yen as of 01.07.2021:\n\n\\[ JPY_{22} = 1213.76 - 3.36 - 38.4 - 4... | math | {
"style": "rule",
"ground_truth": "-23.5"
} | {
"split": "train",
"index": 32281,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the equation on the right, each Chinese character represents one of the ten digits from 0 to 9. The same character represents the same digit, and different characters represent different digits. What is the four-digit number represented by \"数学竞赛\"? Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "1962"
} | {
"split": "train",
"index": 32282,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < \\alpha < \\frac{\\pi}{2}$, $-\\frac{\\pi}{2} < \\beta < 0$, $\\cos\\left(\\frac{\\pi}{4}+\\alpha\\right) = \\frac{1}{3}$, $\\cos\\left(\\frac{\\pi}{4}-\\frac{\\beta}{2}\\right) = \\frac{\\sqrt{3}}{3}$, \nfind \n$(1)$ the value of $\\cos \\alpha$; \n$(2)$ the... | math | {
"style": "rule",
"ground_truth": "\\frac{5\\sqrt{3}}{9}"
} | {
"split": "train",
"index": 32283,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a natural number $N$, if at least six of the nine natural numbers from $1$ to $9$ can divide $N$, then $N$ is called a \"six-divisible number\". Among the natural numbers greater than $2000$, what is the smallest \"six-divisible number\"? Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 32284,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the largest odd positive integer $n$ such that every odd integer $k$ with $1<k<n$ and $\\gcd(k, n)=1$ is a prime. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 32285,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the vector $\\overrightarrow {a} = (3\\cos\\alpha, 2)$ is parallel to the vector $\\overrightarrow {b} = (3, 4\\sin\\alpha)$, find the value of the acute angle $\\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 32286,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( p(x) \\) be a monic quartic polynomial such that \\( p(1) = 1, p(2) = 9, p(3) = 28, \\) and \\( p(4) = 65. \\) Find \\( p(5) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "126"
} | {
"split": "train",
"index": 32287,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to label the faces of a regular octahedron with the integers 18, using each exactly once, so that any two faces that share an edge have numbers that are relatively prime? Physically realizable rotations are considered indistinguishable, but physically un... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 32288,
"solution": "Well, instead of labeling the faces of a regular octahedron, we may label the vertices of a cube. Then, as no two even numbers may be adjacent, the even numbers better form a regular tetrahedron, which can be done in 2 ways (because rotations are indistinguishable ... |
deepscaler | [
{
"role": "user",
"content": "For how many integers $n$ is $\\frac n{20-n}$ the square of an integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 32289,
"solution": "We are given the expression $\\frac{n}{20-n}$ and need to determine for how many integers $n$ this expression is a perfect square.\n\n1. **Examine the domain of $n$:**\n - If $n < 0$ or $n > 20$, the fraction $\\frac{n}{20-n}$ is negative, and thus cannot be a pe... |
deepscaler | [
{
"role": "user",
"content": "Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 32290,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ,$ points $G,$ $H,$ and $I$ are on sides $\\overline{YZ},$ $\\overline{XZ},$ and $\\overline{XY},$ respectively, such that $YG:GZ = XH:HZ = XI:IY = 2:3.$ Line segments $\\overline{XG},$ $\\overline{YH},$ and $\\overline{ZI}$ intersect at points $S,$ $T,$ and $U,... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{55}"
} | {
"split": "train",
"index": 32291,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a square diagram divided into 64 smaller equilateral triangular sections, shading follows a pattern where every alternate horizontal row of triangles is filled. If this pattern begins from the first row at the bottom (considering it as filled), what fraction of the triangle ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 32292,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A high school's second-year students are studying the relationship between students' math and Chinese scores. They conducted a simple random sampling with replacement and obtained a sample of size $200$ from the second-year students. The sample observation data of math scores a... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{7}"
} | {
"split": "train",
"index": 32293,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The probability that a light bulb lasts more than 1000 hours is 0.2. Determine the probability that 1 out of 3 light bulbs fails after 1000 hours of use. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.096"
