data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Alison is eating 2401 grains of rice for lunch. She eats the rice in a very peculiar manner: every step, if she has only one grain of rice remaining, she eats it. Otherwise, she finds the smallest positive integer $d>1$ for which she can group the rice into equal groups of size... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 4800,
"solution": "Note that $2401=7^{4}$. Also, note that the operation is equivalent to replacing $n$ grains of rice with $n \\cdot \\frac{p-1}{p}$ grains of rice, where $p$ is the smallest prime factor of $n$. Now, suppose that at some moment Alison has $7^{k}$ grains of rice. Afte... |
deepscaler | [
{
"role": "user",
"content": "June and Julia live 1 mile apart. It takes June 4 minutes to ride her bike directly to Julia's house. At the same rate, how many minutes would it take June to ride the 3.5 miles from her own house to Bernard's house? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 4801,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16, and 17, in some order. What was his sixth answer? Let's think st... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 4802,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the equations of the two asymptotes of a hyperbola are $y = \\pm \\sqrt{2}x$ and it passes through the point $(3, -2\\sqrt{3})$.\n(1) Find the equation of the hyperbola;\n(2) Let $F$ be the right focus of the hyperbola. A line with a slope angle of $60^{\\circ}$ inte... | math | {
"style": "rule",
"ground_truth": "16 \\sqrt{3}"
} | {
"split": "train",
"index": 4803,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of integers \\( n \\) that satisfy\n\\[ 20 < n^2 < 200. \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 4804,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a meeting of $ 12k$ people, each person exchanges greetings with exactly $ 3k\\plus{}6$ others. For any two people, the number who exchange greetings with both is the same. How many people are at the meeting? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 4805,
"solution": "\nLet the total number of people at the meeting be \\( n = 12k \\). Each person exchanges greetings with exactly \\( 3k + 6 \\) others. We need to determine the value of \\( n \\).\n\nGiven that for any two people, the number of people who exchange greetings with bo... |
deepscaler | [
{
"role": "user",
"content": "For all values of $x$ for which it is defined, $f(x) = \\cot \\frac{x}{4} - \\cot x$ can be written as\n\\[f(x) = \\frac{\\sin kx}{\\sin \\frac{x}{4} \\sin x}.\\]Find the value of $k.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 4806,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the lateral side \\( CD \\) of trapezoid \\( ABCD \\) (\\( AD \\parallel BC \\)), a point \\( M \\) is marked. From vertex \\( A \\), a perpendicular \\( AH \\) is drawn to segment \\( BM \\). It turns out that \\( AD = HD \\). Find the length of segment \\( AD \\), given th... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 4807,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $n$ such that\n\\[(1 + \\tan 1^\\circ)(1 + \\tan 2^\\circ)(1 + \\tan 3^\\circ) \\dotsm (1 + \\tan 30^\\circ) = 2^n.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 4808,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest square of an integer that ends with the longest sequence of the same digits?\n\nFor example, if the longest sequence of the same digits were five, then a suitable number would be 24677777 (of course, if it were the smallest square, but it is not). Zero is n... | math | {
"style": "rule",
"ground_truth": "1444"
} | {
"split": "train",
"index": 4809,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a tournament each player played exactly one game against each of the other players. In each game the winner was awarded $1$ point, the loser got $0$ points, and each of the two players earned $\\frac{1}{2}$ point if the game was a tie. After the completion of the tournament,... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 4810,
"solution": "Suppose that there are $n$ players participating in the tournament. We break this up into a group of the weakest ten, and the other $n-10$ people. Note that the $10$ players who played each other generated a total of $\\dbinom{10}{2} = 45$ points playing each other.... |
deepscaler | [
{
"role": "user",
"content": "For how many values of $k$ is $12^{12}$ the least common multiple of the positive integers $6^6$, $8^8$, and $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 4811,
