data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$: $\\dfrac {x^{2}}{a^{2}}+ \\dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ with its left and right foci being $F_{1}$ and $F_{2}$ respectively, and its eccentricity is $\\dfrac {1}{2}$. Let $M$ be any point on the ellipse and the perimeter of $\\triangle MF_{1}F_{2}$ e... | math | {
"style": "rule",
"ground_truth": "\\dfrac { \\sqrt {15}}{3}"
} | {
"split": "train",
"index": 17849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sides of triangle $DEF$ are in the ratio $3:4:5$. Segment $EG$ is the angle bisector drawn to the shortest side, dividing it into segments $DG$ and $GE$. If the length of side $DE$ (the base) is 12 inches, what is the length, in inches, of the longer segment of side $EF$ on... | math | {
"style": "rule",
"ground_truth": "\\frac{80}{7}"
} | {
"split": "train",
"index": 17850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six positive integers are written on the faces of a cube. Each vertex is labeled with the product of the three numbers on the faces adjacent to the vertex. If the sum of the numbers on the vertices is equal to $1386$, then what is the sum of the numbers written on the faces? Le... | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 17851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An entrepreneur invested \\$12,000 in a three-month savings certificate that paid a simple annual interest rate of $8\\%$. After three months, she invested the total value of her investment in another three-month certificate. After three more months, the investment was worth \\... | math | {
"style": "rule",
"ground_truth": "24\\%"
} | {
"split": "train",
"index": 17852,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that six students are to be seated in three rows of two seats each, with one seat reserved for a student council member who is Abby, calculate the probability that Abby and Bridget are seated next to each other in any row. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 17853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The wholesale department operates a product with a wholesale price of 500 yuan per unit and a gross profit margin of 4%. The inventory capital is 80% borrowed from the bank at a monthly interest rate of 4.2‰, and the storage and operating cost is 0.30 yuan per unit per day. Det... | math | {
"style": "rule",
"ground_truth": "56"
} | {
"split": "train",
"index": 17854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Monica is renovating the floor of her 15-foot by 20-foot dining room. She plans to place two-foot by two-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. Additionally, there is a 1-foot b... | math | {
"style": "rule",
"ground_truth": "78"
} | {
"split": "train",
"index": 17855,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square $EFGH$ is inscribed in the region bound by the parabola $y = x^2 - 8x + 16$ and the $x$-axis. Find the area of square $EFGH$.\n\n[asy]\nunitsize(0.8 cm);\n\nreal parab2 (real x) {\n return(x^2 - 8*x + 16);\n}\n\npair E, F, G, H;\nreal x = -2 + 2*sqrt(3);\n\nE = (4 - x... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 17856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ $D$ lies on $\\overline{BC}$ extended past $C$ such that $BD:DC = 3:1,$ and $E$ lies on $\\overline{AC}$ such that $AE:EC = 5:3.$ Let $P$ be the intersection of lines $BE$ and $AD.$\n\n[asy]\nunitsize(0.8 cm);\n\npair A, B, C, D, E, F, P;\n\nA = (1,4);\nB = ... | math | {
"style": "rule",
"ground_truth": "\\left( \\frac{9}{19}, -\\frac{5}{19}, \\frac{15}{19} \\right)"
} | {
"split": "train",
"index": 17857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cart rolls down a hill, travelling $5$ inches the first second and accelerating so that during each successive $1$-second time interval, it travels $7$ inches more than during the previous $1$-second interval. The cart takes $30$ seconds to reach the bottom of the hill. How f... | math | {
"style": "rule",
"ground_truth": "3195"
} | {
"split": "train",
"index": 17858,
"solution": "1. **Identify the sequence type**: The problem describes a sequence where the distance traveled each second increases by a constant amount. This is an arithmetic sequence.\n\n2. **Determine the first term and common difference**: \n - The first term $a_1 = 5$ inc... |
deepscaler | [
{
"role": "user",
