data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "In the given triangle $ABC$, construct the points $C_{1}$ on side $AB$ and $A_{1}$ on side $BC$ such that the intersection point $P$ of lines $AA_{1}$ and $CC_{1}$ satisfies $AP / PA_{1} = 3 / 2$ and $CP / PC_{1} = 2 / 1$. In what ratio does point $C_{1}$ divide side $AB$? Let'... | math | {
"style": "rule",
"ground_truth": "2/3"
} | {
"split": "train",
"index": 20649,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( ABC \\) be a triangle with \\(\\angle A = 60^\\circ\\). Line \\(\\ell\\) intersects segments \\( AB \\) and \\( AC \\) and splits triangle \\( ABC \\) into an equilateral triangle and a quadrilateral. Let \\( X \\) and \\( Y \\) be on \\(\\ell\\) such that lines \\( BX ... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 20650,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find out the maximum value of the numbers of edges of a solid regular octahedron that we can see from a point out of the regular octahedron.(We define we can see an edge $AB$ of the regular octahedron from point $P$ outside if and only if the intersection of non degenerate tria... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 20651,
"solution": "\nTo determine the maximum number of edges of a regular octahedron that can be seen from a point outside the octahedron, we start by considering the geometric properties of the octahedron and the visibility conditions.\n\nA regular octahedron has 12 edges. The visi... |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $C: \\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1(a>b>0)$, its foci are equal to the minor axis length of the ellipse $Ω:x^{2}+ \\frac{y^{2}}{4}=1$, and the major axis lengths of C and Ω are equal.\n(1) Find the equation of ellipse C;\n(2) Let $F_1$, $F_2$ be t... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 20652,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let triangle $PQR$ be a right triangle in the xy-plane with a right angle at $R$. Given that the length of the hypotenuse $PQ$ is $50$, and that the medians through $P$ and $Q$ lie along the lines $y=x+2$ and $y=3x+5$ respectively, find the area of triangle $PQR$. Let's think s... | math | {
"style": "rule",
"ground_truth": "\\frac{125}{3}"
} | {
"split": "train",
"index": 20653,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence \\(\\left\\{a_{n}\\right\\}\\) is defined as follows:\n\\[ \n\\begin{align*}\na_{1} &= 0, \\\\\na_{2} &= 1, \\\\\na_{n+1} &= \\frac{\\sqrt{6}-\\sqrt{2}}{2} a_{n} - a_{n-1} \\quad \\text{for } n \\geq 2.\n\\end{align*}\n\\]\n\nDetermine the value of \\(a_{2019}\\). ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6} - \\sqrt{2}}{2}"
} | {
"split": "train",
"index": 20654,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify the product \\[\\frac{9}{5}\\cdot\\frac{14}{9}\\cdot\\frac{19}{14} \\dotsm \\frac{5n+4}{5n-1} \\dotsm \\frac{1009}{1004}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1009}{5}"
} | {
"split": "train",
"index": 20655,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sides $\\overline{AB}$ and $\\overline{EF}$ of regular hexagon $ABCDEF$ are extended to meet at point $P$. What is the degree measure of angle $P$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60^\\circ"
} | {
"split": "train",
"index": 20656,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sphere intersects the $xy$-plane in a circle centered at $(3,5,0)$ with a radius of 2. The sphere also intersects the $yz$-plane in a circle centered at $(0,5,-8),$ with radius $r.$ Find $r.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{59}"
} | {
"split": "train",
"index": 20657,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Yannick has a bicycle lock with a 4-digit passcode whose digits are between 0 and 9 inclusive. (Leading zeroes are allowed.) The dials on the lock is currently set at 0000. To unlock the lock, every second he picks a contiguous set of dials, and increases or decreases all of th... | math | {
"style": "rule",
"ground_truth": "(12,2)"
} | {
"split": "train",
"index": 20658,
"solution": "To simplify the solution, we instead consider the equivalent problem of reducing a passcode to 0000 using the given move. Given a passcode $a_{1} a_{2} a_{3} a_{4}$, define a differential of the passcode to be a quintuple ( $d_{1}, d_{2}, d_{3}, d_{4}, d_{5}$ ) suc... |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $mx^{2}+y^{2}=1$ and one of its asymptotes has a slope of $2$, find the value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 20659,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of six-digit palindromes. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "900"
} | {
"split": "train",