"solution": "It is evident that $k$ has only 2s and 3s in its prime factorization, or $k = 2^a3^b$.\n$6^6 = 2^6\\cdot3^6$\n$8^8 = 2^{24}$\n$12^{12} = 2^{24}\\cdot3^{12}$\n The LCM of any numbers an be found by writing out their factorizations and taking the greatest power for ea... |
deepscaler | [
{
"role": "user",
"content": "Let $a$ be a positive number. Consider the set $S$ of all points whose rectangular coordinates $(x, y)$ satisfy all of the following conditions:\n\\begin{enumerate}\n \\item $\\frac{a}{2} \\le x \\le 2a$\n \\item $\\frac{a}{2} \\le y \\le 2a$\n \\item $x+y \\ge a$\n ... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 4812,
"solution": "To solve this problem, we need to analyze the geometric implications of each condition and determine the shape and boundaries of the set $S$.\n\n1. **Understanding the Conditions**:\n - $\\text{(i) }\\frac{a}{2}\\le x\\le 2a$: This restricts $x$ to the interval fr... |
deepscaler | [
{
"role": "user",
"content": "The ratio of a geometric sequence is an integer. We know that there is a term in the sequence which is equal to the sum of some other terms of the sequence. What can the ratio of the sequence be? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 4813,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider triangle \\(ABC\\) where \\(BC = 7\\), \\(CA = 8\\), and \\(AB = 9\\). \\(D\\) and \\(E\\) are the midpoints of \\(BC\\) and \\(CA\\), respectively, and \\(AD\\) and \\(BE\\) meet at \\(G\\). The reflection of \\(G\\) across \\(D\\) is \\(G'\\), and \\(G'E\\) meets \\(... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{145}}{9}"
} | {
"split": "train",
"index": 4814,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=4\\cos(3x+\\phi)(|\\phi|<\\frac{\\pi}{2})$, its graph is symmetrical about the line $x=\\frac{11\\pi}{12}$. When $x_1,x_2\\in(-\\frac{7\\pi}{12},-\\frac{\\pi}{12})$, $x_1\\neq x_2$, and $f(x_1)=f(x_2)$, find $f(x_1+x_2)$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 4815,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\sin(2x + \\frac{\\pi}{3}) - \\sqrt{3}\\sin(2x - \\frac{\\pi}{6})$,\n\n(1) Find the smallest positive period of the function $f(x)$ and its intervals of monotonic increase;\n\n(2) When $x \\in \\left[-\\frac{\\pi}{6}, \\frac{\\pi}{3}\\right]$, find t... | math | {
"style": "rule",
"ground_truth": "-\\sqrt{3}"
} | {
"split": "train",
"index": 4816,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "511"
} | {
"split": "train",
"index": 4817,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distances between the points are given as $A B = 30$, $B C = 80$, $C D = 236$, $D E = 86$, $E A = 40$. What is the distance $E C$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 4818,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence of even counting numbers starting from $2$, find the sum of the first $3000$ terms and the sequence of odd counting numbers starting from $3$, find the sum of the first $3000$ terms, and then calculate their difference. Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "-3000"
} | {
"split": "train",
"index": 4819,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a large bag of decorative ribbons, $\\frac{1}{4}$ are yellow, $\\frac{1}{3}$ are purple, $\\frac{1}{8}$ are orange, and the remaining 45 ribbons are silver. How many of the ribbons are orange? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 4820,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ten distinct positive real numbers are given and the sum of each pair is written (So 45 sums). Between these sums there are 5 equal numbers. If we calculate product of each pair, find the biggest number $k$ such that there may be $k$ equal numbers between them. Let's think step... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 4821,
"solution": "\nGiven ten distinct positive real numbers, consider all distinct pairs \\((a_i, a_j)\\) where \\(1 \\leq i < j \\leq 10\\). For each pair, we calculate the sum \\(S_{ij} = a_i + a_j\\). We are informed that among these 45 sums, 5 of them are equal.\n\nNext, we need... |
deepscaler | [
{
"role": "user",
"content": "What is the units digit in the product of all natural numbers from 1 to 99, inclusive? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 4822,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Complex numbers $p, q, r$ form an equilateral triangle with side length 24 in the complex plane. If $|p + q + r| = 48,$ find $|pq + pr + qr|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "768"