"content": "Positive integers $a$, $b$, $c$, and $d$ satisfy $a > b > c > d$, $a + b + c + d = 2010$, and $a^2 - b^2 + c^2 - d^2 = 2010$. Find the number of possible values of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "501"
} | {
"split": "train",
"index": 17859,
"solution": "Since $a+b$ must be greater than $1005$, it follows that the only possible value for $a-b$ is $1$ (otherwise the quantity $a^2 - b^2$ would be greater than $2010$). Therefore the only possible ordered pairs for $(a,b)$ are $(504, 503)$, $(505, 504)$, ... , $(1004, ... |
deepscaler | [
{
"role": "user",
"content": "Point \\((x,y)\\) is randomly picked from the rectangular region with vertices at \\((0,0), (3000,0), (3000,3001),\\) and \\((0,3001)\\). What is the probability that \\(x > 3y\\)? Express your answer as a common fraction. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "\\frac{1500}{9003}"
} | {
"split": "train",
"index": 17860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Crystal Products Factory in the East Sea had an annual output of 100,000 pieces last year, with each crystal product selling for 100 yuan and a fixed cost of 80 yuan. Starting this year, the factory invested 1 million yuan in technology costs and plans to invest an addition... | math | {
"style": "rule",
"ground_truth": "520"
} | {
"split": "train",
"index": 17861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $x$ is an integer that satisfies the following congruences: \\begin{align*}\n3+x &\\equiv 2^2 \\pmod{3^3} \\\\\n5+x &\\equiv 3^2 \\pmod{5^3} \\\\\n7+x &\\equiv 5^2 \\pmod{7^3}\n\\end{align*}What is the remainder when $x$ is divided by $105$? Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the hyperbola C passes through the point (4, 3) and shares the same asymptotes with $$\\frac {x^{2}}{4}$$ - $$\\frac {y^{2}}{9}$$ = 1, determine the equation of C and its eccentricity. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {\\sqrt {13}} {2}"
} | {
"split": "train",
"index": 17863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( XYZ \\) be a triangle with \\( \\angle X = 60^\\circ \\) and \\( \\angle Y = 45^\\circ \\). A circle with center \\( P \\) passes through points \\( A \\) and \\( B \\) on side \\( XY \\), \\( C \\) and \\( D \\) on side \\( YZ \\), and \\( E \\) and \\( F \\) on side \... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 17864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 6x6x6 cube is formed by assembling 216 unit cubes. Ten unit squares are painted on each of the six faces of the cube, leaving some rows and columns unpainted. Specifically, two non-adjacent columns and two non-adjacent rows on each face are left unpainted. How many of the 216... | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 17865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $g(x)=1-x^2$ and $f(g(x))=\\frac{1-x^2}{x^2}$ when $x\\not=0$, then $f(1/2)$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 17866,
"solution": "1. **Identify the function composition**: We are given $g(x) = 1 - x^2$ and $f(g(x)) = \\frac{1-x^2}{x^2}$ for $x \\neq 0$. We need to find $f\\left(\\frac{1}{2}\\right)$.\n\n2. **Find $y$ such that $g(y) = \\frac{1}{2}$**: We set up the equation based on the defin... |
deepscaler | [
{
"role": "user",
"content": "Given that the perimeter of triangle \\( \\triangle ABC \\) is 20, the radius of the inscribed circle is \\( \\sqrt{3} \\), and \\( BC = 7 \\). Find the value of \\( \\tan A \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 17867,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The minimum positive period of the function $f(x)=2\\sin\\left(\\frac{x}{3}+\\frac{\\pi}{5}\\right)-1$ is ______, and the minimum value is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 17868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of integers $a$ with $1\\le a\\le 2012$ for which there exist nonnegative integers $x,y,z$ satisfying the equation\n\\[x^2(x^2+2z) - y^2(y^2+2z)=a.\\]\n\n*Ray Li.*\n\n<details><summary>Clarifications</summary>[list=1][*] $x,y,z$ are not necessarily distin... | math | {
"style": "rule",
"ground_truth": "1257"
} | {
"split": "train",
"index": 17869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the squares of four consecutive positive integers is 9340. What is the sum of the cubes of these four integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "457064"
} | {
"split": "train",