"index": 20660,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ and $z$ be positive real numbers. Find the minimum value of\n\\[\\frac{4z}{2x + y} + \\frac{4x}{y + 2z} + \\frac{y}{x + z}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 20661,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute without using a calculator: $9!/8!$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 20662,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular dodecagon ($12$ sides) is inscribed in a circle with radius $r$ inches. The area of the dodecagon, in square inches, is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3r^2"
} | {
"split": "train",
"index": 20663,
"solution": "To find the area of a regular dodecagon inscribed in a circle, we can break the dodecagon into 12 congruent isosceles triangles, each having a vertex at the center of the circle.\n\n1. **Calculate the central angle of each triangle:**\n A regular dodecagon has 12... |
deepscaler | [
{
"role": "user",
"content": "Find the natural number $A$ such that there are $A$ integer solutions to $x+y\\geq A$ where $0\\leq x \\leq 6$ and $0\\leq y \\leq 7$ . \n\n*Proposed by David Tang* Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 20664,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a $3 \\times 3$ chessboard, each square contains a knight with $\\frac{1}{2}$ probability. What is the probability that there are two knights that can attack each other? (In chess, a knight can attack any piece which is two squares away from it in a particular direction and ... | math | {
"style": "rule",
"ground_truth": "\\frac{209}{256}"
} | {
"split": "train",
"index": 20665,
"solution": "Notice that a knight on the center square cannot attack any other square on the chessboard, so whether it contains a knight or not is irrelevant. For ease of reference, we label the other eight squares as follows: \\begin{tabular}{|c|c|c|} \\hline 0 & 5 & 2 \\\\ \\... |
deepscaler | [
{
"role": "user",
"content": "Knowing the horizontal component of the tension force, find the minimum force acting on a buoy from the current.\n\nConsider the forces acting on the buoy along the horizontal axis: the force from the current acts in one direction, and the horizontal component of the tension fo... | math | {
"style": "rule",
"ground_truth": "400"
} | {
"split": "train",
"index": 20666,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the point $\\left( 5, \\frac{3 \\pi}{2} \\right)$ in polar coordinates to rectangular coordinates. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(0,-5)"
} | {
"split": "train",
"index": 20667,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum:\n\\[\n\\sum_{n=1}^\\infty \\frac{n^3 + n^2 + n - 1}{(n+3)!}\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": 20668,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When two numbers are sequentially and randomly picked from the set {1, 2, 3, 4}, what is the probability that the product of the two picked numbers is even? 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": 20669,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $15 \\cdot \\frac{7}{10} \\cdot \\frac{1}{9}$. 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": 20670,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $[x]$ denote the greatest integer not exceeding $x$, and let $\\{x\\} = x - [x]$. Find the value of the sum $\\left\\{\\frac{2012+1}{5}\\right\\} + \\left\\{\\frac{2012+2}{5}\\right\\} + \\left\\{\\frac{2012+3}{5}\\right\\} + \\cdots + \\left\\{\\frac{2012+2012}{5}\\right\\... | math | {
"style": "rule",
"ground_truth": "805.4"
} | {
"split": "train",
"index": 20671,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arnold and Kevin are playing a game in which Kevin picks an integer \\(1 \\leq m \\leq 1001\\), and Arnold is trying to guess it. On each turn, Arnold first pays Kevin 1 dollar in order to guess a number \\(k\\) of Arnold's choice. If \\(m \\geq k\\), the game ends and he pays ... | math | {
"style": "rule",
"ground_truth": "859"
} | {
"split": "train",
"index": 20672,
"solution": "We let \\(f(n)\\) denote the smallest amount we can guarantee to pay at most if Arnold's first choice is \\(n\\). For each \\(k<n\\), if Arnold's first choice is \\(k+1\\), in both worst case scenarios, he could end up paying either \\(n-k\\) or \\(11+f(k)\\). It i... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha$ is an acute angle and satisfies $\\cos(\\alpha+\\frac{\\pi}{4})=\\frac{\\sqrt{3}}{3}$. \n$(1)$ Find the value of $\\sin(\\alpha+\\frac{7\\pi}{12})$. \n$(2)$ Find the value of $\\cos(2\\alpha+\\frac{\\pi}{6})$. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{6}-1}{6}"
} | {
"split": "train",
"index": 20673,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the following expression as a simplified fraction. $$1+\\cfrac{3}{4+\\cfrac{5}{6}}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{47}{29}"