} | {
"split": "train",
"index": 4823,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square with area $4$ is inscribed in a square with area $5$, with each vertex of the smaller square on a side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length $a$, and the other of length $b$. What is th... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 4824,
"solution": "1. **Identify the side lengths of the squares**: Given that the area of the smaller square is $4$, its side length is $\\sqrt{4} = 2$. For the larger square with area $5$, the side length is $\\sqrt{5}$.\n\n2. **Set up the relationship between $a$ and $b$**: Each ve... |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum of the repeating decimals $0.\\overline{2}$, $0.\\overline{02}$, and $0.\\overline{0002}$ as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{224422}{9999}"
} | {
"split": "train",
"index": 4825,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A grocer arranges a display of cans where the top row has three cans, and each lower row has two more cans than the row above it. The total number of cans in the display is 169. How many rows does the display contain? Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 4826,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The remainder when the product $1492 \\cdot 1776 \\cdot 1812 \\cdot 1996$ is divided by 5 is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 4827,
"solution": "1. **Identify the last digits of each number**: \n - The last digit of $1492$ is $2$.\n - The last digit of $1776$ is $6$.\n - The last digit of $1812$ is $2$.\n - The last digit of $1996$ is $6$.\n\n2. **Calculate the product of the last digits**:\n - Com... |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $E$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ ($a > b > 0$) whose left focus $F_1$ coincides with the focus of the parabola $y^2 = -4x$, and the eccentricity of ellipse $E$ is $\\frac{\\sqrt{2}}{2}$. A line $l$ with a non-zero slope passes through point $M(m,0... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 4828,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive value of $n$ such that the equation $9x^2+nx+1=0$ has exactly one solution in $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 4829,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 1000 toy bears in a row. The bears come in three colors: white, brown, and black. Among any three consecutive bears, there is at least one bear of each color. Iskander tries to guess the colors of the bears. He made five guesses:\n\n- The 2nd bear from the left is whi... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 4830,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A Mediterranean polynomial has only real roots and it is of the form\n\\[ P(x) = x^{10}-20x^9+135x^8+a_7x^7+a_6x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \\] with real coefficients $a_0\\ldots,a_7$ . Determine the largest real number that occurs as a root of some Mediterranean... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 4831,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction. L... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 4832,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) and \\( b \\) be integers such that \\( ab = 144 \\). Find the minimum value of \\( a + b \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-145"
} | {
"split": "train",
"index": 4833,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a larger geoboard grid of $7 \\times 7$, points are evenly spaced vertically and horizontally. Points $A$ and $B$ are at $(3,3)$ and $(5,3)$ respectively. How many of the remaining points in the grid will allow for triangle $ABC$ to be isosceles? Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 4834,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven members of the family are each to pass through one of seven doors to complete a challenge. The first person can choose any door to activate. After completing the challenge, the adjacent left and right doors will be activated. The next person can choose any unchallenged do... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 4835,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( 2^{a} \\times 3^{b} \\times 5^{c} \\times 7^{d} = 252000 \\), what is the probability that a three-digit number formed by any 3 of the natural numbers \\( a, b, c, d \\) is divisible by 3 and less than 250? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"split": "train",
