data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Indicate the integer closest to the number: \\(\\sqrt{2012-\\sqrt{2013 \\cdot 2011}}+\\sqrt{2010-\\sqrt{2011 \\cdot 2009}}+\\ldots+\\sqrt{2-\\sqrt{3 \\cdot 1}}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 24349,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "I have the following terms of an arithmetic sequence: $\\frac{1}{2}, x-1, 3x, \\ldots$. Solve for $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{2}"
} | {
"split": "train",
"index": 24350,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jane's quiz scores were 98, 97, 92, 85 and 93. What was her mean score? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "93"
} | {
"split": "train",
"index": 24351,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A mischievous child mounted the hour hand on the minute hand's axle and the minute hand on the hour hand's axle of a correctly functioning clock. The question is, how many times within a day does this clock display the correct time? Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 24352,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many even divisors does \\(8!\\) have, and how many of those are also multiples of both 2 and 3? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 24353,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A lucky integer is a positive integer which is divisible by the sum of its digits. What is the least positive multiple of 6 that is not a lucky integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "114"
} | {
"split": "train",
"index": 24354,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ten test papers are to be prepared for the National Olympiad. Each paper has 4 problems, and no two papers have more than 1 problem in common. At least how many problems are needed? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 24355,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A spinner was created by drawing five radii from the center of a circle. The first four radii divide the circle into four equal wedges. The fifth radius divides one of the wedges into two parts, one having twice the area of the other. The five wedges are labeled with the wedge ... | math | {
"style": "rule",
"ground_truth": "7/12"
} | {
"split": "train",
"index": 24356,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a table tennis singles match between players A and B, the match is played in a best-of-seven format (i.e., the first player to win four games wins the match, and the match ends). Assume that both players have an equal chance of winning each game. \n(1) Calculate the probabi... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{16}"
} | {
"split": "train",
"index": 24357,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express 826,000,000 in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.26 \\times 10^{8}"
} | {
"split": "train",
"index": 24358,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\sin x = 3 \\cos x,$ then what is $\\sin x \\cos x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"split": "train",
"index": 24359,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alloy $A$ of two metals has a mass of 6 kg, with the first metal being twice as abundant as the second metal. When placed in a container of water, it exerts a force of $30\\ \\mathrm{N}$ on the bottom. Alloy $B$ of the same metals has a mass of 3 kg, with the first metal being ... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 24360,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point $(x,y)$ is a distance of 15 units from the $x$-axis. It is a distance of 13 units from the point $(2,7)$. It is a distance $n$ from the origin. Given that $x>2$, what is $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{334 + 4\\sqrt{105}}"
} | {
"split": "train",
"index": 24361,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry t... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 24362,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( 10^{x} \\cdot 10^{5}=100^{4} \\), what is the value of \\( x \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 24363,
"solution": "Since \\( 100=10^{2} \\), then \\( 100^{4}=(10^{2})^{4}=10^{8} \\). Therefore, we must solve the equation \\( 10^{x} \\cdot 10^{5}=10^{8} \\), which is equivalent to \\( 10^{x+5}=10^{8} \\). Thus, \\( x+5=8 \\) or \\( x=3 \\)."