} | {
"split": "train",
"index": 20674,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane, a polar coordinate system is established with the origin as the pole and the non-negative half of the x-axis as the polar axis. It is known that point A has polar coordinates $$( \\sqrt{2}, \\frac{\\pi}{4})$$, and the parametric equation of li... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{2}}{5}"
} | {
"split": "train",
"index": 20675,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given rectangle ABCD where E is the midpoint of diagonal BD, point E is connected to point F on segment DA such that DF = 1/4 DA. Find the ratio of the area of triangle DFE to the area of quadrilateral ABEF. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{7}"
} | {
"split": "train",
"index": 20676,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Olga Ivanovna, the homeroom teacher of class 5B, is staging a \"Mathematical Ballet\". She wants to arrange the boys and girls so that every girl has exactly 2 boys at a distance of 5 meters from her. What is the maximum number of girls that can participate in the ballet if it ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 20677,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ such that $\\sqrt{n}-\\sqrt{n-1}<0.02$?\nA) 624 \nB) 625 \nC) 626 \nD) 627 \nE) 628 Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "626"
} | {
"split": "train",
"index": 20678,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In trapezoid $ABCD$ with $\\overline{BC}\\parallel\\overline{AD}$, let $BC = 700$ and $AD = 1400$. Let $\\angle A = 45^\\circ$, $\\angle D = 45^\\circ$, and $P$ and $Q$ be the midpoints of $\\overline{BC}$ and $\\overline{AD}$, respectively. Find the length $PQ$. Let's think st... | math | {
"style": "rule",
"ground_truth": "350"
} | {
"split": "train",
"index": 20679,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A, B, C, D, and E are five students who obtained the top 5 positions (no ties) in a math competition. When taking a photo, they stood in a line and each of them made the following statement:\n\nA said: The two students next to me have rankings lower than mine;\nB said: The two ... | math | {
"style": "rule",
"ground_truth": "23514"
} | {
"split": "train",
"index": 20680,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Some expressions containing square roots can be written as the square of another expression, such as $3+2\\sqrt{2}={(1+\\sqrt{2})}^{2}$. Let $a+b\\sqrt{2}=(m+n\\sqrt{2})^{2}$ (where $a$, $b$, $m$, $n$ are all positive integers), then we have $a+b\\sqrt{2}=m^{2}+2n^{2}+2mn\\sqrt... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{6}+\\frac{\\sqrt{7}}{6}"
} | {
"split": "train",
"index": 20681,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The region consisting of all points in three-dimensional space within 3 units of line segment $\\overline{AB}$ has volume $216\\pi$. What is the length $\\textit{AB}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 20682,
"solution": "1. **Understanding the Geometry**: The region described is a cylinder with hemispheres capping both ends. The radius of the cylinder and hemispheres is $3$ units.\n\n2. **Volume of Hemispheres**: Each hemisphere has a radius of $3$ units. The volume $V$ of a sphere... |
deepscaler | [
{
"role": "user",
"content": "Find the number of integer values of $k$ in the closed interval $[-500,500]$ for which the equation $\\log(kx)=2\\log(x+2)$ has exactly one real solution. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "501"
} | {
"split": "train",
"index": 20683,
"solution": "[asy] Label f; f.p=fontsize(5); xaxis(-3,3,Ticks(f,1.0)); yaxis(-3,26,Ticks(f,1.0)); real f(real x){return (x+2)^2;} real g(real x){return x*-1;} real h(real x){return x*-2;} real i(real x){return x*-3;} real j(real x){return x*8;} draw(graph(f,-2,3),green); draw(g... |
deepscaler | [
{
"role": "user",
"content": "A 7' × 11' table sits in the corner of a square room. The table is to be rotated so that the side formerly 7' now lies along what was previously the end side of the longer dimension. Determine the smallest integer value of the side S of the room needed to accommodate this move.... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 20684,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the country Betia, there are 125 cities, some of which are connected by express trains that do not stop at intermediate stations. It is known that any four cities can be visited in a circular order. What is the minimum number of city pairs connected by express trains? Let's ... | math | {
"style": "rule",
"ground_truth": "7688"
} | {
"split": "train",
"index": 20685,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB = 9$, $BC = 12$, $AC = 15$, and $CD$ is the angle bisector. Find the length of $CD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 \\sqrt{10}"