"index": 17870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A coin is altered so that the probability that it lands on heads is less than $\\frac{1}{2}$ and when the coin is flipped four times, the probability of an equal number of heads and tails is $\\frac{1}{6}$. What is the probability that the coin lands on heads? Let's think step ... | math | {
"style": "rule",
"ground_truth": "\\frac{3-\\sqrt{3}}{6}"
} | {
"split": "train",
"index": 17871,
"solution": "1. **Define the probability of heads**: Let $x$ be the probability that the coin lands on heads. Consequently, the probability that the coin lands on tails is $1 - x$.\n\n2. **Set up the probability equation for 2 heads and 2 tails in 4 flips**: The number of ways ... |
deepscaler | [
{
"role": "user",
"content": "It is known that 9 cups of tea cost less than 10 rubles, and 10 cups of tea cost more than 11 rubles. How much does one cup of tea cost? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "111"
} | {
"split": "train",
"index": 17872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\tan \\alpha = -2$, find the value of the following expressions:\n\n$(1) \\frac{\\sin \\alpha - 3 \\cos \\alpha}{\\sin \\alpha + \\cos \\alpha}$\n\n$(2) \\frac{1}{\\sin \\alpha \\cdot \\cos \\alpha}$ Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{2}"
} | {
"split": "train",
"index": 17873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A box contains $6$ balls, of which $3$ are yellow, $2$ are blue, and $1$ is red. Three balls are drawn from the box.\n\n$(1)$ If the $3$ yellow balls are numbered as $A$, $B$, $C$, the $2$ blue balls are numbered as $d$, $e$, and the $1$ red ball is numbered as $x$, use $(a,b,c... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 17874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "50 people, consisting of 30 people who all know each other, and 20 people who know no one, are present at a conference. Determine the number of handshakes that occur among the individuals who don't know each other. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "1170"
} | {
"split": "train",
"index": 17875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The water tank in the diagram below is in the shape of an inverted right circular cone. The radius of its base is 8 feet, and its height is 64 feet. The water in the tank is $40\\%$ of the tank's capacity. The height of the water in the tank can be written in the form $a\\sqrt[... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 17876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a $7 \\times 7$ grid of squares. Let $f:\\{1,2,3,4,5,6,7\\} \\rightarrow\\{1,2,3,4,5,6,7\\}$ be a function; in other words, $f(1), f(2), \\ldots, f(7)$ are each (not necessarily distinct) integers from 1 to 7 . In the top row of the grid, the numbers from 1 to 7 are wr... | math | {
"style": "rule",
"ground_truth": "1470"
} | {
"split": "train",
"index": 17877,
"solution": "Consider the directed graph with $1,2,3,4,5,6,7$ as vertices, and there is an edge from $i$ to $j$ if and only if $f(i)=j$. Since the bottom row is equivalent to the top one, we have $f^{6}(x)=x$. Therefore, the graph must decompose into cycles of length $6,3,2$, o... |
deepscaler | [
{
"role": "user",
"content": "If $f(x) = \\frac{1 + x}{1 - 3x}, f_1(x) = f(f(x)), f_2(x) = f(f_1(x)),$ and in general $f_n(x) = f(f_{n-1}(x)),$ then $f_{1993}(3)=$\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 17878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many perfect squares are between 100 and 500? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 17879,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arnaldo claimed that one billion is the same as one million millions. Professor Piraldo corrected him and said, correctly, that one billion is the same as one thousand millions. What is the difference between the correct value of one billion and Arnaldo's assertion? Let's think... | math | {
"style": "rule",
"ground_truth": "999000000000"
} | {
"split": "train",
"index": 17880,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An inverted cone with base radius $12 \\mathrm{cm}$ and height $18 \\mathrm{cm}$ is full of water. The water is poured into a tall cylinder whose horizontal base has radius of $24 \\mathrm{cm}$. What is the height in centimeters of the water in the cylinder? Let's think step by... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"split": "train",
"index": 17881,
