data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given that \\( \\text{rem} \\left(\\frac{5}{7}, \\frac{3}{4}\\right) \\) must be calculated, determine the value of the remainder. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{7}"
} | {
"split": "train",
"index": 27949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A TV station broadcasts 5 advertisements in a row, among which there are 3 different commercial advertisements and 2 different World Expo promotional advertisements. The last advertisement broadcasted is a World Expo promotional advertisement, and the methods in which the 2 Wor... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 27950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the binary number $110101_{(2)}$ to decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "53"
} | {
"split": "train",
"index": 27951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( x = 3 \\) and \\( y = 7 \\), then what is the value of \\( \\frac{x^5 + 3y^3}{9} \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "141"
} | {
"split": "train",
"index": 27952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ is an internal angle of a triangle, and $\\sin α + \\cos α = \\frac{1}{5}$. \n$(1)$ Find the value of $\\tan α$; \n$(2)$ Find the value of $\\frac{\\sin(\\frac{3π}{2}+α)\\sin(\\frac{π}{2}-α)\\tan^{3}(π-α)}{\\cos(\\frac{π}{2}+α)\\cos(\\frac{3π}{2}-α)}$. Let's th... | math | {
"style": "rule",
"ground_truth": "-\\frac{4}{3}"
} | {
"split": "train",
"index": 27953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the nonconstant polynomial $P(x)$ such that\n\\[P(P(x)) = (x^2 + x + 1) P(x).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^2 + x"
} | {
"split": "train",
"index": 27954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest possible number in decimal notation where all the digits are different, and the sum of its digits is 37. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "976543210"
} | {
"split": "train",
"index": 27955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the ratio of bananas to yogurt to honey is 3:2:1, and that Linda has 10 bananas, 9 cups of yogurt, and 4 tablespoons of honey, determine the maximum number of servings of smoothies Linda can make. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 27956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( S = \\{1,2, \\cdots, 15\\} \\). From \\( S \\), extract \\( n \\) subsets \\( A_{1}, A_{2}, \\cdots, A_{n} \\), satisfying the following conditions:\n(i) \\(\\left|A_{i}\\right|=7, i=1,2, \\cdots, n\\);\n(ii) \\(\\left|A_{i} \\cap A_{j}\\right| \\leqslant 3,1 \\leqslant... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 27957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that positive real numbers \\( a \\) and \\( b \\) satisfy \\( ab(a+b)=4 \\), find the minimum value of \\( 2a + b \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 27958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Which of the following quantities is the largest? (Write $A$, $B$, or $C$.) \\[ A.\\ \\ \\frac{2006}{2005}+\\frac{2006}{2007} \\qquad B.\\ \\ \\frac{2006}{2007}+\\frac{2008}{2007} \\qquad C.\\ \\ \\frac{2007}{2006}+\\frac{2007}{2008} \\] Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "\\text{A}"
} | {
"split": "train",
"index": 27959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of permutations of the sequence $1,2,3,4,5$ for which the first term is not $1$. A permutation is chosen randomly from $S$. The probability that the second term is $2$, in lowest terms, is $a/b$. What is $a+b$? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 27960,
"solution": "1. **Define the set $S$:** \n The set $S$ consists of all permutations of the sequence $1, 2, 3, 4, 5$ where the first term is not $1$. Since there are $5! = 120$ total permutations of five distinct numbers, and there are $4! = 24$ permutations where $1$ is the ... |
deepscaler | [
{
"role": "user",
"content": "If \\( 20 \\times 21 \\times 22 \\times \\ldots \\times 2020 = 26^{k} \\times m \\), where \\( m \\) is an integer, what is the maximum value of \\( k \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "165"
} | {
"split": "train",