} | {
"split": "train",
"index": 20686,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a_1, a_2, b_1, b_2, b_3$ are real numbers, and $-1, a_1, a_2, -4$ form an arithmetic sequence, $-4, b_1, b_2, b_3, -1$ form a geometric sequence, calculate the value of $\\left(\\frac{a_2 - a_1}{b_2}\\right)$. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 20687,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The set \\( A = \\left\\{ x \\left\\lvert\\, x = \\left\\lfloor \\frac{5k}{6} \\right\\rfloor \\right., k \\in \\mathbb{Z}, 100 \\leqslant k \\leqslant 999 \\right\\} \\), where \\(\\left\\lfloor x \\right\\rfloor\\) denotes the greatest integer less than or equal to \\( x \\).... | math | {
"style": "rule",
"ground_truth": "750"
} | {
"split": "train",
"index": 20688,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the least positive integer $n$ such that $$\\frac 1{\\sin 45^\\circ\\sin 46^\\circ}+\\frac 1{\\sin 47^\\circ\\sin 48^\\circ}+\\cdots+\\frac 1{\\sin 133^\\circ\\sin 134^\\circ}=\\frac 1{\\sin n^\\circ}.$$ Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 20689,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of the expression\n\n$$\n\\frac{a}{x} + \\frac{a+b}{x+y} + \\frac{a+b+c}{x+y+z}\n$$\n\nwhere \\( a, b, c \\in [2,3] \\), and the triplet of numbers \\( x, y, z \\) is some permutation of the triplet \\( a, b, c \\). Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "15/4"
} | {
"split": "train",
"index": 20690,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diameter \\( AB \\) and the chord \\( CD \\) intersect at point \\( M \\). Given that \\( \\angle CMB = 73^\\circ \\) and the angular measure of arc \\( BC \\) is \\( 110^\\circ \\). Find the measure of arc \\( BD \\). Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 20691,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer $b$ for which $x^2 + bx + 2023$ factors into a product of two polynomials, each with integer coefficients. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "136"
} | {
"split": "train",
"index": 20692,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 10 numbers written in a circle, and their sum is 100. It is known that the sum of any three consecutive numbers is not less than 29.\n\nDetermine the smallest number \\( A \\) such that in any such set of numbers, each number does not exceed \\( A \\). Let's think ste... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 20693,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A digital clock displays time in a 24-hour format (from 00:00 to 23:59). Find the largest possible sum of the digits in this time display. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 20694,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer which cannot be expressed in the form \\(\\frac{2^{a}-2^{b}}{2^{c}-2^{d}}\\) where \\(a, b, c, d\\) are non-negative integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 20695,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The vertices of the broken line $A B C D E F G$ have coordinates $A(-1, -7), B(2, 5), C(3, -8), D(-3, 4), E(5, -1), F(-4, -2), G(6, 4)$.\n\nFind the sum of the angles with vertices at points $B, E, C, F, D$. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 20696,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cuckoo clock rings \"cuckoo\" every hour, with the number of rings corresponding to the hour shown by the hour hand (e.g., at 7:00, it rings 7 times). One morning, Maxim approached the clock at 9:05 and started moving the minute hand until 7 hours had passed. How many times d... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 20697,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $R$ be the set of all possible remainders when a number of the form $2^n$, $n$ a nonnegative integer, is divided by 1000. Let $S$ be the sum of the elements in $R$. Find the remainder when $S$ is divided by 1000. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 20698,
"solution": "If we write out the remainders when powers of $2$ are divided by $1000$, we must eventually write a number we have already written down. After this happens, we will fall into a cycle, and thus, nothing new will be written down.\n The answer extraction of the proble... |
deepscaler | [
{
"role": "user",
"content": "What perfect-square integer is closest to 273? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "289"
} | {
"split": "train",
"index": 20699,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of ordered pairs $(x, y)$ such that $0 < x \\le 1, 0<y\\le 1,$ and $\\left[\\log_2{\\left(\\frac 1x\\right)}\\right]$ and $\\left[\\log_5{\\left(\\frac 1y\\right)}\\right]$ are both even. Given that the area of the graph of $S$ is $m/n,$ where $m$ and $n$ are... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 20700,