"index": 4836,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fraction \\(\\frac{1}{99^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},\\) where $n$ is the length of the period of the repeating decimal expansion. What is the sum $b_0+b_1+\\cdots+b_{n-1}$? Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "883"
} | {
"split": "train",
"index": 4837,
"solution": "To solve the problem, we first need to understand the decimal expansion of $\\frac{1}{99^2}$ and then find the sum of the digits in one period of the repeating decimal.\n\n1. **Calculate $\\frac{1}{99}$:**\n \\[\n \\frac{1}{99} = 0.\\overline{01}\n \\]\n Thi... |
deepscaler | [
{
"role": "user",
"content": "Inside triangle \\(ABC\\), a random point \\(M\\) is chosen. What is the probability that the area of one of the triangles \\(ABM\\), \\(BCM\\), or \\(CAM\\) is greater than the sum of the areas of the other two? Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "0.75"
} | {
"split": "train",
"index": 4838,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the following are equal to $x^x+x^x$ for all $x>0$?\n$\\textbf{I:}$ $2x^x$ $\\qquad\\textbf{II:}$ $x^{2x}$ $\\qquad\\textbf{III:}$ $(2x)^x$ $\\qquad\\textbf{IV:}$ $(2x)^{2x}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 4839,
"solution": "We are given the expression $x^x + x^x$ and need to determine which of the options I, II, III, and IV are equal to this expression for all $x > 0$.\n\n1. **Expression Simplification**:\n \\[\n x^x + x^x = 2x^x\n \\]\n This simplification follows from the bas... |
deepscaler | [
{
"role": "user",
"content": "Determine the number of digits in the value of $2^{15} \\times 5^{11}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 4840,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function \\( f(n) \\) is defined on the set of natural numbers \\( N \\) as follows:\n\\[ f(n) = \\begin{cases} \nn - 3, & \\text{ if } n \\geqslant 1000, \\\\\nf[f(n + 7)], & \\text{ if } n < 1000. \n\\end{cases} \\]\n\nWhat is the value of \\( f(90) \\)? Let's think step ... | math | {
"style": "rule",
"ground_truth": "999"
} | {
"split": "train",
"index": 4841,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point is randomly thrown onto the segment [3, 8] and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}-2 k-3\\right) x^{2}+(3 k-5) x+2=0$ satisfy the condition $x_{1} \\leq 2 x_{2}$. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "4/15"
} | {
"split": "train",
"index": 4842,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $N = 3x + 4y + 5z$, where $x$ equals 1 or -1, and $y$ equals 1 or -1, and $z$ equals 1 or -1. How many of the following statements are true? - $N$ can equal 0. - $N$ is always odd. - $N$ cannot equal 4. - $N$ is always even. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 4843,
"solution": "When $N = 3x + 4y + 5z$ with each of $x, y$ and $z$ equal to either 1 or -1, there are 8 possible combinations of values for $x, y$ and $z$. From this information, $N$ cannot equal 0, $N$ is never odd, $N$ can equal 4, and $N$ is always even. Therefore, exactly one ... |
deepscaler | [
{
"role": "user",
"content": "How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 4844,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\overrightarrow {AD}=3 \\overrightarrow {DC}$, $\\overrightarrow {BP}=2 \\overrightarrow {PD}$, if $\\overrightarrow {AP}=λ \\overrightarrow {BA}+μ \\overrightarrow {BC}$, then $λ+μ=\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "- \\frac {1}{3}"
} | {
"split": "train",
"index": 4845,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the quadrilateral \\(ABCD\\), it is given that \\(\\cos \\angle BAD = \\frac{3}{4}\\), \\(\\angle BAC = \\angle DAC\\), \\(AD < AB\\), and \\(AB = 5\\), \\(AC = BD = \\sqrt{14}\\). If \\(\\overrightarrow{AC} = \\lambda \\overrightarrow{AB} + \\mu \\overrightarrow{AD}\\) (\\(... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{5}"
} | {
"split": "train",
"index": 4846,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the $8$ vertices of a cube, choose any $4$ vertices. The probability that these $4$ points lie in the same plane is ______ (express the result as a simplified fraction). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6}{35}"
} | {
"split": "train",