"index": 27961,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When \\( q(x) = Dx^4 + Ex^2 + Fx + 6 \\) is divided by \\( x - 2 \\), the remainder is 14. Find the remainder when \\( q(x) \\) is divided by \\( x + 2 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 27962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( r(x) \\) have a domain of \\(\\{ -2, -1, 0, 1 \\}\\) and a range of \\(\\{ 1, 3, 5, 7 \\}\\). Let \\( s(x) \\) have a domain of \\(\\{ 0, 1, 2, 3, 4, 5 \\}\\) and be defined by \\( s(x) = 2x + 1 \\). What is the sum of all possible values of \\( s(r(x)) \\)? Let's think... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 27963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the interior of a triangle \\( ABC \\) with area 1, points \\( D \\), \\( E \\), and \\( F \\) are chosen such that \\( D \\) is the midpoint of \\( AE \\), \\( E \\) is the midpoint of \\( BF \\), and \\( F \\) is the midpoint of \\( CD \\). Find the area of triangle \\( DE... | math | {
"style": "rule",
"ground_truth": "1/7"
} | {
"split": "train",
"index": 27964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height dropped from the vertex \\( A_{4} \\) to the face \\( A_{1} A_{2} A_{3} \\).\n\n\\( A_{1}(1, 0, 2) \\)\n\n\\( A_{2}(1, 2, -1) \\)\n\n\\( A_{3}(2, -2, 1) \\)\n\n\\( ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{7}{11}}"
} | {
"split": "train",
"index": 27965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1.$ What is the remainder when the polynomial $g(x^{12})$ is divided by the polynomial $g(x)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 27966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$\\frac{1}{1+\\frac{1}{2+\\frac{1}{3}}}=$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{10}"
} | {
"split": "train",
"index": 27967,
"solution": "To solve the expression $\\frac{1}{1+\\frac{1}{2+\\frac{1}{3}}}$, we start by simplifying the innermost fraction and work our way outward.\n\n1. **Simplify the innermost fraction:**\n \\[\n 2 + \\frac{1}{3} = \\frac{6}{3} + \\frac{1}{3} = \\frac{6+1}{3} = \\fra... |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ such that $\\frac{n}{n+103}$ is equal to a terminating decimal? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 27968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a complex number $z = (a^2 - 4) + (a + 2)i$ where $a \\in \\mathbb{R}$: \n(Ⅰ) If $z$ is a pure imaginary number, find the value of the real number $a$; \n(Ⅱ) If the point corresponding to $z$ in the complex plane lies on the line $x + 2y + 1 = 0$, find the value of the ... | math | {
"style": "rule",
"ground_truth": "a = -1"
} | {
"split": "train",
"index": 27969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence ${a_n}$ that satisfies $a_1=1$ and $a_n=a_1+ \\frac {1}{2}a_2+ \\frac {1}{3}a_3+…+ \\frac {1}{n-1}a_{n-1}$ for $n\\geqslant 2, n\\in\\mathbb{N}^*$, if $a_k=2017$, then $k=$ \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "4034"
} | {
"split": "train",
"index": 27970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.\n[quote]For example, 4 can be partitioned in five distinct ways:\n4\n3 + 1\n2 + 2\n2 + 1 + 1\n1 + 1 + 1 + 1[/qu... | math | {
"style": "rule",
"ground_truth": "1, 3, 5"
} | {
"split": "train",
"index": 27971,
"solution": "\nWe need to determine all positive integers \\( n \\) such that \n\\[\np(n) + p(n+4) = p(n+2) + p(n+3),\n\\]\nwhere \\( p(n) \\) denotes the partition function, which counts the number of ways \\( n \\) can be partitioned into positive integers.\n\nTo solve this, ... |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ the midpoint of $\\overline{BC}$ is $(1,5,-1),$ the midpoint of $\\overline{AC}$ is $(0,4,-2),$ and the midpoint of $\\overline{AB}$ is $(2,3,4).$ Find the coordinates of vertex $A.$ Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "(1, 2, 3)"
} | {
"split": "train",
"index": 27972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the area of a hexagon where the sides alternate between lengths of 2 and 4 units, and the triangles cut from each corner have base 2 units and altitude 3 units? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 27973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest natural number that can be added to 40,317 to make it a palindrome? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "87"
} | {
"split": "train",
"index": 27974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an \\(8 \\times 8\\) table, some cells are black, and the rest are white. In each white cell, the total number of black cells located in the same row or column is written. Nothing is written in the black cells. What is the maximum possible value of the sum of the numbers in ... | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 27975,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line \\( l \\), parallel to the diagonal \\( AC_1 \\) of a unit cube \\( ABCDA_1B_1C_1D_1 \\), is equidistant from the lines \\( BD \\), \\( A_1D_1 \\), and \\( CB_1 \\). Find the distances from the line \\( l \\) to these lines. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{6}"
} | {
"split": "train",