} |
deepscaler | [
{
"role": "user",
"content": "Given that $f(x)$ and $g(x)$ are functions defined on $\\mathbb{R}$, and $g(x) \\neq 0$, $f''(x)g(x) < f(x)g''(x)$, $f(x)=a^{x}g(x)$, $\\frac{f(1)}{g(1)}+ \\frac{f(-1)}{g(-1)}= \\frac{5}{2}$, determine the probability that the sum of the first $k$ terms of the sequence $\\left\... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 24364,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the integers \\( a, b, \\) and \\( c \\) satisfy:\n\\[\na + b + c = 3, \\quad a^3 + b^3 + c^3 = 3,\n\\]\nthen what is the maximum value of \\( a^2 + b^2 + c^2 \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 24365,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic sequence $\\{a_n\\}$, the sum of the first $n$ terms is $S_n$, and it is known that $a_2=1$, $S_4=8$. Find $a_5$ and $S_{10}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 24366,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The perimeter of $\\triangle ABC$ is equal to the perimeter of rectangle $DEFG$. What is the area of $\\triangle ABC$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 24367,
"solution": "The perimeter of $\\triangle ABC$ is equal to $(3x+4)+(3x+4)+2x=8x+8$. The perimeter of rectangle $DEFG$ is equal to $2 \\times (2x-2)+2 \\times (3x-1)=4x-4+6x-2=10x-6$. Since these perimeters are equal, we have $10x-6=8x+8$ which gives $2x=14$ and so $x=7$. Thus, ... |
deepscaler | [
{
"role": "user",
"content": "Given a cyclic quadrilateral \\(ABCD\\) with a circumradius of \\(200\\sqrt{2}\\) and sides \\(AB = BC = CD = 200\\). Find the length of side \\(AD\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "500"
} | {
"split": "train",
"index": 24368,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $t(x) = \\sqrt{3x+1}$ and $f(x)=5-t(x)$. What is $t(f(5))$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 24369,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two perpendicular lines, $2x + my - 1 = 0$ and $3x - 2y + n = 0$, with the foot of the perpendicular from the point $(2, p)$, find the value of $m + n + p$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 24370,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be positive real numbers such that $x + y = 10.$ Find the minimum value of $\\frac{1}{x} + \\frac{1}{y}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 24371,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, three circles of radius 2 with centers $X$, $Y$, and $Z$ are tangent to one another and to the sides of $\\triangle DEF$. Each circle touches two sides of the triangle.\n\nFind the perimeter of triangle $DEF$. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}"
} | {
"split": "train",
"index": 24372,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, there is a circle $C_{1}$: $(x-2)^{2}+(y-4)^{2}=20$. With the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. For $C_{2}$: $\\theta= \\frac {\\pi}{3}(\\rho\\in\\mathb... | math | {
"style": "rule",
"ground_truth": "8+5\\sqrt {3}"
} | {
"split": "train",
"index": 24373,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle ABC, the sides opposite to angles A, B, and C are a, b, and c respectively. Given the equation acosB - bcosA + 2c = 0, find the value of $\\frac{tanA}{tanB}$. 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": 24374,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number in the set $\\{50, 51, 52, 53, ... , 999\\}$ is randomly selected. What is the probability that it is a two-digit number? 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{1}{19}"
} | {
"split": "train",
"index": 24375,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Geoff and Trevor each roll a fair eight-sided die (the sides are labeled 1 through 8). What is the probability that the product of the numbers they roll is even or a prime number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{8}"
} | {
"split": "train",
"index": 24376,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nGiven a rectangle \\(ABCD\\). On two sides of the rectangle, different points are chosen: six points on \\(AB\\) and seven points on \\(BC\\). How many different triangles can be formed with vertices at the chosen points? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "231"
} | {
"split": "train",
"index": 24377,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $$\\sum_{n_{60}=0}^{2} \\sum_{n_{59}=0}^{n_{60}} \\cdots \\sum_{n_{2}=0}^{n_{3}} \\sum_{n_{1}=0}^{n_{2}} \\sum_{n_{0}=0}^{n_{1}} 1$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1953"
} | {
"split": "train",
"index": 24378,
"solution": "The given sum counts the number of non-decreasing 61-tuples of integers $\\left(n_{0}, \\ldots, n_{60}\\right)$ from the set $\\{0,1,2\\}$. Such 61-tuples are in one-to-one correspondence with strictly increasing 61-tuples of integers $\\left(m_{0}, \\ldots, m_{60}... |