"solution": "1. **Calculate the volume of the water in the cone**: \n The formula for the volume $V$ of a cone is given by:\n \\[\n V = \\frac{1}{3} \\pi r^2 h\n \\]\n where $r$ is the radius of the base and $h$ is the height of the cone. For the given cone, $r = 12 ... |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer with exactly 12 positive integer divisors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 17882,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x)= \\frac{2x}{x+1}$, calculate the value of the expression $f\\left( \\frac{1}{2016}\\right)+f\\left( \\frac{1}{2015}\\right)+f\\left( \\frac{1}{2014}\\right)+\\ldots+f\\left( \\frac{1}{2}\\right)+f(1)+f(2)+\\ldots+f(2014)+f(2015)+f(2016)$. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "4031"
} | {
"split": "train",
"index": 17883,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the line $l_{1}:ax+2y+6=0$ is parallel to the line $l_{2}:x+\\left(a-1\\right)y+\\left(a^{2}-1\\right)=0$, determine the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kelvin the Frog has a pair of standard fair 8-sided dice (each labelled from 1 to 8). Alex the sketchy Kat also has a pair of fair 8-sided dice, but whose faces are labelled differently (the integers on each Alex's dice need not be distinct). To Alex's dismay, when both Kelvin ... | math | {
"style": "rule",
"ground_truth": "24, 28, 32"
} | {
"split": "train",
"index": 17885,
"solution": "Define the generating function of an event $A$ as the polynomial $$g(A, x)=\\sum p_{i} x^{i}$$ where $p_{i}$ denotes the probability that $i$ occurs during event $A$. We note that the generating is multiplicative; i.e. $$g(A \\text { AND } B, x)=g(A) g(B)=\\sum p_{... |
deepscaler | [
{
"role": "user",
"content": "A unit has a total of 620 staff members. To investigate the time workers spend commuting, it was decided to survey 62 workers using a systematic sampling method. The entire staff was divided into 62 segments with equal intervals, and a simple random sampling method was used to ... | math | {
"style": "rule",
"ground_truth": "394"
} | {
"split": "train",
"index": 17886,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What digit $A$ will make the number $83A5$ divisible by $9$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all prime numbers whose representation in base 14 has the form $101010...101$ (alternating ones and zeros). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "197"
} | {
"split": "train",
"index": 17888,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)=\\sin x+a\\cos x$ has a symmetry axis on $x=\\frac{5π}{3}$, determine the maximum value of the function $g(x)=a\\sin x+\\cos x$. 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": 17889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many children did my mother have?\n\nIf you asked me this question, I would only tell you that my mother dreamed of having at least 19 children, but she couldn't make this dream come true; however, I had three times more sisters than cousins, and twice as many brothers as s... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 17890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve $\\arcsin x + \\arcsin (1 - x) = \\arccos x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0, \\frac{1}{2}"
} | {
"split": "train",
"index": 17891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least positive integer $k$ such that, in every convex 1001-gon, the sum of any k diagonals is greater than or equal to the sum of the remaining diagonals? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "249750"
} | {
"split": "train",
"index": 17892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a rectangular array of single digits \\(d_{i,j}\\) with 10 rows and 7 columns, such that \\(d_{i+1, j} - d_{i, j}\\) is always 1 or -9 for all \\(1 \\leq i \\leq 9\\) and all \\(1 \\leq j \\leq 7\\). For \\(1 \\leq i \\leq 10\\), let \\(m_{i}\\) be the median of \\(d_{... | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"split": "train",
"index": 17893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The four complex roots of\n\\[2z^4 + 8iz^3 + (-9 + 9i)z^2 + (-18 - 2i)z + (3 - 12i) = 0,\\]when plotted in the complex plane, form a rhombus. Find the area of the rhombus. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}"
} | {
"split": "train",