"index": 27976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express $361_9 + 4C5_{13}$ as a base 10 integer, where $C$ denotes the digit whose value is 12 in base 13. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1135"
} | {
"split": "train",
"index": 27977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Square $BCFE$ is inscribed in right triangle $AGD$, as shown below. If $AB = 28$ units and $CD = 58$ units, what is the area of square $BCFE$?\n\n[asy]\ndraw((9,15.6)--(10.7,14.6)--(11.7,16.3));\ndraw((0,0)--(10,17.3)--(40,0)--cycle);\ndraw((7,0)--(19,0)--(19,12.1)--(7,12.1)--c... | math | {
"style": "rule",
"ground_truth": "1624"
} | {
"split": "train",
"index": 27978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rudolph bikes at a constant rate and stops for a five-minute break at the end of every mile. Jennifer bikes at a constant rate which is three-quarters the rate that Rudolph bikes, but Jennifer takes a five-minute break at the end of every two miles. Jennifer and Rudolph begin b... | math | {
"style": "rule",
"ground_truth": "620"
} | {
"split": "train",
"index": 27979,
"solution": "Let $r$ be the time Rudolph takes disregarding breaks and $\\frac{4}{3}r$ be the time Jennifer takes disregarding breaks. We have the equation \\[r+5\\left(49\\right)=\\frac{4}{3}r+5\\left(24\\right)\\] \\[125=\\frac13r\\] \\[r=375.\\] Thus, the total time they tak... |
deepscaler | [
{
"role": "user",
"content": "Let $a$ and $b$ be positive real numbers such that $a^3 + b^3 = a + b.$ Simplify\n\\[\\frac{a}{b} + \\frac{b}{a} - \\frac{1}{ab}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 27980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The side lengths of a triangle are 14 cm, 48 cm and 50 cm. How many square centimeters are in the area of the triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "336"
} | {
"split": "train",
"index": 27981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(ABC\\), the sides \\(AC = 14\\) and \\(AB = 6\\) are given. A circle with center \\(O\\), constructed on side \\(AC\\) as the diameter, intersects side \\(BC\\) at point \\(K\\). It is given that \\(\\angle BAK = \\angle ACB\\). Find the area of triangle \\(BOC\\... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 27982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Fibonacci numbers are defined by $F_1=F_2=1$ and $F_n=F_{n-1}+F_{n-2}$ for $n>2$ . It is well-known that the sum of any $10$ consecutive Fibonacci numbers is divisible by $11$ . Determine the smallest integer $N$ so that the sum of any $N$ consecutive Fibonacc... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 27983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the set of all triangles $OPQ$ where $O$ is the origin and $P$ and $Q$ are distinct points in the plane with nonnegative integer coordinates $(x,y)$ such that $51x + y = 2048$. Find the number of such distinct triangles whose area is a positive integer. Let's think ste... | math | {
"style": "rule",
"ground_truth": "400"
} | {
"split": "train",
"index": 27984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The teacher asked the students to calculate \\(\\overline{AB} . C + D . E\\). Xiao Hu accidentally missed the decimal point in \\(D . E\\), getting an incorrect result of 39.6; while Da Hu mistakenly saw the addition sign as a multiplication sign, getting an incorrect result of... | math | {
"style": "rule",
"ground_truth": "26.1"
} | {
"split": "train",
"index": 27985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given three positive numbers \\( a, b, \\mathrm{and} c \\) satisfying \\( a \\leq b+c \\leq 3a \\) and \\( 3b^2 \\leq a(a+c) \\leq 5b^2 \\), what is the minimum value of \\(\\frac{b-2c}{a}\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{18}{5}"
} | {
"split": "train",
"index": 27986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine for how many different values of $p<2000$, there exists a quadrilateral $ABCD$ with integer side lengths, perimeter $p$, right angles at $D$ and $C$, $AB=3$, and $CD=AD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "996"
} | {
"split": "train",
"index": 27987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of the $20$ balls is tossed independently and at random into one of the $5$ bins. Let $p$ be the probability that some bin ends up with $3$ balls, another with $5$ balls, and the other three with $4$ balls each. Let $q$ be the probability that every bin ends up with $4$ ba... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 27988,