deepscaler | [
{
"role": "user",
"content": "Given a cone and a cylinder made of rubber, the cone has a base radius of $5$ and a height of $4$, while the cylinder has a base radius of $2$ and a height of $8$. If they are remade into a new cone and a new cylinder with the same base radius, while keeping the total volume an... | math | {
"style": "rule",
"ground_truth": "r = \\sqrt{7}"
} | {
"split": "train",
"index": 24379,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the solution set of the inequality system about $x$ is $\\left\\{\\begin{array}{l}{x+1≤\\frac{2x-5}{3}}\\\\{a-x＞1}\\end{array}\\right.$ is $x\\leqslant -8$, and the solution of the fractional equation about $y$ is $4+\\frac{y}{y-3}=\\frac{a-1}{3-y}$ is a non-negative integer... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 24380,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=|x-1|+|x+1|$.\n(I) Solve the inequality $f(x) < 3$;\n(II) If the minimum value of $f(x)$ is $m$, let $a > 0$, $b > 0$, and $a+b=m$, find the minimum value of $\\frac{1}{a}+ \\frac{2}{b}$. Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}+ \\sqrt{2}"
} | {
"split": "train",
"index": 24381,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Amy and Belinda each roll a sheet of 6-inch by 8-inch paper to form a cylindrical tube. Amy tapes the two 8-inch sides together without overlap. Belinda tapes the two 6-inch sides together without overlap. What is $\\pi$ times the positive difference of the volumes of the two t... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 24382,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two integers are relatively prime if they don't share any common factors, i.e. if their greatest common divisor is 1. Define $\\varphi(n)$ as the number of positive integers that are less than $n$ and relatively prime to $n$. Define $\\varphi_{d}(n)$ as the number of positive i... | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 24383,
"solution": "For fixed $n$, the pattern of integers relatively prime to $n$ repeats every $n$ integers, so $\\varphi_{d}(n)=d \\varphi(n)$. Therefore the expression in the problem equals $\\varphi(n)^{3}$. The cube root of 64000 is $40 . \\varphi(p)=p-1$ for any prime $p$. Sinc... |
deepscaler | [
{
"role": "user",
"content": "If there exist $n$ real numbers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfying $x_{1}+2 x_{2}+\\cdots+ n x_{n}=2009$ and $x_{1}+x_{2}+\\cdots+x_{n}=0$, where each $x_{i}= \\pm 7$ for $i=1,2, \\cdots, n$, determine the minimum value of $n$. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 24384,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The constant term in the expansion of $(x^2-2)\\left(x-\\frac{2}{\\sqrt{x}}\\right)^{6}$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-480"
} | {
"split": "train",
"index": 24385,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that the sum of the squares of two complex numbers $x$ and $y$ is $7$ and the sum of the cubes is $10$. What is the largest real value that $x + y$ can have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 24386,
"solution": "Begin by assuming that $x$ and $y$ are roots of some polynomial of the form $w^2+bw+c$, such that by Vieta's Formulæ and some algebra (left as an exercise to the reader), $b^2-2c=7$ and $3bc-b^3=10$. Substituting $c=\\frac{b^2-7}{2}$, we deduce that $b^3-21b-20=0$,... |
deepscaler | [
{
"role": "user",
"content": "How many real numbers $x$ are solutions to the following equation? \\[ |x-1| = |x-2| + |x-3| \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 24387,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the equations \\(3x - 4y - 2z = 0\\) and \\(x - 2y + 5z = 0\\) with \\(z \\neq 0\\), find the numerical value of \\(\\frac{2x^2 - xy}{y^2 + 4z^2}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{744}{305}"
} | {
"split": "train",
"index": 24388,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. The vectors $m=(\\cos (A-B),\\sin (A-B))$, $n=(\\cos B,-\\sin B)$, and $m\\cdot n=-\\frac{3}{5}$.\n\n(1) Find the value of $\\sin A$.\n(2) If $a=4\\sqrt{2}$, $b=5$, find the measure ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 24389,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x+y=9$ and $xy=10$, what is the value of $x^3+y^3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "459"
} | {
"split": "train",
"index": 24390,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A three-digit number has distinct digits. By arbitrarily swapping the positions of its digits, five other three-digit numbers can be obtained. If the sum of these six three-digit numbers equals 2220, then among all the numbers that meet this condition, the smallest three-digit ... | math | {