"index": 17894,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the greatest whole number that will satisfy this inequality: $4x-3 < 2 - x $. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 17895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When 5 integers are arranged in ascending order, the median is 6. If the only mode of this data set is 8, determine the possible maximum sum of these 5 integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 17896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the geometric sequence $5$, $\\dfrac{15}{4}$, $\\dfrac{45}{16}$, $\\dfrac{135}{64}$, $\\ldots$. Find the tenth term of the sequence. Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{98415}{262144}"
} | {
"split": "train",
"index": 17897,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sqrt{3}\\sin x\\cos x-{\\cos }^2x$. \n$(1)$ Find the smallest positive period of $f(x)$; \n\n$(2)$ If $f(x)=-1$, find the value of $\\cos \\left(\\dfrac{2\\pi }{3}-2x\\right)$. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{1}{2}"
} | {
"split": "train",
"index": 17898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest two-digit whole number, the product of whose digits is 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 17899,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f_{1}(x)=\\sqrt{1-x}$, and for integers $n \\geq 2$, let \\[f_{n}(x)=f_{n-1}\\left(\\sqrt{n^2 - x}\\right).\\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N,$ the domain of $f_N$ consists of a single point $\\{c\\}.$ Com... | math | {
"style": "rule",
"ground_truth": "-231"
} | {
"split": "train",
"index": 17900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the sequence \\(\\{a_n\\}\\) where \\(a_n = n^3 + 4\\) for \\(n \\in \\mathbf{N}_+\\). Let \\(d_n = \\gcd(a_n, a_{n+1})\\), which is the greatest common divisor of \\(a_n\\) and \\(a_{n+1}\\). Find the maximum value of \\(d_n\\). Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "433"
} | {
"split": "train",
"index": 17901,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A builder has two identical bricks. She places them side by side in three different ways, resulting in shapes with surface areas of 72, 96, and 102. What is the surface area of one original brick? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 17902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ$, where $\\angle X = 90^\\circ$, $YZ = 20$, and $\\tan Z = 3\\cos Y$. What is the length of $XY$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{40\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 17903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two cubic dice are thrown in succession, where \\\\(x\\\\) represents the number shown by the first die, and \\\\(y\\\\) represents the number shown by the second die. \n\\\\((1)\\\\) Find the probability that point \\\\(P(x,y)\\\\) lies on the line \\\\(y=x-1\\\\); \n\\\\((2... | math | {
"style": "rule",
"ground_truth": "\\dfrac{17}{36}"
} | {
"split": "train",
"index": 17904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the roots of $z^2 - z = 5 - 5i.$\n\nEnter the roots, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3 - i, -2 + i"
} | {
"split": "train",
"index": 17905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$ denote the set of all integers $n$ such that $1 \\leq n \\leq 10000$, and moreover the sum of the decimal digits of $n$ is 2. Find the sum of the squares of the elements of $A$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7294927"
} | {
"split": "train",
"index": 17906,
"solution": "From the given conditions, we want to calculate $$\\sum_{i=0}^{3} \\sum_{j=i}^{3}\\left(10^{i}+10^{j}\\right)^{2}$$ By observing the formula, we notice that each term is an exponent of $10.10^{6}$ shows up 7 times, $10^{5}$ shows up 2 times, $10^{4}$ shows up 9 tim... |
deepscaler | [
{
"role": "user",
"content": "In parallelogram $EFGH$, point $Q$ is on $\\overline{EF}$ such that $\\frac {EQ}{EF} = \\frac {23}{1005}$, and point $R$ is on $\\overline{EH}$ such that $\\frac {ER}{EH} = \\frac {23}{2011}$. Let $S$ be the point of intersection of $\\overline{EG}$ and $\\overline{QR}$. Find $... | math | {
"style": "rule",
"ground_truth": "131"
} | {
"split": "train",
"index": 17907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vasya and Petya are participating in a school sports-entertainment game. They only have one pair of roller skates between the two of them, and need to traverse a distance of 3 km as quickly as possible. They start simultaneously, with one running and the other roller-skating. A... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"split": "train",