"index": 4847,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x_1$ satisfy $2x+2^x=5$, and $x_2$ satisfy $2x+2\\log_2(x-1)=5$. Calculate the value of $x_1+x_2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {7}{2}"
} | {
"split": "train",
"index": 4848,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square has sides of length 3 units. A second square is formed having sides that are $120\\%$ longer than the sides of the first square. This process is continued sequentially to create a total of five squares. What will be the percent increase in the perimeter from the first ... | math | {
"style": "rule",
"ground_truth": "107.4\\%"
} | {
"split": "train",
"index": 4849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express $\\frac{31}{2\\cdot5^6}$ as a terminating decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.000992"
} | {
"split": "train",
"index": 4850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a circle $O: x^2 + y^2 = 1$ and a point $A(-2, 0)$, if there exists a fixed point $B(b, 0)$ ($b \\neq -2$) and a constant $\\lambda$ such that for any point $M$ on the circle $O$, it holds that $|MB| = \\lambda|MA|$. The maximum distance from point $P(b, \\lambda)$ to the... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{2}"
} | {
"split": "train",
"index": 4851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $F$ is a point on diagonal $BC$ of the unit square $ABCD$ such that $\\triangle{ABF}$ is isosceles right triangle with $AB$ as the hypotenuse, consider a strip inside $ABCD$ parallel to $AD$ ranging from $y=\\frac{1}{4}$ to $y=\\frac{3}{4}$ of the unit square, calculate t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 4852,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two workers were assigned to produce a batch of identical parts; after the first worked for \\(a\\) hours and the second for \\(0.6a\\) hours, it turned out that they had completed \\(\\frac{5}{n}\\) of the entire job. After working together for another \\(0.6a\\) hours, they f... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 4853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The shortest distance from a point on the parabola $x^2=y$ to the line $y=2x+m$ is $\\sqrt{5}$. Find the value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 4854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $L$ be the number formed by $2022$ digits equal to $1$, that is, $L=1111\\dots 111$.\nCompute the sum of the digits of the number $9L^2+2L$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4044"
} | {
"split": "train",
"index": 4855,
"solution": "\nGiven a number \\( L \\) consisting of 2022 digits, all equal to 1, we aim to compute the sum of the digits of the number \\( 9L^2 + 2L \\).\n\n### Step 1: Express \\( L \\) Numerically\nThe number \\( L \\) can be expressed numerically as a sequence of ones, math... |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, and $c$ be three positive real numbers such that $a(a+b+c)=bc$. Determine the maximum value of $\\frac{a}{b+c}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}-1}{2}"
} | {
"split": "train",
"index": 4856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A$, $B$, $C$, and $T$ are in space such that each of $\\overline{TA}$, $\\overline{TB}$, and $\\overline{TC}$ is perpendicular to the other two. If $TA = TB = 12$ and $TC = 6$, then what is the distance from $T$ to face $ABC$? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{6}"
} | {
"split": "train",
"index": 4857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For all positive integers $n$ less than $2002$, let \n\\begin{eqnarray*} a_n =\\left\\{ \\begin{array}{lr} 11, & \\text{if } n \\text{ is divisible by } 13 \\text{ and } 14;\\\\ 13, & \\text{if } n \\text{ is divisible by } 14 \\text{ and } 11;\\\\ 14, & \\text{if } n \\text{ i... | math | {
"style": "rule",
"ground_truth": "448"
} | {
"split": "train",
"index": 4858,
"solution": "1. **Identify the conditions for $a_n$:**\n - $a_n = 11$ if $n$ is divisible by both 13 and 14. The least common multiple (LCM) of 13 and 14 is $\\operatorname{lcm}(13, 14) = 182$.\n - $a_n = 13$ if $n$ is divisible by both 14 and 11. The least common multiple o... |
deepscaler | [
{
"role": "user",
"content": "The distance between the two intersections of $x=y^4$ and $x+y^2=1$ is $\\sqrt{u+v\\sqrt5}$. Find the ordered pair, $(u,v)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-2,2)"
} | {
"split": "train",