"style": "rule",
"ground_truth": "127"
} | {
"split": "train",
"index": 24391,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The roots of the equation $x^{2}-2x = 0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:\n[Note: Abscissas means x-coordinate.] Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "y = x$, $y = x-2"
} | {
"split": "train",
"index": 24392,
"solution": "To solve this problem, we need to find the roots of the equation $x^2 - 2x = 0$ and check which pair of equations does not yield these roots when their graphs intersect.\n\n1. **Finding the roots of the equation $x^2 - 2x = 0$:**\n \\[\n x^2 - 2x = 0 \\implies ... |
deepscaler | [
{
"role": "user",
"content": "The ratio of the sums of the first n terms of the arithmetic sequences {a_n} and {b_n} is given by S_n / T_n = (2n) / (3n + 1). Find the ratio of the fifth terms of {a_n} and {b_n}. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{9}{14}"
} | {
"split": "train",
"index": 24393,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A laser is placed at the point $(3,5)$. The laser beam travels in a straight line. Larry wants the beam to hit and bounce off the $y$-axis, then hit and bounce off the $x$-axis, then hit the point $(7,5)$. What is the total distance the beam will travel along this path? Let's t... | math | {
"style": "rule",
"ground_truth": "10\\sqrt{2}"
} | {
"split": "train",
"index": 24394,
"solution": "1. **Identify Points and Reflections**:\n Let $A = (3,5)$ and $D = (7,5)$. We need to find points $B$ on the $y$-axis and $C$ on the $x$-axis where the laser beam bounces off.\n\n2. **Reflection Properties**:\n When a beam hits and bounces off a coordinate axis... |
deepscaler | [
{
"role": "user",
"content": "Alex, Mel, and Chelsea play a game that has $6$ rounds. In each round there is a single winner, and the outcomes of the rounds are independent. For each round the probability that Alex wins is $\\frac{1}{2}$, and Mel is twice as likely to win as Chelsea. What is the probabil... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{36}"
} | {
"split": "train",
"index": 24395,
"solution": "1. **Assign probabilities to each player:**\n Let $m$ be the probability that Mel wins a round, and $c$ be the probability that Chelsea wins a round. We know that:\n - Alex's probability of winning is $\\frac{1}{2}$.\n - Mel is twice as likely to win as Chels... |
deepscaler | [
{
"role": "user",
"content": "$ABCD$ is a trapezium such that $\\angle ADC=\\angle BCD=60^{\\circ}$ and $AB=BC=AD=\\frac{1}{2}CD$. If this trapezium is divided into $P$ equal portions $(P>1)$ and each portion is similar to trapezium $ABCD$ itself, find the minimum value of $P$.\n\nThe sum of tens and unit d... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 24396,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given complex numbers $\\mathrm{z}_{\\mathrm{i}} (\\mathrm{i} = 1, 2, 3, 4, 5)$ satisfying: \n$$\\left\\{\\begin{array}{c}\n\\left|z_{1}\\right| \\leq 1, \\quad \\left|z_{2}\\right| \\leq 1 \\\\\n\\left|2 z_{3}-(\\mathrm{z}_{1}+\\mathrm{z}_{2})\\right| \\leq \\left|\\mathrm{z}_... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 24397,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To bake $12$ cookies, I use $2$ quarts of milk. There are $2$ pints in a quart. How many pints of milk do I need to bake $3$ cookies? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 24398,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x+\\sqrt{81}=25$, what is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 24399,
"solution": "If $x+\\sqrt{81}=25$, then $x+9=25$ or $x=16$."
} |
deepscaler | [
{
"role": "user",
"content": "In multiplying two positive integers $a$ and $b$, Ron reversed the digits of the two-digit number $a$. His erroneous product was $161.$ What is the correct value of the product of $a$ and $b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "224"
} | {
"split": "train",
"index": 24400,
"solution": "1. **Identify the Error in Multiplication**: Ron reversed the digits of $a$ and then multiplied by $b$ to get $161$. We need to find the correct $a$ and $b$ such that reversing $a$ and multiplying by $b$ results in $161$.\n\n2. **Prime Factorization of $161$**: \n ... |
deepscaler | [
{
"role": "user",
"content": "Given a line $l$ whose inclination angle $\\alpha$ satisfies the condition $\\sin \\alpha +\\cos \\alpha = \\frac{1}{5}$, determine the slope of $l$. 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": 24401,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of \\(0.9 + 0.99\\) is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.89"
} | {
"split": "train",