"solution": "1. **Define the sets and probabilities**: Let $A$ be the set of all configurations where the balls are distributed as $3{-}5{-}4{-}4{-}4$ among the bins, and let $B$ be the set of all configurations where the balls are distributed as $4{-}4{-}4{-}4{-}4$. Define $p ... |
deepscaler | [
{
"role": "user",
"content": "What is the remainder of $5^{2010}$ when it is divided by 7? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 27989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The equation $y = -6t^2 - 10t + 56$ describes the height (in feet) of a ball thrown downward at 10 feet per second from a height of 56 feet from the surface from Mars. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hund... | math | {
"style": "rule",
"ground_truth": "2.33"
} | {
"split": "train",
"index": 27990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $(\\sqrt{3}b-c)\\cos A=a\\cos C$, find the value of $\\cos A$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 27991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bin contains 10 black balls and 9 white balls. 4 balls are drawn at random. What is the probability of drawing 3 balls of one color and 1 ball of another color? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{160}{323}"
} | {
"split": "train",
"index": 27992,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the quadratic equation $3x^{2}-6x-7=0$, the coefficient of the quadratic term is ____ and the constant term is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 27993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\dbinom{10}{8}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 27994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A student passes through three intersections with traffic lights, labeled \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\), on the way to school. It is known that the probabilities of encountering a red light at intersections \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are \\\\( \\dfrac... | math | {
"style": "rule",
"ground_truth": "\\dfrac {235}{3}"
} | {
"split": "train",
"index": 27995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $N$ is a positive integer between 1000000 and 10000000, inclusive, what is the maximum possible value for the sum of the digits of $25 \\times N$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "67"
} | {
"split": "train",
"index": 27996,
"solution": "Since $N$ is between 1000000 and 10000000, inclusive, then $25 \\times N$ is between 25000000 and 250000000, inclusive, and so $25 \\times N$ has 8 digits or it has 9 digits. We consider the value of $25 \\times N$ as having 9 digits, with the possibility that the ... |
deepscaler | [
{
"role": "user",
"content": "Shari walks at a constant rate of 3 miles per hour. After 1.5 hours, how many miles did she walk? Express your answer as a decimal to the nearest tenth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"split": "train",
"index": 27997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a 4-digit perfect square, knowing that the number formed by the first two digits is one more than the number formed by the last two digits. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8281"
} | {
"split": "train",
"index": 27998,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jeffrey writes the numbers 1 and $100000000=10^{8}$ on the blackboard. Every minute, if $x, y$ are on the board, Jeffrey replaces them with $\\frac{x+y}{2} \\text{ and } 2\\left(\\frac{1}{x}+\\frac{1}{y}\\right)^{-1}$. After 2017 minutes the two numbers are $a$ and $b$. Find $\... | math | {
"style": "rule",
"ground_truth": "10000"
} | {
"split": "train",
"index": 27999,
"solution": "Note that the product of the integers on the board is a constant. Indeed, we have that $\\frac{x+y}{2} \\cdot 2\\left(\\frac{1}{x}+\\frac{1}{y}\\right)^{-1}=xy$. Therefore, we expect that the answer to the problem is approximately $\\sqrt{1 \\cdot 10^{8}}=10^{4}$. ... |
deepscaler | [
{
"role": "user",
"content": "All the positive integers greater than 1 are arranged in five columns (A, B, C, D, E) as shown. Continuing the pattern, in what column will the integer 800 be written?\n\n[asy]\nlabel(\"A\",(0,0),N);\nlabel(\"B\",(10,0),N);\nlabel(\"C\",(20,0),N);\nlabel(\"D\",(30,0),N);\nlabel... | math | {
"style": "rule",
"ground_truth": "\\text{B}"
} | {
"split": "train",
"index": 28000,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When $x^9-x$ is factored as completely as possible into polynomials and monomials with integral coefficients, the number of factors is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 28001,
"solution": "1. **Factor out the greatest common factor**: \n The polynomial $x^9 - x$ can be rewritten by factoring out the common factor of $x$, giving:\n \\[\n x^9 - x = x(x^8 - 1)\n \\]\n\n2. **Factorize $x^8 - 1$ using difference of squares**:\n The expression $x... |