"index": 4859,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How can you measure 15 minutes using a 7-minute hourglass and an 11-minute hourglass? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 4860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the acute angle $\\theta$ satisfies $\\sin (\\pi \\cos \\theta) = \\cos (\\pi \\sin \\theta)$, then what is $\\sin 2\\theta$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 4861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that six balls are numbered 1, 2, 3, 4, 5, and 6, and the requirement that ball number 1 must be adjacent to ball number 2, and ball number 5 must not be adjacent to ball number 6, calculate the total number of different arrangements. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 4862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Tasty Candy Company always puts the same number of pieces of candy into each one-pound bag of candy they sell. Mike bought 4 one-pound bags and gave each person in his class 15 pieces of candy. Mike had 23 pieces of candy left over. Betsy bought 5 one-pound bags and gave 23... | math | {
"style": "rule",
"ground_truth": "302"
} | {
"split": "train",
"index": 4863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\cos(2x - \\frac{\\pi}{3}) + 2\\sin^2x$,\n(I) Find the period of the function $f(x)$ and the intervals where it is monotonically increasing;\n(II) When $x \\in [0, \\frac{\\pi}{2}]$, find the maximum and minimum values of the function $f(x)$. Let's t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 4864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ann and Barbara were comparing their ages and found that Barbara is as old as Ann was when Barbara was as old as Ann had been when Barbara was half as old as Ann is. If the sum of their present ages is $44$ years, then Ann's age is Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 4865,
"solution": "1. **Define Variables:**\n Let $a$ and $b$ be the current ages of Ann and Barbara, respectively. We know that the sum of their ages is $a + b = 44$.\n\n2. **Express Age Difference:**\n Define $y$ as the difference in their ages, so $y = a - b$. Note that $y$ rem... |
deepscaler | [
{
"role": "user",
"content": "Nine lines parallel to the base of a triangle divide the other sides each into $10$ equal segments and the area into $10$ distinct parts. If the area of the largest of these parts is $38$, calculate the area of the original triangle. Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 4866,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has $AB=13,BC=14$ and $AC=15$. Let $P$ be the point on $\\overline{AC}$ such that $PC=10$. There are exactly two points $D$ and $E$ on line $BP$ such that quadrilaterals $ABCD$ and $ABCE$ are trapezoids. What is the distance $DE?$ Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "12\\sqrt2"
} | {
"split": "train",
"index": 4867,
"solution": "1. **Assign Coordinates to Points**:\n - Place $A$, $B$, and $C$ on the Cartesian plane such that $B$ is at the origin $(0,0)$.\n - Using the distance formula and the given side lengths, we find coordinates for $A$ and $C$:\n - $AB = 13$, $BC = 14$, and $AC ... |
deepscaler | [
{
"role": "user",
"content": "What is the largest value of $x$ such that the expression \\[\\dfrac{x+1}{8x^2-65x+8}\\] is not defined? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 4868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given circles $P, Q,$ and $R$ where $P$ has a radius of 1 unit, $Q$ a radius of 2 units, and $R$ a radius of 1 unit. Circles $Q$ and $R$ are tangent to each other externally, and circle $R$ is tangent to circle $P$ externally. Compute the area inside circle $Q$ but outside circ... | math | {
"style": "rule",
"ground_truth": "2\\pi"
} | {
"split": "train",
"index": 4869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the intersection of the lines $9x-4y=6$ and $7x+y=17$. Express your answer as an ordered pair $(x,y)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(2,3)"
} | {
"split": "train",
"index": 4870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression \\[ (a^2+b)^2 - (a^2-b)^2, \\]if $a=4$ and $b=1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 4871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 16 people standing in a circle: each of them is either truthful (always tells the truth) or a liar (always lies). Everyone said that both of their neighbors are liars. What is the maximum number of liars that can be in this circle? Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 4872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine all real numbers $x$ for which the function $$g(x) = \\frac{1}{2+\\frac{1}{1+\\frac{1}{x-1}}}$$ is undefined, and find their sum. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}"