"index": 24402,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Parallelogram $ABCD$ has $AB=CD=6$ and $BC=AD=10$ , where $\\angle ABC$ is obtuse. The circumcircle of $\\triangle ABD$ intersects $BC$ at $E$ such that $CE=4$ . Compute $BD$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{6}"
} | {
"split": "train",
"index": 24403,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the lines $l_{1}$: $\\left(3+a\\right)x+4y=5-3a$ and $l_{2}$: $2x+\\left(5+a\\right)y=8$, if $l_{1}$ is parallel to $l_{2}$, determine the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 24404,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sides of triangle \\(ABC\\) are divided by points \\(M, N\\), and \\(P\\) such that \\(AM : MB = BN : NC = CP : PA = 1 : 4\\). Find the ratio of the area of the triangle bounded by lines \\(AN, BP\\), and \\(CM\\) to the area of triangle \\(ABC\\). Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "3/7"
} | {
"split": "train",
"index": 24405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of positive integers $n$ for which \r\n\r\n(i) $n \\leq 1991$ ; \r\n\r\n(ii) 6 is a factor of $(n^2 + 3n +2)$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1328"
} | {
"split": "train",
"index": 24406,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of the expression \\((\\sin 3x + \\sin 2y + \\sin z)(\\cos 3x + \\cos 2y + \\cos z)\\). \n\n(Possible points: 15) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"split": "train",
"index": 24407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "1. In the Cartesian coordinate system, given three points A(5, 4), B(k, 10), and C(12, -2), for what value of k are the vectors $$\\overrightarrow {AB}$$ and $$\\overrightarrow {BC}$$ collinear?\n2. In the Cartesian coordinate system, given O as the origin, $$\\overrightarrow {... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 24408,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a convex quadrilateral \\(ABCD\\), \\(\\overrightarrow{BC} = 2 \\overrightarrow{AD}\\). Point \\(P\\) is a point in the plane of the quadrilateral such that \\(\\overrightarrow{PA} + 2020 \\overrightarrow{PB} + \\overrightarrow{PC} + 2020 \\overrightarrow{PD} = \\mathbf{0}\\... | math | {
"style": "rule",
"ground_truth": "337/2021"
} | {
"split": "train",
"index": 24409,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Angle bisectors $AA', BB'$ and $CC'$ are drawn in triangle $ABC$ with angle $\\angle B= 120^o$ . Find $\\angle A'B'C'$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 24410,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 100 points located on a line. Mark the midpoints of all possible segments with endpoints at these points. What is the minimum number of marked points that can result? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "197"
} | {
"split": "train",
"index": 24411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive value of $x$ such that $x + 4321$ results in a palindrome and that palindrome is at least 200 more than 4321? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "233"
} | {
"split": "train",
"index": 24412,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "My friend Julia likes numbers that are divisible by 4. How many different last two digits are possible in numbers that Julia likes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 24413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, $AC=2AB=4$ and $\\cos A=\\frac{1}{8}$. Calculate the length of side $BC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"split": "train",
"index": 24414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cao has 6 legs, 3 on each side. A walking pattern for the cao is defined as an ordered sequence of raising and lowering each of the legs exactly once (altogether 12 actions), starting and ending with all legs on the ground. The pattern is safe if at any point, he has at least... | math | {
"style": "rule",
"ground_truth": "1416528"
} | {
"split": "train",
"index": 24415,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three cubes, each with faces numbered from 1 to 6, are tossed. What is the probability that the sum of the numbers shown on the top faces of all three cubes is divisible by 3? Express your answer as a common fraction. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 24416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $(2^3)^3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "512"
} | {
"split": "train",
"index": 24417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct, real, infinite geometric series each have a sum of $1$ and have the same second term. The third term of one of the series is $1/8$, and the second term of both series can be written in the form $\\frac{\\sqrt{m}-n}p$, where $m$, $n$, and $p$ are positive integers ... | math | {