"solution": "$\\left\\lfloor\\log_2\\left(\\frac{1}{x}\\right)\\right\\rfloor$ is even when\n\\[x \\in \\left(\\frac{1}{2},1\\right) \\cup \\left(\\frac{1}{8},\\frac{1}{4}\\right) \\cup \\left(\\frac{1}{32},\\frac{1}{16}\\right) \\cup \\cdots\\]\n Likewise: $\\left\\lfloor\\log... |
deepscaler | [
{
"role": "user",
"content": "For a row of six students, calculate:\n(1) How many different arrangements are there if student A cannot be in the first or the last position?\n(2) How many different arrangements are there if students A, B, and C cannot stand next to each other? (Formulate your answer with exp... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 20701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The angle bisectors \\( A L_{1} \\) and \\( B L_{2} \\) of triangle \\( A B C \\) intersect at point \\( I \\). It is known that \\( A I : I L_{1} = 3 \\) and \\( B I : I L_{2} = 2 \\). Find the ratio of the sides of triangle \\( A B C \\). Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "3:4:5"
} | {
"split": "train",
"index": 20702,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x^{3}+ax^{2}+bx+a^{2}$ has an extremum of $10$ at $x=1$, find the value of $f(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 20703,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One way to pack a 100 by 100 square with 10000 circles, each of diameter 1, is to put them in 100 rows with 100 circles in each row. If the circles are repacked so that the centers of any three tangent circles form an equilateral triangle, what is the maximum number of addition... | math | {
"style": "rule",
"ground_truth": "1443"
} | {
"split": "train",
"index": 20704,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $2.4 \\times 0.2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.48"
} | {
"split": "train",
"index": 20705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kelvin the Frog lives in the 2-D plane. Each day, he picks a uniformly random direction (i.e. a uniformly random bearing $\\theta\\in [0,2\\pi]$ ) and jumps a mile in that direction. Let $D$ be the number of miles Kelvin is away from his starting point after ten days. Det... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 20706,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what single digit $n$ does 91 divide the 9-digit number $12345 n 789$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 20707,
"solution": "Solution 1: 123450789 leaves a remainder of 7 when divided by 91, and 1000 leaves a remainder of 90, or -1, so adding 7 multiples of 1000 will give us a multiple of 91. Solution 2: For those who don't like long division, there is a quicker way. First notice that $9... |
deepscaler | [
{
"role": "user",
"content": "If $\\cos (π+α)=- \\frac { \\sqrt {10}}{5}$ and $α∈(- \\frac {π}{2},0)$, find the value of $\\tan ( \\frac {3π}{2}+α)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac { \\sqrt {6}}{3}"
} | {
"split": "train",
"index": 20708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In duck language, only letters $q$ , $a$ , and $k$ are used. There is no word with two consonants after each other, because the ducks cannot pronounce them. However, all other four-letter words are meaningful in duck language. How many such words are there? \nIn duck langua... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 20709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}=(\\cos \\alpha,\\sin \\alpha)$, $\\overrightarrow{b}=(\\cos x,\\sin x)$, $\\overrightarrow{c}=(\\sin x+2\\sin \\alpha,\\cos x+2\\cos \\alpha)$, where $(0 < \\alpha < x < \\pi)$.\n$(1)$ If $\\alpha= \\frac {\\pi}{4}$, find the minimum value of ... | math | {
"style": "rule",
"ground_truth": "- \\frac { \\sqrt {3}}{5}"
} | {
"split": "train",
"index": 20710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < β < \\dfrac{π}{2} < α < π$, and $\\cos (α- \\dfrac{β}{2} )= \\dfrac{5}{13} $, $\\sin ( \\dfrac{α}{2}-β)= \\dfrac{3}{5} $. Find the values of:\n$(1) \\tan (α- \\dfrac{β}{2} )$\n$(2) \\cos ( \\dfrac{α+β}{2} )$ Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "\\dfrac{56}{65}"
} | {
"split": "train",
"index": 20711,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $|x+2|+|1-x|=9-|y-5|-|1+y|$, find the maximum and minimum values of $x+y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 20712,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Amerigo Vespucci has a map of America drawn on the complex plane. The map does not distort distances. Los Angeles corresponds to $0$ on this complex plane, and Boston corresponds to $2600i$. Meanwhile, Knoxville corresponds to the point $780+1040i$. With these city-point corres... | math | {
"style": "rule",