deepscaler | [
{
"role": "user",
"content": " \nPeter Ivanovich, along with 49 other men and 50 women, are seated in a random order around a round table. We call a man satisfied if a woman is sitting next to him. Find:\n\na) The probability that Peter Ivanovich is satisfied.\n\nb) The expected number of satisfied men. Let... | math | {
"style": "rule",
"ground_truth": "\\frac{1250}{33}"
} | {
"split": "train",
"index": 28002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For positive real numbers \\(a\\), \\(b\\), and \\(c\\), compute the maximum value of\n\\[\n\\frac{abc(a + b + c + ab)}{(a + b)^3 (b + c)^3}.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 28003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What value of $x$ satisfies\n\\[x- \\frac{3}{4} = \\frac{5}{12} - \\frac{1}{3}?\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 28004,
"solution": "1. Start with the given equation:\n \\[\n x - \\frac{3}{4} = \\frac{5}{12} - \\frac{1}{3}\n \\]\n\n2. Add $\\frac{3}{4}$ to both sides to isolate $x$:\n \\[\n x = \\frac{5}{12} - \\frac{1}{3} + \\frac{3}{4}\n \\]\n\n3. To simplify the right-hand side, f... |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has vertices $A(0, 10)$, $B(3, 0)$, $C(9, 0)$. A horizontal line with equation $y=s$ intersects line segment $\\overline{AB}$ at $P$ and line segment $\\overline{AC}$ at $Q$, forming $\\triangle APQ$ with area 18. Compute $s$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "10 - 2\\sqrt{15}"
} | {
"split": "train",
"index": 28005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\overrightarrow{a}=(2,3)$, $\\overrightarrow{b}=(-4,7)$, and $\\overrightarrow{a}+\\overrightarrow{c}=\\overrightarrow{0}$, find the projection of $\\overrightarrow{c}$ on the direction of $\\overrightarrow{b}$. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{65}}{5}"
} | {
"split": "train",
"index": 28006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three times Dick's age plus Tom's age equals twice Harry's age. \nDouble the cube of Harry's age is equal to three times the cube of Dick's age added to the cube of Tom's age. \nTheir respective ages are relatively prime to each other. The sum of the squares of their ages is Le... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 28007,
"solution": "We are given two equations involving the ages of Dick, Tom, and Harry, denoted as $d$, $t$, and $h$ respectively:\n1. \\(3d + t = 2h\\)\n2. \\(2h^3 = 3d^3 + t^3\\)\n\nWe start by expressing $t$ in terms of $d$ and $h$ from the first equation:\n\\[ t = 2h - 3d \\]\n... |
deepscaler | [
{
"role": "user",
"content": "Let $n > 2$ be an integer and let $\\ell \\in \\{1, 2,\\dots, n\\}$. A collection $A_1,\\dots,A_k$ of (not necessarily distinct) subsets of $\\{1, 2,\\dots, n\\}$ is called $\\ell$-large if $|A_i| \\ge \\ell$ for all $1 \\le i \\le k$. Find, in terms of $n$ and $\\ell$, the lar... | math | {
"style": "rule",
"ground_truth": "\\frac{\\ell^2 - 2\\ell + n}{n(n-1)}"
} | {
"split": "train",
"index": 28008,
"solution": "To solve the problem, we need to find the largest real number \\( c \\) such that the inequality\n\n\\[\n\\sum_{i=1}^k \\sum_{j=1}^k x_i x_j \\frac{|A_i \\cap A_j|^2}{|A_i| \\cdot |A_j|} \\ge c \\left(\\sum_{i=1}^k x_i\\right)^2\n\\]\n\nholds for all positive integ... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sec x - \\tan x = \\frac{5}{4},$ find all possible values of $\\sin x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 28009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cylindrical log has diameter $12$ inches. A wedge is cut from the log by making two planar cuts that go entirely through the log. The first is perpendicular to the axis of the cylinder, and the plane of the second cut forms a $45^\\circ$ angle with the plane of the first cut.... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 28010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures $120^{\\circ}$, what is the measure of the smallest angle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60^\\circ"
} | {
"split": "train",
"index": 28011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the scores X of 10000 people approximately follow a normal distribution N(100,13^2), it is given that P(61 < X < 139)=0.997, find the number of people scoring no less than 139 points in this exam. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 28012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alexio now has 150 cards numbered from 1 to 150, inclusive, and places them in a box. He chooses a card at random. What is the probability that the number on the card he picks is a multiple of 4, 5 or 6? Express your answer as a reduced fraction. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{15}"