"style": "rule",
"ground_truth": "518"
} | {
"split": "train",
"index": 24418,
"solution": "Let the second term of each series be $x$. Then, the common ratio is $\\frac{1}{8x}$, and the first term is $8x^2$.\n So, the sum is $\\frac{8x^2}{1-\\frac{1}{8x}}=1$. Thus, $64x^3-8x+1 = (4x-1)(16x^2+4x-1) = 0 \\Rightarrow x = \\frac{1}{4}, \\frac{-1 \\pm \\sqrt{5... |
deepscaler | [
{
"role": "user",
"content": "When the mean, median, and mode of the list\n\\[10,2,5,2,4,2,x\\]\nare arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 24419,
"solution": "1. **Calculate the Mean**: \n The mean of the list $10, 2, 5, 2, 4, 2, x$ is calculated as follows:\n \\[\n \\text{Mean} = \\frac{10 + 2 + 5 + 2 + 4 + 2 + x}{7} = \\frac{25 + x}{7}.\n \\]\n\n2. **Determine the Mode**: \n The mode is the number that appear... |
deepscaler | [
{
"role": "user",
"content": "What is the area and perimeter of the smallest square that can contain a circle with a radius of 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 24420,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\triangle ABC$ with $AC=1$, $\\angle ABC= \\frac{2\\pi}{3}$, $\\angle BAC=x$, let $f(x)= \\overrightarrow{AB} \\cdot \\overrightarrow{BC}$.\n\n$(1)$ Find the analytical expression of $f(x)$ and indicate its domain;\n\n$(2)$ Let $g(x)=6mf(x)+1$ $(m < 0)$, if the range of... | math | {
"style": "rule",
"ground_truth": "- \\frac{5}{2}"
} | {
"split": "train",
"index": 24421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any positive integer \\( n \\), let \\( f(n) \\) represent the last digit of \\( 1 + 2 + 3 + \\cdots + n \\). For example, \\( f(1) = 1 \\), \\( f(2) = 3 \\), \\( f(5) = 5 \\), and so on. Find the value of \\( f(2) + f(4) + f(6) + \\cdots + f(2012) \\). Let's think step by ... | math | {
"style": "rule",
"ground_truth": "3523"
} | {
"split": "train",
"index": 24422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a simple pendulum with a period of $T=1$ second in summer. In winter, the length of the pendulum shortens by 0.01 centimeters. How many seconds faster is this pendulum in winter over a 24-hour period compared to summer? (Round to the nearest second).\n\nNote: The formu... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 24423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "I have two cents and Bill has $n$ cents. Bill wants to buy some pencils, which come in two different packages. One package of pencils costs 6 cents for 7 pencils, and the other package of pencils costs a dime for a dozen pencils (i.e. 10 cents for 12 pencils). Bill notes that h... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 24424,
"solution": "Suppose that Bill buys $a$ packages of 7 and $b$ packages of 12 in the first scenario and $c$ packages of 7 and $d$ packages of 12 in the second scenario. Then we have the following system: $$ \\begin{aligned} & 6 a+10 b=n \\\\ & 6 c+10 d=n+2 \\\\ & 7 a+12 b>7 c+12... |
deepscaler | [
{
"role": "user",
"content": "In an isosceles trapezoid \\(ABCD\\), the side \\(AB\\) and the shorter base \\(BC\\) are both equal to 2, and \\(BD\\) is perpendicular to \\(AB\\). Find the area of this trapezoid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 24425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = x^2 - (2t + 1)x + t \\ln x$ where $t \\in \\mathbb{R}$,\n\n(1) If $t = 1$, find the extreme values of $f(x)$.\n\n(2) Let $g(x) = (1 - t)x$, and suppose there exists an $x_0 \\in [1, e]$ such that $f(x_0) \\geq g(x_0)$ holds. Find the maximum value of ... | math | {
"style": "rule",
"ground_truth": "\\frac{e(e - 2)}{e - 1}"
} | {
"split": "train",
"index": 24426,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle{ABC}$ with $AB = 12$, $BC = 13$, and $AC = 15$, let $M$ be a point on $\\overline{AC}$ such that the incircles of $\\triangle{ABM}$ and $\\triangle{BCM}$ have equal radii. Then $\\frac{AM}{CM} = \\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integ... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 24427,
"solution": "Let $CM=x, AM=rx, BM=d$. $x+rx=15\\Rightarrow x=\\frac{15}{1+r}$.\n Similar to Solution 1, we have \\[r=\\frac{[AMB]}{[CMB]}=\\frac{12+rx+d}{13+x+d} \\Rightarrow d=\\frac{13r-12}{1-r}\\] as well as \\[12^2\\cdot x + 13^2 rx=15x\\cdot rx+15d^2 (\\text{via Stewart's ... |
deepscaler | [
{
"role": "user",
"content": "Compute the number of labelings $f:\\{0,1\\}^{3} \\rightarrow\\{0,1, \\ldots, 7\\}$ of the vertices of the unit cube such that $$\\left|f\\left(v_{i}\\right)-f\\left(v_{j}\\right)\\right| \\geq d\\left(v_{i}, v_{j}\\right)^{2}$$ for all vertices $v_{i}, v_{j}$ of the unit cube,... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 24428,