"index": 17908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given positive real numbers \\(a, b, c\\) satisfy \\(2(a+b)=ab\\) and \\(a+b+c=abc\\), find the maximum value of \\(c\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"split": "train",
"index": 17909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $-4\\leq x\\leq-2$ and $2\\leq y\\leq4$, what is the largest possible value of $\\frac{x+y}{x}$? 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": 17910,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $n$: $2^n\\cdot 4^n=64^{n-36}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 17911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $y= \\frac{x^2+2x+8}{x-4}$, at what value of $x$ will there be a vertical asymptote? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of parallelogram $ABCD$ is $51\\sqrt{55}$ and $\\angle{DAC}$ is a right angle. If the side lengths of the parallelogram are integers, what is the perimeter of the parallelogram? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 17913,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four fair eight-sided dice (with faces showing 1 to 8) are rolled. What is the probability that the sum of the numbers on the top faces equals 32? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4096}"
} | {
"split": "train",
"index": 17914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the regression line equation obtained from a certain sample data is $y=1.5x+45$, where $x\\in\\{1,7,10,13,19\\}$, find the value of $\\overline{y}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 17915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the family of curves\n$$\n2(2 \\sin \\theta - \\cos \\theta + 3) x^{2} - (8 \\sin \\theta + \\cos \\theta + 1) y = 0,\n$$\nwhere $\\theta$ is a parameter. Find the maximum length of the chord that these curves cut on the line $y = 2 x$. Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "8\\sqrt{5}"
} | {
"split": "train",
"index": 17916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions $y=p(x)$ and $y=q(x)$, each with leading coefficient 1? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 17917,
"solution": "1. **Identify the Problem**: We need to find the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions $y=p(x)$ and $y=q(x)$, where both have leading coefficients of 1.\n\n2. **Set Up the Equation for Intersectio... |
deepscaler | [
{
"role": "user",
"content": "For how many positive integers $n$ less than or equal to 500 is $$(\\sin (t+\\frac{\\pi}{4})+i\\cos (t+\\frac{\\pi}{4}))^n=\\sin (nt+\\frac{n\\pi}{4})+i\\cos (nt+\\frac{n\\pi}{4})$$ true for all real $t$? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 17918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence \\(\\left\\{a_{n}\\right\\}\\), which satisfies\n\\[ \na_{1}=0,\\left|a_{n+1}\\right|=\\left|a_{n}-2\\right| \n\\]\n\nLet \\(S\\) be the sum of the first 2016 terms of the sequence \\(\\left\\{a_{n}\\right\\}\\). Determine the maximum value of \\(S\\). Let's ... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 17919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can $100$ be written as the sum of three positive integers $x, y$ , and $z$ satisfying $x < y < z$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "784"
} | {
"split": "train",
"index": 17920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If one vertex and the two foci of an ellipse form an equilateral triangle, determine the eccentricity of this ellipse. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{2}"
} | {
"split": "train",
"index": 17921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0} \\ln \\left(\\left(e^{x^{2}}-\\cos x\\right) \\cos \\left(\\frac{1}{x}\\right)+\\operatorname{tg}\\left(x+\\frac{\\pi}{3}\\right)\\right)\n$$ Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} \\ln (3)"
} | {
"split": "train",
"index": 17922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$\\triangle ABC\\sim\\triangle DBE$, $BC=20\\text{ cm}.$ How many centimeters long is $DE$? Express your answer as a decimal to the nearest tenth. [asy]\ndraw((0,0)--(20,0)--(20,12)--cycle);\ndraw((13,0)--(13,7.8));\nlabel(\"$B$\",(0,0),SW);\nlabel(\"$E$\",(13,0),S);\nlabel(\"$... | math | {
"style": "rule",
"ground_truth": "7.8"
} | {
"split": "train",