} | {
"split": "train",
"index": 4873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In obtuse triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given $a=7$, $b=3$, and $\\cos C= \\frac{ 11}{14}$.\n\n1. Find the values of $c$ and angle $A$.\n2. Find the value of $\\sin (2C- \\frac{ \\pi }{6})$. Let's ... | math | {
"style": "rule",
"ground_truth": "\\frac{ 71}{98}"
} | {
"split": "train",
"index": 4874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nLet \\( n \\) be a fixed integer, \\( n \\geq 2 \\).\n\n1. Determine the smallest constant \\( c \\) such that the inequality \\[\n\\sum_{1 \\leq i < j \\leq n} x_i x_j (x_i^2 + x_j^2) \\leq c \\left( \\sum_{i=1}^n x_i \\right)^4 \n\\] holds for all non-negative real numbers ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 4875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Is there an integer $x$ such that $x \\equiv 1 \\ (\\text{mod} \\ 6)$, $x \\equiv 9 \\ (\\text{mod} \\ 14)$, and $x \\equiv 7 \\ (\\text{mod} \\ 15)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 4876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be a point inside triangle $ABC$. Let $G_1$, $G_2$, and $G_3$ be the centroids of triangles $PBC$, $PCA$, and $PAB$, respectively. If the area of triangle $ABC$ is 18, then find the area of triangle $G_1 G_2 G_3$.\n\n[asy]\nimport geometry;\n\nunitsize(2 cm);\n\npair ... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 4877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A $44$-gon $Q_1$ is constructed in the Cartesian plane, and the sum of the squares of the $x$-coordinates of the vertices equals $176$. The midpoints of the sides of $Q_1$ form another $44$-gon, $Q_2$. Finally, the midpoints of the sides of $Q_2$ form a third $44$-gon, $Q_3$. F... | math | {
"style": "rule",
"ground_truth": "44"
} | {
"split": "train",
"index": 4878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line passes through the vectors $\\mathbf{a}$ and $\\mathbf{b}$. For a certain value of $k$, the vector\n\\[ k \\mathbf{a} + \\frac{5}{8} \\mathbf{b} \\]\nmust also lie on the line. Find $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"split": "train",
"index": 4879,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $a=2$, $b=3$, $\\cos C=\\frac{1}{3}$. The radius of the circumcircle is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9 \\sqrt{2}}{8}"
} | {
"split": "train",
"index": 4880,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively, with $b=4$ and $\\frac{\\cos B}{\\cos C} = \\frac{4}{2a - c}$.\n(1) Find the measure of angle $B$;\n(2) Find the maximum area of $\\triangle ABC$. Let's think... | math | {
"style": "rule",
"ground_truth": "4\\sqrt{3}"
} | {
"split": "train",
"index": 4881,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathcal{P}$ be a convex polygon with $50$ vertices. A set $\\mathcal{F}$ of diagonals of $\\mathcal{P}$ is said to be *$minimally friendly$* if any diagonal $d \\in \\mathcal{F}$ intersects at most one other diagonal in $\\mathcal{F}$ at a point interior... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 4882,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of 0-1 binary sequences formed by six 0's and six 1's such that no three 0's are together. For example, 110010100101 is such a sequence but 101011000101 and 110101100001 are not. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "357"
} | {
"split": "train",
"index": 4883,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,b,c$ be the roots of $x^3-9x^2+11x-1=0$, and let $s=\\sqrt{a}+\\sqrt{b}+\\sqrt{c}$. Find $s^4-18s^2-8s$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-37"
} | {
"split": "train",
"index": 4884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ $\\angle B = 30^\\circ,$ $AB = 150,$ and $AC = 50 \\sqrt{3}.$ Find the sum of all possible values of $BC.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "150 \\sqrt{3}"
} | {
"split": "train",