} | {
"split": "train",
"index": 32294,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\cos x \\, dx}{(1+\\cos x+\\sin x)^{2}}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\ln(2) - \\frac{1}{2}"
} | {
"split": "train",
"index": 32295,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The trip from Carville to Nikpath requires $4\\frac 12$ hours when traveling at an average speed of 70 miles per hour. How many hours does the trip require when traveling at an average speed of 60 miles per hour? Express your answer as a decimal to the nearest hundredth. Let's ... | math | {
"style": "rule",
"ground_truth": "5.25"
} | {
"split": "train",
"index": 32296,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system xOy, the parametric equations of the curve C are $$\\begin{cases} x=1+2\\cos\\theta, \\\\ y= \\sqrt {3}+2\\sin\\theta\\end{cases}$$ (where θ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and th... | math | {
"style": "rule",
"ground_truth": "4 \\sqrt {3}"
} | {
"split": "train",
"index": 32297,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\\(f(x)\\) is a linear function, and the equation \\(f(f(x)) = x + 1\\) has no solutions. Find all possible values of \\(f(f(f(f(f(2022)))))-f(f(f(2022)))-f(f(2022))\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2022"
} | {
"split": "train",
"index": 32298,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Maria needs to provide her waist size in centimeters for a custom dress order. She knows her waist measures 28 inches. If she has been advised to add an extra 1 inch for a comfortable fit and there are 12 inches in a foot, and 31 centimeters in a foot, how many centimeters shou... | math | {
"style": "rule",
"ground_truth": "74.9"
} | {
"split": "train",
"index": 32299,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle $U$ has a circumference of $18\\pi$ inches, and segment $AB$ is a diameter. If the measure of angle $UAV$ is $45^{\\circ}$, what is the length, in inches, of segment $AV$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9\\sqrt{2 - \\sqrt{2}}"
} | {
"split": "train",
"index": 32300,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Through the end of a chord that divides the circle in the ratio 3:5, a tangent is drawn. Find the acute angle between the chord and the tangent. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "67.5"
} | {
"split": "train",
"index": 32301,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $x - \\frac{1}{x} = 4$, what is $x^3 - \\frac{1}{x^3}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 32302,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of diagonals that can be drawn in a polygon of 100 sides is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4850"
} | {
"split": "train",
"index": 32303,
"solution": "To find the number of diagonals in a polygon, we use the formula:\n\\[\n\\frac{n(n-3)}{2}\n\\]\nwhere $n$ is the number of sides of the polygon. This formula arises because each vertex of the polygon can connect to $n-3$ other vertices to form a diagonal (it cannot... |
deepscaler | [
{
"role": "user",
"content": "Let the even function $f(x)$ satisfy $f(x+6) = f(x) + f(3)$ for any $x \\in \\mathbb{R}$, and when $x \\in (-3, -2)$, $f(x) = 5x$. Find the value of $f(201.2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-14"
} | {
"split": "train",
"index": 32304,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6300"
} | {
"split": "train",
"index": 32305,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all solutions to\n\\[\\sqrt{x + 3 - 4 \\sqrt{x - 1}} + \\sqrt{x + 8 - 6 \\sqrt{x - 1}} = 1.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[5,10]"
} | {
"split": "train",
"index": 32306,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\sqrt{5! \\cdot (5!)^2}$ expressed as a positive integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "240\\sqrt{30}"
} | {
"split": "train",
"index": 32307,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the positive integer \\( n \\), if the expansion of \\( (xy - 5x + 3y - 15)^n \\) is combined and simplified, and \\( x^i y^j \\) (where \\( i, j = 0, 1, \\ldots, n \\)) has at least 2021 terms, what is the minimum value of \\( n \\)? Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "44"
} | {
"split": "train",