"index": 17923,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select two distinct numbers a, b from the set {0,1,2,3,4,5,6} to form a complex number a+bi, and determine the total number of such complex numbers with imaginary parts. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 17924,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two quadratic equations with unequal leading coefficients,\n$$\n(a-1) x^{2} - \\left(a^{2}+2\\right) x + \\left(a^{2}+2a\\right) = 0\n$$\nand\n$$\n(b-1) x^{2} - \\left(b^{2}+2\\right) x + \\left(b^{2}+2b\\right) = 0\n$$\n(where \\(a\\) and \\(b\\) are positive integers), have a... | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 17925,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $AB=5$, $BC=7$, $AC=9$, and $D$ is on $\\overline{AC}$ with $BD=5$. Find the ratio of $AD:DC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19/8"
} | {
"split": "train",
"index": 17926,
"solution": "1. **Apply the Law of Cosines in $\\triangle ABC$**:\n \\[\n c^2 = a^2 + b^2 - 2ab \\cos C\n \\]\n Here, $c = BC = 7$, $a = AB = 5$, and $b = AC = 9$. Plugging in these values, we get:\n \\[\n 7^2 = 5^2 + 9^2 - 2 \\cdot 5 \\cdot 9 \\cdot \\cos A\n \\]... |
deepscaler | [
{
"role": "user",
"content": "Let $P = (\\sqrt{2007}+\\sqrt{2008}),$ $Q = (-\\sqrt{2007}-\\sqrt{2008}),$ $R = (\\sqrt{2007}-\\sqrt{2008}),$ and $S = (-\\sqrt{2008}+\\sqrt{2007}).$ Calculate $PQRS.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are denoted as $a$, $b$, $c$ respectively, and it is given that $b^{2}=ac$ and $a^{2}+bc=c^{2}+ac$. Calculate the value of $\\dfrac {c}{b\\sin B}$. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "\\dfrac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 17928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when the product $1734\\times 5389 \\times 80,\\!607$ is divided by 10? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17929,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(b_1, b_2, ... b_{12})$ be a list of the 12 integers from 4 to 15 inclusive such that for each $2 \\le i \\le 12$, either $b_i + 1$ or $b_i - 1$ or both appear somewhere before $b_i$ in the list. How many such lists are there? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "2048"
} | {
"split": "train",
"index": 17930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: \\(\\frac{2 \\times 4.6 \\times 9 + 4 \\times 9.2 \\times 18}{1 \\times 2.3 \\times 4.5 + 3 \\times 6.9 \\times 13.5} =\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{18}{7}"
} | {
"split": "train",
"index": 17931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tetrahedron $A B C D$ has side lengths $A B=6, B D=6 \\sqrt{2}, B C=10, A C=8, C D=10$, and $A D=6$. The distance from vertex $A$ to face $B C D$ can be written as $\\frac{a \\sqrt{b}}{c}$, where $a, b, c$ are positive integers, $b$ is square-free, and $\\operatorname{gcd}(a, c... | math | {
"style": "rule",
"ground_truth": "2851"
} | {
"split": "train",
"index": 17932,
"solution": "First, we see that faces $A B D, A B C$, and $A C D$ are all right triangles. Now, $A B D$ can be visualized as the base, and it can be seen that side $A C$ is then the height of the tetrahedron, as $A C$ should be perpendicular to both $A B$ and $A D$. Therefore, ... |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 17933,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the following four conclusions: \n\\\\((1)\\\\) The center of symmetry of the function \\\\(f(x)= \\dfrac {x-1}{2x+1}\\\\) is \\\\((- \\dfrac {1}{2},- \\dfrac {1}{2})\\\\); \n\\\\((2)\\\\) If the equation in \\\\(x\\\\), \\\\(x- \\dfrac {1}{x}+k=0\\\\), has no real root... | math | {
"style": "rule",
"ground_truth": "(3)(4)"
} | {
"split": "train",
"index": 17934,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $A B C$ has $A B=4, B C=5$, and $C A=6$. Points $A^{\\prime}, B^{\\prime}, C^{\\prime}$ are such that $B^{\\prime} C^{\\prime}$ is tangent to the circumcircle of $\\triangle A B C$ at $A, C^{\\prime} A^{\\prime}$ is tangent to the circumcircle at $B$, and $A^{\\prime} ... | math | {
"style": "rule",
"ground_truth": "\\frac{80}{3}"
} | {
"split": "train",
"index": 17935,
"solution": "Note that by equal tangents, $B^{\\prime} A=B^{\\prime} C, C^{\\prime} A=C^{\\prime} B$, and $A^{\\prime} B=A^{\\prime} C$. Moreover, since the line segments $A^{\\prime} B^{\\prime}, B^{\\prime} C^{\\prime}$, and $C^{\\prime} A^{\\prime}$ are tangent to the circum... |
deepscaler | [
{
"role": "user",