"index": 4885,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A secret facility is a rectangle measuring $200 \\times 300$ meters. Outside the facility, there is one guard at each of the four corners. An intruder approached the perimeter of the facility from the outside, and all the guards ran towards the intruder using the shortest paths... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 4886,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cylinder $B$'s height is equal to the radius of cylinder $A$ and cylinder $B$'s radius is equal to the height $h$ of cylinder $A$. If the volume of cylinder $A$ is twice the volume of cylinder $B$, the volume of cylinder $A$ can be written as $N \\pi h^3$ cubic units. What is t... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 4887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An urn contains $k$ balls labeled with $k$, for all $k = 1, 2, \\ldots, 2016$. What is the minimum number of balls we must draw, without replacement and without looking at the balls, to ensure that we have 12 balls with the same number? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "22122"
} | {
"split": "train",
"index": 4888,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The increasing sequence of positive integers $a_1,$ $a_2,$ $a_3,$ $\\dots$ has the property that\n\\[a_{n + 2} = a_{n + 1} + a_n\\]for all $n \\ge 1.$ If $a_7 = 120,$ then find $a_8.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "194"
} | {
"split": "train",
"index": 4889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers divide the number $10! = 1 \\times 2 \\times 3 \\times 4 \\times 5 \\times 6 \\times 7 \\times 8 \\times 9 \\times 10$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "270"
} | {
"split": "train",
"index": 4890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Charlyn walks completely around the boundary of a square whose sides are each 5 km long. From any point on her path she can see exactly 1 km horizontally in all directions. What is the area of the region consisting of all points Charlyn can see during her walk, expressed in squ... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 4891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=2\\sqrt{3}\\sin ^{2}x+2\\sin x\\cos x-\\sqrt{3}$, where $x\\in\\left[ \\frac{\\pi}{3}, \\frac{11\\pi}{24}\\right]$.\n\n(1) Find the range of the function $f(x)$.\n\n(2) Suppose that the lengths of two sides of an acute-angled triangle $ABC$ are the maxi... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 4892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a regular tetrahedron with an edge length of \\(2 \\sqrt{6}\\), a sphere is centered at the centroid \\(O\\) of the tetrahedron. The total length of the curves where the sphere intersects with the four faces of the tetrahedron is \\(4 \\pi\\). Find the radius of the spher... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 4893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the polar coordinate system, the distance from the center of the circle $\\rho=4\\cos\\theta$ ($\\rho\\in\\mathbb{R}$) to the line $\\theta= \\frac {\\pi}{3}$ can be found using the formula for the distance between a point and a line in polar coordinates. Let's think step by... | math | {
"style": "rule",
"ground_truth": "\\sqrt {3}"
} | {
"split": "train",
"index": 4894,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number \\( n \\) for which the number \\( A = n^3 + 12n^2 + 15n + 180 \\) is divisible by 23. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 4895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 4896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $m$ is a positive integer, and given that $\\mathop{\\text{lcm}}[40, m] = 120$ and $\\mathop{\\text{lcm}}[m, 45] = 180$, what is $m$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "m = 36"
} | {
"split": "train",
"index": 4897,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two arithmetic sequences $\\{a\\_n\\}$ and $\\{b\\_n\\}$ with the sum of their first $n$ terms being $S\\_n$ and $T\\_n$ respectively. If $\\frac{S\\_n}{T\\_n} = \\frac{2n}{3n+1}$, find the value of $\\frac{a\\_{11}}{b\\_{11}}$. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{21}{32}"
} | {
"split": "train",
"index": 4898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c, n$ be positive real numbers such that $\\frac{a+b}{a}=3, \\frac{b+c}{b}=4$, and $\\frac{c+a}{c}=n$. Find $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{6}"
} | {
"split": "train",
"index": 4899,
"solution": "We have $$1=\\frac{b}{a} \\cdot \\frac{c}{b} \\cdot \\frac{a}{c}=(3-1)(4-1)(n-1)$$ Solving for $n$ yields $n=\\frac{7}{6}$."
} |
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