} | {
"split": "train",
"index": 28013,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Twelve mayoral candidates each made a statement about how many times lies had been told before their turn. The first candidate said, \"Before me, one lie was told.\" The second candidate said, \"Now, two lies have been told.\" The third candidate said, \"Now, three lies have be... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 28014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability that a randomly selected set of 5 numbers from the set of the first 15 positive integers has a sum divisible by 3? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 28015,
"solution": "The possibilities for the numbers are: all five are divisible by 3, three are divisible by 3, one is $\\equiv 1(\\bmod 3)$ and one is $\\equiv 2(\\bmod 3)$, two are divisible by 3, and the other three are either $\\equiv 1 \\quad(\\bmod 3)$ or $\\equiv 2(\\bmod 3)$... |
deepscaler | [
{
"role": "user",
"content": "The vertices of a regular nonagon (9-sided polygon) are to be labeled with the digits 1 through 9 in such a way that the sum of the numbers on every three consecutive vertices is a multiple of 3. Two acceptable arrangements are considered to be indistinguishable if one can be o... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 28016,
"solution": "Notice that there are three pairs of congruent integers mod 3 ($(1,4,7),(2,5,8),(3,6,9)$). There are $3!$ ways to order each pair individually and $3!$ ways to order the pairs as a group. Rotations are indistinguishable, so in total there are $6^4/9=\\boxed{144}$ w... |
deepscaler | [
{
"role": "user",
"content": "A sequence of numbers $t_{1}, t_{2}, t_{3}, \\ldots$ has its terms defined by $t_{n}=\\frac{1}{n}-\\frac{1}{n+2}$ for every integer $n \\geq 1$. What is the largest positive integer $k$ for which the sum of the first $k$ terms is less than 1.499? Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "1998"
} | {
"split": "train",
"index": 28017,
"solution": "We note that $t_{1}=\\frac{1}{1}-\\frac{1}{3}=\\frac{2}{3} \\approx 0.67$, $t_{1}+t_{2}=\\left(\\frac{1}{1}-\\frac{1}{3}\\right)+\\left(\\frac{1}{2}-\\frac{1}{4}\\right)=\\frac{2}{3}+\\frac{1}{4}=\\frac{11}{12} \\approx 0.92$, $t_{1}+t_{2}+t_{3}=\\left(\\frac{1}{1}... |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ be unit vectors such that\n\\[\\mathbf{a} + \\mathbf{b} + \\sqrt{3} \\mathbf{c} = \\mathbf{0}.\\]Find the angle between $\\mathbf{a}$ and $\\mathbf{b},$ in degrees.\n\nNote: A unit vector is a vector of magnitude 1. Let's thin... | math | {
"style": "rule",
"ground_truth": "60^\\circ"
} | {
"split": "train",
"index": 28018,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability that all 4 blue marbles are drawn before all 3 yellow marbles are drawn? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{7}"
} | {
"split": "train",
"index": 28019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x=2$ and $y=3$, express the value of the following as a common fraction: $$\n\\frac\n{~\\frac{1}{y}~}\n{\\frac{1}{x}}\n$$ 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": 28020,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circles $\\mathcal{P}$ and $\\mathcal{Q}$ have radii $1$ and $4$, respectively, and are externally tangent at point $A$. Point $B$ is on $\\mathcal{P}$ and point $C$ is on $\\mathcal{Q}$ so that line $BC$ is a common external tangent of the two circles. A line $\\ell$ through $... | math | {
"style": "rule",
"ground_truth": "129"
} | {
"split": "train",
"index": 28021,
"solution": "Let $P$ and $Q$ be the centers of circles $\\mathcal{P}$ and $\\mathcal{Q}$ , respectively.\n Let $M$ be midpoint $BC, \\beta = \\angle ACB.$\n Upper diagram shows that\n$\\sin 2\\beta = \\frac {4}{5}$ and $AC = 2 AB.$ Therefore $\\cos 2\\beta = \\frac {3}{5}.$\n L... |
deepscaler | [
{
"role": "user",
"content": "Convert the binary number $10110100$ to a decimal number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 28022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Call the pentominoes found in the last problem square pentominoes. Just like dominos and ominos can be used to tile regions of the plane, so can square pentominoes. In particular, a square pentomino tiling of a region of the plane is a way of covering it (and only it) completel... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 28023,
"solution": "Since 5 does not divide 144, there are 0."