"content": "The ratio of the sum of the first $n$ terms of two arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$ is $\\frac{S_n}{T_n} = \\frac{7n+1}{4n+2}$. Calculate the value of $\\frac{a_{11}}{b_{11}}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{74}{43}"
} | {
"split": "train",
"index": 17936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $\\{a_n\\}$ satisfies $a_{n+1}+(-1)^n a_n = 2n-1$. Find the sum of the first $80$ terms of $\\{a_n\\}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3240"
} | {
"split": "train",
"index": 17937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the polar equation of curve $C_1$ is $\\rho^2=\\frac {2}{3+\\cos2\\theta}$, establish a rectangular coordinate system with the pole O as the origin and the polar axis as the positive direction of the x-axis. After stretching all the x-coordinates of points on curve $C_1$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{13\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 17938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{14}"
} | {
"split": "train",
"index": 17939,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$\\dfrac{10-9+8-7+6-5+4-3+2-1}{1-2+3-4+5-6+7-8+9}=$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 17940,
"solution": "1. **Simplify the Numerator**: \n The numerator of the given fraction is $10-9+8-7+6-5+4-3+2-1$. We can group the terms in pairs:\n \\[\n (10-9) + (8-7) + (6-5) + (4-3) + (2-1)\n \\]\n Each pair simplifies to $1$, so:\n \\[\n 1 + 1 + 1 + 1 + 1 = 5\n ... |
deepscaler | [
{
"role": "user",
"content": "If point $P$ is the golden section point of segment $AB$, and $AP < BP$, $BP=10$, then $AP=\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5\\sqrt{5} - 5"
} | {
"split": "train",
"index": 17941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are three pairs of real numbers $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ that satisfy both $x^3 - 3xy^2 = 2017$ and $y^3 - 3x^2y = 2016$. Compute $\\left(2 - \\frac{x_1}{y_1}\\right)\\left(2 - \\frac{x_2}{y_2}\\right)\\left(2 - \\frac{x_3}{y_3}\\right)$. Let's think step... | math | {
"style": "rule",
"ground_truth": "\\frac{26219}{2016}"
} | {
"split": "train",
"index": 17942,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the greatest positive integer $N$ with the following property: there exist integers $x_1, . . . , x_N$ such that $x^2_i - x_ix_j$ is not divisible by $1111$ for any $i\\ne j.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"split": "train",
"index": 17943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\cos \\theta = \\frac{12}{13}, \\theta \\in \\left( \\pi, 2\\pi \\right)$, find the values of $\\sin \\left( \\theta - \\frac{\\pi}{6} \\right)$ and $\\tan \\left( \\theta + \\frac{\\pi}{4} \\right)$. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{17}"
} | {
"split": "train",
"index": 17944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "It takes person A 1 minute and 20 seconds to complete a lap, and person B meets person A every 30 seconds. Determine the time it takes for person B to complete a lap. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 17945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At the end of 1994, Walter was half as old as his grandmother. The sum of the years in which they were born was 3838. How old will Walter be at the end of 1999? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 17946,
"solution": "1. **Assign variables to ages**: Let Walter's age in 1994 be $x$. Then, his grandmother's age in 1994 is $2x$ because Walter is half as old as his grandmother.\n\n2. **Set up the equation for their birth years**: Walter was born in $1994 - x$ and his grandmother wa... |
deepscaler | [
{
"role": "user",
"content": "A spinner is divided into six congruent sectors, numbered from 1 to 6. Jane and her brother each spin the spinner once. If the non-negative difference of their numbers is less than 4, Jane wins. Otherwise, her brother wins. What is the probability that Jane wins? Let's think st... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 17947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $b_1, b_2, b_3, \\dots$ satisfies $b_1 = 25$, $b_9 = 125$, and for $n \\ge 3$, $b_n$ is the geometric mean of the first $n - 1$ terms. Find $b_2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "625"
} | {
"split": "train",
"index": 17948,
"solution": ""
} |
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