"index": 32308,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Factor the expression $81x^4 - 256y^4$ and find the sum of all integers in its complete factorization $(ax^2 + bxy + cy^2)(dx^2 + exy + fy^2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 32309,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A store prices an item so that when 5% sales tax is added to the price in cents, the total cost rounds naturally to the nearest multiple of 5 dollars. What is the smallest possible integer dollar amount $n$ to which the total cost could round?\nA) $50$ \nB) $55$ \nC) $60$ \... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 32310,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all solutions to the equation $\\displaystyle\\sqrt[3]{2 - \\frac{x}{2}} = -3$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "58"
} | {
"split": "train",
"index": 32311,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The real numbers \\( x, y, z \\) satisfy \\( x + y + z = 2 \\) and \\( xy + yz + zx = 1 \\). Find the maximum possible value of \\( x - y \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{3}}{3}"
} | {
"split": "train",
"index": 32312,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For real numbers $a$ and $b$, define $a\\textdollar b = (a - b)^2$. What is $(x - y)^2\\textdollar(y - x)^2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 32313,
"solution": "Given the operation $a \\textdollar b = (a - b)^2$, we need to evaluate $(x - y)^2 \\textdollar (y - x)^2$.\n\n1. **Substitute into the operation definition**:\n \\[\n (x - y)^2 \\textdollar (y - x)^2 = \\left((x - y)^2 - (y - x)^2\\right)^2\n \\]\n\n2. **Sim... |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)=x^{3}-3x^{2}$, find the value of $f( \\frac {1}{2015})+f( \\frac {2}{2015})+f( \\frac {3}{2015})+…+f( \\frac {4028}{2015})+f( \\frac {4029}{2015})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-8058"
} | {
"split": "train",
"index": 32314,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given three coplanar vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, and $\\overrightarrow{c}$, where $\\overrightarrow{a}=(\\sqrt{2}, 2)$, $|\\overrightarrow{b}|=2\\sqrt{3}$, $|\\overrightarrow{c}|=2\\sqrt{6}$, and $\\overrightarrow{a}$ is parallel to $\\overrightarrow{c... | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 32315,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$ shown in the figure, $AB=7$, $BC=8$, $CA=9$, and $\\overline{AH}$ is an altitude. Points $D$ and $E$ lie on sides $\\overline{AC}$ and $\\overline{AB}$, respectively, so that $\\overline{BD}$ and $\\overline{CE}$ are angle bisectors, intersecting $\\overline... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}\\sqrt{5}"
} | {
"split": "train",
"index": 32316,
"solution": "1. **Calculate the semi-perimeter and area of $\\triangle ABC$ using Heron's Formula:**\n - Semi-perimeter, $s = \\frac{AB + BC + CA}{2} = \\frac{7 + 8 + 9}{2} = 12$.\n - Area, $K = \\sqrt{s(s-a)(s-b)(s-c)} = \\sqrt{12(12-7)(12-8)(12-9)} = \\sqrt{12 \\cdot 5 \\... |
deepscaler | [
{
"role": "user",
"content": "A square is inscribed in the ellipse\n\\[\\frac{x^2}{5} + \\frac{y^2}{10} = 1,\\]\nso that its sides are parallel to the coordinate axes. Find the area of the square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{40}{3}"
} | {
"split": "train",
"index": 32317,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n = 2^4 \\cdot 3^5 \\cdot 4^6\\cdot 6^7$. How many natural-number factors does $n$ have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "312"
} | {
"split": "train",
"index": 32318,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seryozha and Misha, while walking in the park, stumbled upon a meadow surrounded by linden trees. Seryozha walked around the meadow, counting the trees. Misha did the same, but started at a different tree (although he walked in the same direction). The tree that was the 20th fo... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 32319,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiao Ming collected 20 pieces of data in a survey, as follows: \n$95\\ \\ \\ 91\\ \\ \\ 93\\ \\ \\ 95\\ \\ \\ 97\\ \\ \\ 99\\ \\ \\ 95\\ \\ \\ 98\\ \\ \\ 90\\ \\ \\ 99$ \n$96\\ \\ \\ 94\\ \\ \\ 95\\ \\ \\ 97\\ \\ \\ 96\\ \\ \\ 92\\ \\ \\ 94\\ \\ \\ 95\\ \\ \\ 96\\ \\ \\ 98$ ... | math | {
"style": "rule",
"ground_truth": "0.4"
} | {
"split": "train",
"index": 32320,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C: \\frac{x^{2}}{4} + y^{2} = 1$, with $O$ being the origin of coordinates, and a line $l$ intersects the ellipse $C$ at points $A$ and $B$, and $\\angle AOB = 90^{\\circ}$.\n\n(Ⅰ) If the line $l$ is parallel to the x-axis, find the area of $\\triangle AOB$; ... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 32321,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A box contains chips, each of which is red, white, or blue. The number of blue chips is at least half the number of white chips, and at most one third the number of red chips. The number which are white or blue is at least $55$. The minimum number of red chips is Let's think st... | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 32322,