"ground_truth": "1300"
} | {
"split": "train",
"index": 20713,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be nonnegative real numbers such that $a + b + c = 1.$ Find the maximum value of\n\\[\\frac{ab}{a + b} + \\frac{ac}{a + c} + \\frac{bc}{b + c}.\\] 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": 20714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four new students are to be assigned to three classes: A, B, and C, with at least one student in each class. Student A cannot be assigned to class A. How many different assignment plans are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 20715,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "No two people stand next to each other, find the probability that, out of the ten people sitting around a circular table, no two adjacent people will stand after flipping their fair coins. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{123}{1024}"
} | {
"split": "train",
"index": 20716,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $b^2$ if the foci of the ellipse $\\frac{x^2}{25} + \\frac{y^2}{b^2} = 1$ and the foci of the hyperbola\n\\[\\frac{x^2}{196} - \\frac{y^2}{121} = \\frac{1}{49}\\] coincide. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{908}{49}"
} | {
"split": "train",
"index": 20717,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At Typico High School, $60\\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\\%$ say that they dislike it, and the rest say that they like... | math | {
"style": "rule",
"ground_truth": "25\\%"
} | {
"split": "train",
"index": 20718,
"solution": "1. **Assume Total Number of Students**: Let's assume there are 100 students at Typico High School for simplicity in calculation.\n\n2. **Students Who Like Dancing**: \n - Given that 60% of the students like dancing.\n - Therefore, $60\\% \\times 100 = 60$ stude... |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow {m}=(\\cos\\alpha- \\frac { \\sqrt {2}}{3}, -1)$, $\\overrightarrow {n}=(\\sin\\alpha, 1)$, and $\\overrightarrow {m}$ is collinear with $\\overrightarrow {n}$, and $\\alpha\\in[-\\pi,0]$. \n(Ⅰ) Find the value of $\\sin\\alpha+\\cos\\alpha$; \n... | math | {
"style": "rule",
"ground_truth": "\\frac {7}{12}"
} | {
"split": "train",
"index": 20719,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be real numbers such that $9a^2 + 4b^2 + 25c^2 = 1.$ Find the maximum value of\n\\[8a + 3b + 5c.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7\\sqrt{2}"
} | {
"split": "train",
"index": 20720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The bases of a trapezoid are 2 cm and 3 cm long. A line passing through the intersection point of the diagonals and parallel to the bases intersects the legs at points X and Y. What is the distance between points X and Y? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "2.6"
} | {
"split": "train",
"index": 20721,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Leah has $13$ coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth? Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 20722,
"solution": "1. **Understanding the problem**: Leah has a total of 13 coins consisting of pennies and nickels. If she had one more nickel, she would have an equal number of pennies and nickels.\n\n2. **Setting up equations**: Let $p$ be the number of pennies and $n$ be the numb... |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin \\alpha - \\cos \\alpha = \\frac{\\sqrt{10}}{5}$, $\\alpha \\in (\\pi, 2\\pi)$,\n\n$(1)$ Find the value of $\\sin \\alpha + \\cos \\alpha$;\n\n$(2)$ Find the value of $\\tan \\alpha - \\frac{1}{\\tan \\alpha}$. Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "-\\frac{8}{3}"
} | {
"split": "train",
"index": 20723,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the degree measure of angle $LOQ$ when polygon $\\allowbreak LMNOPQ$ is a regular hexagon? [asy]\ndraw((-2,0)--(-1,1.73205081)--(1,1.73205081)--(2,0)--(1,-1.73205081)--(-1,-1.73205081)--cycle);\ndraw((-1,-1.73205081)--(1,1.73205081)--(1,-1.73205081)--cycle);\nlabel(\"L\... | math | {
"style": "rule",
"ground_truth": "30^\\circ"
} | {
"split": "train",
"index": 20724,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest three-digit positive integer $n$ for which the sum of the first $n$ positive integers is not a divisor of the product of the first $n$ positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "996"
} | {
"split": "train",
"index": 20725,
"solution": "\n1. **Understanding the Problem:**\n We need to find the largest three-digit integer $n$ such that the sum of the first $n$ positive integers is not a divisor of the product of the first $n$ positive integers.\n\n2. **Sum and Product Formulas:**\n - The sum of... |
deepscaler | [
{
"role": "user",