"solution": "Let $B=\\{0,1\\}^{3}$, let $E=\\{(x, y, z) \\in B: x+y+z$ is even $\\}$, and let $O=\\{(x, y, z) \\in B$ : $x+y+z$ is odd $\\}$. As all pairs of vertices within $E$ (and within $O$ ) are $\\sqrt{2}$ apart, is easy to see that $\\{f(E), f(O)\\}=\\{\\{0,2,4,6\\},\\{1... |
deepscaler | [
{
"role": "user",
"content": " $2016$ bugs are sitting in different places of $1$ -meter stick. Each bug runs in one or another direction with constant and equal speed. If two bugs face each other, then both of them change direction but not speed. If bug reaches one of the ends of the stick, then it flies... | math | {
"style": "rule",
"ground_truth": "1008^2"
} | {
"split": "train",
"index": 24429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ with right angle at $C$, $\\angle BAC < 45^\\circ$ and $AB = 4$. Point $P$ on $\\overline{AB}$ is chosen such that $\\angle APC = 2\\angle ACP$ and $CP = 1$. The ratio $\\frac{AP}{BP}$ can be represented in the form $p + q\\sqrt{r}$, where $p$, $q$, $r$ are posit... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 24430,
"solution": "Let $\\angle{ACP}$ be equal to $x$. Then by Law of Sines, $PB = -\\frac{\\cos{x}}{\\cos{3x}}$ and $AP = \\frac{\\sin{x}}{\\sin{3x}}$. We then obtain $\\cos{3x} = 4\\cos^3{x} - 3\\cos{x}$ and $\\sin{3x} = 3\\sin{x} - 4\\sin^3{x}$. Solving, we determine that $\\sin^2... |
deepscaler | [
{
"role": "user",
"content": "Given a polynomial $f(x) = 2x^7 + x^6 + x^4 + x^2 + 1$, calculate the value of $V_2$ using the Horner's method when $x=2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 24431,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A function $f(x, y, z)$ is linear in $x, y$, and $z$ such that $f(x, y, z)=\\frac{1}{x y z}$ for $x, y, z \\in\\{3,4\\}$. What is $f(5,5,5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{216}"
} | {
"split": "train",
"index": 24432,
"solution": "We use a similar method to the previous problem. Notice that $f(x, y, 5)=2 f(x, y, 4)-f(x, y, 3)$. Let $f_{2}$ denote the function from the previous problem and $f_{3}$ the function from this problem. Since $3 f_{3}(x, y, 3)$ is linear in $x$ and $y$, and $3 f_{3}(... |
deepscaler | [
{
"role": "user",
"content": "Arrange numbers $ 1,\\ 2,\\ 3,\\ 4,\\ 5$ in a line. Any arrangements are equiprobable. Find the probability such that the sum of the numbers for the first, second and third equal to the sum of that of the third, fourth and fifth. Note that in each arrangement each number are... | math | {
"style": "rule",
"ground_truth": "1/15"
} | {
"split": "train",
"index": 24433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of $y=ax^2+bx+c$ is given below, where $a$, $b$, and $c$ are integers. Find $a$.\n\n[asy]\nsize(140);\nLabel f;\n\nf.p=fontsize(4);\n\nxaxis(-3,3,Ticks(f, 1.0));\n\nyaxis(-4,4,Ticks(f, 1.0));\n\nreal f(real x)\n\n{\n\nreturn -2x^2+4x+1;\n\n}\n\ndraw(graph(f,-.7,2.7),... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 24434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$: $\\frac{{x}^{2}}{3}+{y}^{2}=1$ with left focus and right focus as $F_{1}$ and $F_{2}$ respectively, the line $y=x+m$ intersects $C$ at points $A$ and $B$. Determine the value of $m$ such that the area of $\\triangle F_{1}AB$ is twice the area of $\\triangl... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 24435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x+y = 6$ and $x^2-y^2 = 12$, then what is $x-y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 24436,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $E, U, L, S, R,$ and $T$ represent the digits $1, 2, 3, 4, 5, 6$ (each letter represents a unique digit), and the following conditions are satisfied:\n1. $E + U + L = 6$\n2. $S + R + U + T = 18$\n3. $U \\times T = 15$\n4. $S \\times L = 8$\n\nDetermine the six-digit ... | math | {
"style": "rule",
"ground_truth": "132465"
} | {
"split": "train",
"index": 24437,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In quadrilateral $ABCD$ , $AB \\parallel CD$ and $BC \\perp AB$ . Lines $AC$ and $BD$ intersect at $E$ . If $AB = 20$ , $BC = 2016$ , and $CD = 16$ , find the area of $\\triangle BCE$ .\n\n*Proposed by Harrison Wang* Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "8960"
} | {
"split": "train",
"index": 24438,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c, d$ be real numbers such that $\\min (20 x+19,19 x+20)=(a x+b)-|c x+d|$ for all real numbers $x$. Find $a b+c d$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "380"
} | {
"split": "train",
"index": 24439,
"solution": "In general, $\\min (p, q)=\\frac{p+q}{2}-\\left|\\frac{p-q}{2}\\right|$. Letting $p=20 x+19$ and $q=19 x+20$ gives $a=b=19.5$ and $c=d= \\pm 0.5$. Then the answer is $19.5^{2}-0.5^{2}=19 \\cdot 20=380$."