"solution": "Let the number of white chips be denoted as $w$, the number of blue chips as $b$, and the number of red chips as $r$. According to the problem, we have the following conditions:\n1. $b \\geq \\frac{1}{2} w$\n2. $b \\leq \\frac{1}{3} r$\n3. $w + b \\geq 55$\n\nWe ai... |
deepscaler | [
{
"role": "user",
"content": "Given in triangle $\\triangle ABC$ the internal angles are $A$, $B$, and $C$, and the centroid is $G$. If $2\\sin A \\cdot \\overrightarrow{GA} + \\sqrt{3}\\sin B \\cdot \\overrightarrow{GB} + 3\\sin C \\cdot \\overrightarrow{GC} = \\overrightarrow{0}$, then $\\cos B = \\_\\_\\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{12}"
} | {
"split": "train",
"index": 32323,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest common divisor of $121^2 + 233^2 + 345^2$ and $120^2 + 232^2 + 346^2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 32324,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the area of a cross-section of sphere O is $\\pi$, and the distance from the center O to this cross-section is 1, then the radius of this sphere is __________, and the volume of this sphere is __________. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "\\frac{8\\sqrt{2}}{3}\\pi"
} | {
"split": "train",
"index": 32325,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number from the set $\\{30, 31, 32, \\ldots, 500\\}$ is randomly selected. What is the probability that the number is greater than 100 but less than or equal to 200? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "\\frac{100}{471}"
} | {
"split": "train",
"index": 32326,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $991+993+995+997+999=5000-N$, then $N=$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 32327,
"solution": "1. **Identify the problem and express each term in a form that reveals a pattern:**\n \\[\n 991+993+995+997+999=5000-N\n \\]\n We can rewrite each term as $1000$ minus a small number:\n \\[\n (1000-9) + (1000-7) + (1000-5) + (1000-3) + (1000-1)\n \\]\... |
deepscaler | [
{
"role": "user",
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{50} = \\cos x.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 32328,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of subsets $S$ of $\\{1,2,3, \\ldots, 10\\}$ with the following property: there exist integers $a<b<c$ with $a \\in S, b \\notin S, c \\in S$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "968"
} | {
"split": "train",
"index": 32329,
"solution": "968. There are $2^{10}=1024$ subsets of $\\{1,2, \\ldots, 10\\}$ altogether. Any subset without the specified property must be either the empty set or a block of consecutive integers. To specify a block of consecutive integers, we either have just one element (10 c... |
deepscaler | [
{
"role": "user",
"content": "Three candles can burn for 30, 40, and 50 minutes, respectively (but are not ignited simultaneously). It is known that the three candles are burning simultaneously for 10 minutes, and only one candle is burning for 20 minutes. How long are exactly two candles burning simultaneo... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 32330,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vasya wrote down 11 natural numbers in one notebook. Petya wrote down the greatest common divisors of each pair of numbers recorded in Vasya's notebook in another notebook. It turned out that every number written in one of the two notebooks is also in the other notebook. What i... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 32331,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sequence $\\{a_n\\}$ have a sum of the first $n$ terms denoted by $S_n$. It is known that $4S_n = 2a_n - n^2 + 7n$ ($n \\in \\mathbb{N}^*$). Find $a_{11}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 32332,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a cubic function $f(x)=ax^{3}+bx^{2}+cx+d(a\\neq 0)$, define the \"nice point\" of the function as the point $(x_{0},f(x_{0}))$ where $x_{0}$ is a real root of the equation $f''(x)=0$. It has been observed that every cubic function has a \"nice point,\" a symmetry center,... | math | {
"style": "rule",
"ground_truth": "2010"
} | {
"split": "train",
"index": 32333,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\\le2$ and $|x|+|y|+|z-2|\\le2$? 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": 32334,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate or simplify: \n1. $\\log_2 \\sqrt{2}+\\log_9 27+3^{\\log_3 16}$; \n2. $0.25^{-2}+\\left( \\frac{8}{27} \\right)^{-\\frac{1}{3}}-\\frac{1}{2}\\lg 16-2\\lg 5+\\left( \\frac{1}{2} \\right)^{0}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{33}{2}"