} |
deepscaler | [
{
"role": "user",
"content": "$\\frac{9}{7 \\times 53} =$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{0.9}{0.7 \\times 53}"
} | {
"split": "train",
"index": 28024,
"solution": "To solve the problem, we need to convert the fraction $\\frac{9}{7 \\times 53}$ into a form that matches one of the given options. We start by expressing the numbers in decimal form and then simplify the expression.\n\n1. **Convert integers to decimals:**\n - The... |
deepscaler | [
{
"role": "user",
"content": "Given that point $P$ is the circumcenter of $\\triangle ABC$, and $\\overrightarrow{PA} + \\overrightarrow{PB} + \\lambda \\overrightarrow{PC} = 0$, $\\angle C = 120^{\\circ}$, determine the value of the real number $\\lambda$. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 28025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}=(\\cos x,\\sin x)$, $\\overrightarrow{b}=( \\sqrt {3}\\sin x,\\sin x)$, where $x\\in R$, define the function $f(x)= \\overrightarrow{a}\\cdot \\overrightarrow{b}- \\dfrac {1}{2}$.\n(1) Find the smallest positive period of the function $f(x)$;\... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{1}{2}"
} | {
"split": "train",
"index": 28026,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest possible value of $x+y$ such that $x^{2} + y^{2} =90$ and $xy=27$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 28027,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, $c$ be positive numbers, and $a+b+9c^2=1$. The maximum value of $\\sqrt{a} + \\sqrt{b} + \\sqrt{3}c$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{21}}{3}"
} | {
"split": "train",
"index": 28028,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the discriminant of $3x^2 + \\left(3 + \\frac 13\\right)x + \\frac 13$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{64}{9}"
} | {
"split": "train",
"index": 28029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular picture frame is constructed from 1.5-inch-wide pieces of wood. The area of just the frame is \\(27\\) square inches, and the length of one of the interior edges of the frame is \\(4.5\\) inches. Determine the sum of the lengths of the four interior edges of the f... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 28030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABC$ be a triangle with $\\angle BAC = 90^o$ and $D$ be the point on the side $BC$ such that $AD \\perp BC$ . Let $ r, r_1$ , and $r_2$ be the inradii of triangles $ABC, ABD$ , and $ACD$ , respectively. If $r, r_1$ , and $r_2$ are positive integers and one ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 28031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that\n\\[f(x) f(-x) = f(x^2).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 28032,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Equilateral $\\triangle ABC$ has side length $1$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle. What is the area of hexagon $DEFGHI$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3+\\sqrt3"
} | {
"split": "train",
"index": 28033,
"solution": "1. **Identify the Configuration**: We start by noting that $\\triangle ABC$ is equilateral with side length $1$. Squares $ABDE$, $BCHI$, and $CAFG$ are constructed outside the triangle. We need to find the area of hexagon $DEFGHI$.\n\n2. **Understanding the Hexagon... |
deepscaler | [
{
"role": "user",
"content": "A set of positive integers is said to be pilak if it can be partitioned into 2 disjoint subsets \\(F\\) and \\(T\\), each with at least 2 elements, such that the elements of \\(F\\) are consecutive Fibonacci numbers, and the elements of \\(T\\) are consecutive triangular number... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 28034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die? ... | math | {
"style": "rule",
"ground_truth": "438"
} | {
"split": "train",
"index": 28035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be the point on line segment $\\overline{AB}$ such that $AP:PB = 3:2.$ Then\n\\[\\overrightarrow{P} = t \\overrightarrow{A} + u \\overrightarrow{B}\\]for some constants $t$ and $u.$ Enter the ordered pair $(t,u).$\n\n[asy]\nunitsize(1 cm);\n\npair A, B, P;\n\nA = (0,0... | math | {
"style": "rule",
"ground_truth": "\\left( \\frac{2}{5}, \\frac{3}{5} \\right)"
} | {
"split": "train",