"content": "A new model car travels 4.4 kilometers more per liter of gasoline than an old model car. Additionally, the fuel consumption per 100 km for the new model is 2 liters less than that of the old model. How many liters of gasoline does the new model car consume per 100 km? Round the... | math | {
"style": "rule",
"ground_truth": "5.82"
} | {
"split": "train",
"index": 20726,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "a) Vanya flips a coin 3 times, and Tanya flips a coin 2 times. What is the probability that Vanya gets more heads than Tanya?\n\nb) Vanya flips a coin $n+1$ times, and Tanya flips a coin $n$ times. What is the probability that Vanya gets more heads than Tanya? Let's think step ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 20727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}=(1,2)$ and $\\overrightarrow{b}=(0,3)$, the projection of $\\overrightarrow{b}$ in the direction of $\\overrightarrow{a}$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 20728,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are $270$ students at Colfax Middle School, where the ratio of boys to girls is $5 : 4$. There are $180$ students at Winthrop Middle School, where the ratio of boys to girls is $4 : 5$. The two schools hold a dance and all students from both schools attend. What fraction ... | math | {
"style": "rule",
"ground_truth": "\\frac{22}{45}"
} | {
"split": "train",
"index": 20729,
"solution": "1. **Calculate the number of girls at Colfax Middle School:**\n - The total number of students at Colfax Middle School is $270$.\n - The ratio of boys to girls at Colfax Middle School is $5:4$. Let the number of boys be $5x$ and the number of girls be $4x$.\n ... |
deepscaler | [
{
"role": "user",
"content": "I need to learn vocabulary words for my Spanish exam. There are 500 words and the exam grade is the percentage of these words that I recall correctly. Assuming I will recall correctly the words I learn and assuming my guesses will not yield any points, what is the least number ... | math | {
"style": "rule",
"ground_truth": "425"
} | {
"split": "train",
"index": 20730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\triangle ABC$ be a right triangle such that $B$ is a right angle. A circle with diameter of $BC$ meets side $AC$ at $D.$ If the area of $\\triangle ABC$ is $150$ and $AC = 25,$ then what is $BD$? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 20731,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nThere are 1001 people sitting around a round table, each of whom is either a knight (always tells the truth) or a liar (always lies). It turned out that next to each knight there is exactly one liar, and next to each liar there is exactly one knight. What is the minimum numbe... | math | {
"style": "rule",
"ground_truth": "501"
} | {
"split": "train",
"index": 20732,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the product $(\\frac{4}{8})(\\frac{8}{12})(\\frac{12}{16})\\cdots(\\frac{2016}{2020})$. 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{2}{505}"
} | {
"split": "train",
"index": 20733,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an airspace, there are clouds. It turned out that the space can be divided into parts by ten planes so that each part contains no more than one cloud. Through how many clouds could an airplane fly at most while following a straight course? Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 20734,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a, b, c$, and $d$ are pairwise distinct positive integers that satisfy \\operatorname{lcm}(a, b, c, d)<1000$ and $a+b=c+d$, compute the largest possible value of $a+b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "581"
} | {
"split": "train",
"index": 20735,
"solution": "Let $a^{\\prime}=\\frac{\\operatorname{lcm}(a, b, c, d)}{a}$. Define $b^{\\prime}, c^{\\prime}$, and $d^{\\prime}$ similarly. We have that $a^{\\prime}, b^{\\prime}, c^{\\prime}$, and $d^{\\prime}$ are pairwise distinct positive integers that satisfy $$\\frac{1}{a^... |
deepscaler | [
{
"role": "user",
"content": "Compute the distance between the parallel lines given by\n\\[\\begin{pmatrix} 2 \\\\ -3 \\end{pmatrix} + t \\begin{pmatrix} 1 \\\\ -7 \\end{pmatrix}\\]and\n\\[\\begin{pmatrix} 1 \\\\ -5 \\end{pmatrix} + s \\begin{pmatrix} 1 \\\\ -7 \\end{pmatrix}.\\] Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "\\frac{9 \\sqrt{2}}{10}"
} | {
"split": "train",
"index": 20736,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When three standard dice are tossed, the numbers $a, b, c$ are obtained. Find the probability that $abc = 72$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{24}"
} | {
"split": "train",