} | {
"split": "train",
"index": 32335,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the smallest positive integer \\( m \\) for which \\( m^3 - 90 \\) is divisible by \\( m + 9 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 32336,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\frac{3}{5} + \\frac{2}{3} + 1\\frac{1}{15}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\frac{1}{3}"
} | {
"split": "train",
"index": 32337,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Real numbers $r$ and $s$ are roots of $p(x)=x^3+ax+b$, and $r+4$ and $s-3$ are roots of $q(x)=x^3+ax+b+240$. Enter all possible values of $b,$ separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-330,90"
} | {
"split": "train",
"index": 32338,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a device purchased at $40 less a 15% discount, and a goal of achieving a 25% selling profit based on the cost after allowing a 10% discount on the final sales price, determine the marked price of the device in dollars. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "47.22"
} | {
"split": "train",
"index": 32339,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $60^{\\circ}$, $|\\overrightarrow{a}|=1$, and $|\\overrightarrow{b}|=2$,\n(1) Find $(2\\overrightarrow{a}-\\overrightarrow{b})\\cdot\\overrightarrow{a}$;\n(2) Find $|2\\overrightarrow{a}+\\o... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 32340,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane, the number of integer points (points where both the x-coordinate and y-coordinate are integers) that satisfy the system of inequalities \n\\[\n\\begin{cases}\ny \\leq 3x, \\\\\ny \\geq \\frac{1}{3}x, \\\\\nx + y \\leq 100\n\\end{cases}\n\\]\ni... | math | {
"style": "rule",
"ground_truth": "2551"
} | {
"split": "train",
"index": 32341,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a nonnegative integer. Determine the number of ways that one can choose $(n+1)^2$ sets $S_{i,j}\\subseteq\\{1,2,\\ldots,2n\\}$ , for integers $i,j$ with $0\\leq i,j\\leq n$ , such that:\n$\\bullet$ for all $0\\leq i,j\\leq n$ , the set $S_{i,j}$ has $i+j$ elements; a... | math | {
"style": "rule",
"ground_truth": "(2n)! \\cdot 2^{n^2}"
} | {
"split": "train",
"index": 32342,
"solution": "Note that there are $(2n)!$ ways to choose $S_{1, 0}, S_{2, 0}... S_{n, 0}, S_{n, 1}, S_{n, 2}... S_{n, n}$ , because there are $2n$ ways to choose which number $S_{1, 0}$ is, $2n-1$ ways to choose which number to append to make $S_{2, 0}$ , $2n-2$ ways to choose w... |
deepscaler | [
{
"role": "user",
"content": "The graph of the equation $9x+223y=2007$ is drawn on graph paper with each square representing one unit in each direction. How many of the $1$ by $1$ graph paper squares have interiors lying entirely below the graph and entirely in the first quadrant?\n Let's think step by step... | math | {
"style": "rule",
"ground_truth": "888"
} | {
"split": "train",
"index": 32343,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let's call a number palindromic if it reads the same left to right as it does right to left. For example, the number 12321 is palindromic.\n\na) Write down any five-digit palindromic number that is divisible by 5.\n\nb) How many five-digit palindromic numbers are there that are... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 32344,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\Delta ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, and it is given that $a\\sin C=\\sqrt{3}c\\cos A$.\n\n1. Find the size of angle $A$.\n2. If $a=\\sqrt{13}$ and $c=3$, find the area of $\\Delta ABC$. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 32345,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the coordinate plane \\(xOy\\), given points \\(A(1,3)\\), \\(B\\left(8 \\frac{1}{3}, 1 \\frac{2}{3}\\right)\\), and \\(C\\left(7 \\frac{1}{3}, 4 \\frac{2}{3}\\right)\\), the extended lines \\(OA\\) and \\(BC\\) intersect at point \\(D\\). Points \\(M\\) and \\(N\\) are on s... | math | {
"style": "rule",
"ground_truth": "\\frac{5 \\sqrt{10}}{3}"
} | {
"split": "train",
"index": 32346,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f(x)$ satisfies\n\\[ f(xy) = 3xf(y) \\]\nfor all real numbers $x$ and $y$. If $f(1) = 10$, find $f(5)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 32347,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the number of zeros at the end of 2015!. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "502"
} | {
"split": "train",
"index": 32348,
"solution": ""
} |
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