} |
deepscaler | [
{
"role": "user",
"content": "Given that points \\( B \\) and \\( C \\) are in the fourth and first quadrants respectively, and both lie on the parabola \\( y^2 = 2px \\) where \\( p > 0 \\). Let \\( O \\) be the origin, and \\(\\angle OBC = 30^\\circ\\) and \\(\\angle BOC = 60^\\circ\\). If \\( k \\) is th... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 24440,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A car travels due east at a speed of $\\frac{5}{4}$ miles per minute on a straight road. Simultaneously, a circular storm with a 51-mile radius moves south at $\\frac{1}{2}$ mile per minute. Initially, the center of the storm is 110 miles due north of the car. Calculate the ave... | math | {
"style": "rule",
"ground_truth": "\\frac{880}{29}"
} | {
"split": "train",
"index": 24441,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the point $P(-\\sqrt{3}, y)$ is on the terminal side of angle $\\alpha$ and $\\sin\\alpha = \\frac{\\sqrt{13}}{13}$, find the value of $y$. 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": 24442,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An $n \\times n$ complex matrix $A$ is called $t$-normal if $A A^{t}=A^{t} A$ where $A^{t}$ is the transpose of $A$. For each $n$, determine the maximum dimension of a linear space of complex $n \\times n$ matrices consisting of t-normal matrices. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac{n(n+1)}{2}"
} | {
"split": "train",
"index": 24443,
"solution": "Answer: The maximum dimension of such a space is $\\frac{n(n+1)}{2}$. The number $\\frac{n(n+1)}{2}$ can be achieved, for example the symmetric matrices are obviously t-normal and they form a linear space with dimension $\\frac{n(n+1)}{2}$. We shall show that this ... |
deepscaler | [
{
"role": "user",
"content": "Given $$|\\vec{a}|=3, |\\vec{b}|=2$$. If $$\\vec{a} \\cdot \\vec{b} = -3$$, then the angle between $$\\vec{a}$$ and $$\\vec{b}$$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}\\pi"
} | {
"split": "train",
"index": 24444,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum of the first 4 terms of the geometric sequence $\\{a_n\\}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 24445,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column. If there must be at least two chairs in every ro... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 24446,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, the grid is made up of squares. What is the area of the shaded region? [asy]\n\nsize(8cm);\n\n// Fill area\nfill((0, 0)--(0, 2)--(3, 2)--(3, 3)--(7, 3)--(7, 4)--(12, 4)--cycle, gray(0.75));\n\ndefaultpen(1);\n\n// Draw grid\ndraw((0, 0)--(12, 0));\ndraw((0, 1)--... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 24447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In each part of this problem, cups are arranged in a circle and numbered \\(1, 2, 3, \\ldots\\). A ball is placed in cup 1. Then, moving clockwise around the circle, a ball is placed in every \\(n\\)th cup. The process ends when cup 1 contains two balls. \n\n(a) There are 12 cu... | math | {
"style": "rule",
"ground_truth": "360"
} | {
"split": "train",
"index": 24448,
"solution": ""
} |
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