"index": 20737,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A local government intends to encourage entrepreneurship by rewarding newly established small and micro enterprises with an annual output value between 500,000 and 5,000,000 RMB. The reward scheme follows these principles: The bonus amount $y$ (in ten thousand RMB) increases wi... | math | {
"style": "rule",
"ground_truth": "315"
} | {
"split": "train",
"index": 20738,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An equivalent of the expression\n$\\left(\\frac{x^2+1}{x}\\right)\\left(\\frac{y^2+1}{y}\\right)+\\left(\\frac{x^2-1}{y}\\right)\\left(\\frac{y^2-1}{x}\\right)$, $xy \\not= 0$,\nis: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2xy+\\frac{2}{xy}"
} | {
"split": "train",
"index": 20739,
"solution": "1. **Start by rewriting the expression**:\n \\[\n \\left(\\frac{x^2+1}{x}\\right)\\left(\\frac{y^2+1}{y}\\right)+\\left(\\frac{x^2-1}{y}\\right)\\left(\\frac{y^2-1}{x}\\right)\n \\]\n\n2. **Simplify each term separately**:\n - For the first term:\n \\[\... |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $5^{207}$ is divided by 7? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 20740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convex polygons $P_1$ and $P_2$ are drawn in the same plane with $n_1$ and $n_2$ sides, respectively, $n_1\\le n_2$. If $P_1$ and $P_2$ do not have any line segment in common, then the maximum number of intersections of $P_1$ and $P_2$ is: Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "n_1n_2"
} | {
"split": "train",
"index": 20741,
"solution": "1. **Understanding the Problem**: We are given two convex polygons $P_1$ and $P_2$ with $n_1$ and $n_2$ sides respectively, where $n_1 \\leq n_2$. The polygons do not share any line segment, and we need to find the maximum number of intersections between these two ... |
deepscaler | [
{
"role": "user",
"content": "What is the value of $(2^0 - 1 + 5^2 - 0)^{-1} \\times 5?$ 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": 20742,
"solution": "1. **Evaluate the expression inside the parentheses**: \n \\[\n 2^0 - 1 + 5^2 - 0\n \\]\n - \\(2^0 = 1\\) because any non-zero number raised to the power of 0 is 1.\n - \\(5^2 = 25\\) because squaring 5 gives 25.\n - Therefore, the expression simplifies... |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $E$: $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1(a > b > 0)$, its minor axis length is $2$, and the eccentricity is $\\frac{\\sqrt{6}}{3}$. The line $l$ passes through the point $(-1,0)$ and intersects the ellipse $E$ at points $A$ and $B$. $O$ is the coordi... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}}{3}"
} | {
"split": "train",
"index": 20743,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a grid of height 2 stretching infinitely in one direction. Between any two edge-adjacent cells of the grid, there is a door that is locked with probability $\\frac{1}{2}$ independent of all other doors. Philip starts in a corner of the grid (in the starred cell). Compu... | math | {
"style": "rule",
"ground_truth": "\\frac{32}{7}"
} | {
"split": "train",
"index": 20744,
"solution": "For clarity, we will number our grid, with $(0,0)$ being the corner that Philip starts in, and the grid stretching in the positive $x$ direction, i.e. all elements of the grid are of the form $(x, y)$, with $y \\in\\{0,1\\}$ and $x \\in \\mathbb{N}$. We will use re... |
deepscaler | [
{
"role": "user",
"content": "Let \\( X \\), \\( Y \\), and \\( Z \\) be nonnegative integers such that \\( X+Y+Z = 15 \\). What is the maximum value of \\[ X\\cdot Y\\cdot Z + X\\cdot Y + Y\\cdot Z + Z\\cdot X ? \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 20745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $(2^5+7^3)(2^3-(-2)^2)^8$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24576000"
} | {
"split": "train",
"index": 20746,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In quadrilateral $ABCD$, $\\angle B$ is a right angle, diagonal $\\overline{AC}$ is perpendicular to $\\overline{CD}$, $AB=18$, $BC=21$, and $CD=14$. Find the perimeter of $ABCD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 20747,
"solution": "From the problem statement, we construct the following diagram:\n[asy] pointpen = black; pathpen = black + linewidth(0.65); pair C=(0,0), D=(0,-14),A=(-(961-196)^.5,0),B=IP(circle(C,21),circle(A,18)); D(MP(\"A\",A,W)--MP(\"B\",B,N)--MP(\"C\",C,E)--MP(\"D\",D,E)--A-... |
deepscaler | [
{
"role": "user",
"content": "The extensions of a telephone exchange have only 2 digits, from 00 to 99. Not all extensions are in use. By swapping the order of two digits of an extension in use, you either get the same number or the number of an extension not in use. What is the highest possible number of e... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 20748,
"solution": ""
} |
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