"index": 28036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given 500 points inside a convex 1000-sided polygon, along with the polygon's vertices (a total of 1500 points), none of which are collinear, the polygon is divided into triangles with these 1500 points as the vertices of the triangles. There are no other vertices apart from th... | math | {
"style": "rule",
"ground_truth": "1998"
} | {
"split": "train",
"index": 28037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right cylindrical oil tank is $15$ feet tall and its circular bases have diameters of $4$ feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is $3$ feet deep. How deep, in feet, would the oil have been if the tank had been sta... | math | {
"style": "rule",
"ground_truth": "12.1"
} | {
"split": "train",
"index": 28038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When two distinct digits are randomly chosen in $N=123456789$ and their places are swapped, one gets a new number $N'$ (for example, if 2 and 4 are swapped, then $N'=143256789$ ). The expected value of $N'$ is equal to $\\frac{m}{n}$ , where $m$ and $n$ are relative... | math | {
"style": "rule",
"ground_truth": "555556"
} | {
"split": "train",
"index": 28039,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the terminal side of angle $\\varphi$ passes through point P(1, -1), and points A($x_1$, $y_1$) and B($x_2$, $y_2$) are any two points on the graph of the function $f(x) = \\sin(\\omega x + \\varphi)$ ($\\omega > 0$). If $|f(x_1) - f(x_2)| = 2$, the minimum value of ... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 28040,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the numbers \\(1,2, \\cdots, 14\\), select \\(a_{1}, a_{2}, a_{3}\\) in ascending order such that \\(a_{2} - a_{1} \\geq 3\\) and \\(a_{3} - a_{2} \\geq 3\\). How many different ways are there to select the numbers satisfying these conditions? Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 28041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two congruent squares, $ABCD$ and $EFGH$, each with a side length of $20$ units, overlap to form a $20$ by $35$ rectangle $AEGD$. Calculate the percentage of the area of rectangle $AEGD$ that is shaded. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "14\\%"
} | {
"split": "train",
"index": 28042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers \\(a, b, c, d\\) belong to the interval \\([-6, 6]\\). Find the maximum value of the expression \\(a + 2b + c + 2d - ab - bc - cd - da\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "156"
} | {
"split": "train",
"index": 28043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Meghal is playing a game with 2016 rounds $1,2, \\cdots, 2016$. In round $n$, two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the faces is $\\frac{2 \\pi}{n+2}$. Meghal shoots a laser at these mirrors and her score for ... | math | {
"style": "rule",
"ground_truth": "1019088"
} | {
"split": "train",
"index": 28044,
"solution": "Let points $O, A_{1}, A_{2}$ lie in a plane such that $\\angle A_{1} O A_{2}=\\frac{2 \\pi}{n+2}$. We represent the mirrors as line segments extending between $O$ and $A_{1}$, and $O$ and $A_{2}$. Also let points $A_{3}, A_{4}, \\cdots, A_{n+2}$ lie in the plane su... |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $D$ and $E$ are the midpoints of $\\overline{AC}$ and $\\overline{BC}$ respectively, where $A(0,8)$, $B(0,0)$, and $C(10,0)$. Find the sum of the slope and $y$-intercept of the line passing through the points $C$ and $D$. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{36}{5}"
} | {
"split": "train",
"index": 28045,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the units digit of $31^3+13^3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 28046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function\\\\(f(x)= \\\\begin{cases} (-1)^{n}\\\\sin \\\\dfrac {πx}{2}+2n,\\\\;x∈\\[2n,2n+1) \\\\\\\\ (-1)^{n+1}\\\\sin \\\\dfrac {πx}{2}+2n+2,\\\\;x∈\\[2n+1,2n+2)\\\\end{cases}(n∈N)\\\\)，if the sequence\\\\(\\\\{a\\_{m}\\\\}\\\\) satisfies\\\\(a\\_{m}=f(m)\\\\;(m∈N^{\... | math | {
"style": "rule",
"ground_truth": "909"
} | {
"split": "train",
"index": 28047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "8 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 28048,
"solution": ""
} |
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