data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "\nToday is 17.02.2008. Natasha noticed that in this date, the sum of the first four digits is equal to the sum of the last four digits. When will this coincidence happen for the last time this year? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25.12.2008"
} | {
"split": "train",
"index": 1600,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A basketball player has a constant probability of $.4$ of making any given shot, independent of previous shots. Let $a_n$ be the ratio of shots made to shots attempted after $n$ shots. The probability that $a_{10} = .4$ and $a_n\\le.4$ for all $n$ such that $1\\le n\\le9$ is gi... | math | {
"style": "rule",
"ground_truth": "660"
} | {
"split": "train",
"index": 1601,
"solution": "We graph the $10$ shots on a grid. Suppose that a made shot is represented by a step of $(0,1)$, and a missed shot is represented by $(1,0)$. Then the basketball player's shots can be represented by the number of paths from $(0,0)$ to $(6,4)$ that always stay below ... |
deepscaler | [
{
"role": "user",
"content": "Given the sets $M=\\{2, 4, 6, 8\\}$, $N=\\{1, 2\\}$, $P=\\left\\{x \\mid x= \\frac{a}{b}, a \\in M, b \\in N\\right\\}$, determine the number of proper subsets of set $P$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 1602,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(n)$ return the number of distinct ordered pairs of positive integers $(a, b)$ such that for each ordered pair, $a^2 + b^2 = n$. Note that when $a \\neq b$, $(a, b)$ and $(b, a)$ are distinct. What is the smallest positive integer $n$ for which $f(n) = 3$? Let's think ste... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 1603,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ be the largest root of $x^4 - 2009x + 1$ . Find the nearest integer to $\\frac{1}{x^3-2009}$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-13"
} | {
"split": "train",
"index": 1604,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle $ABC$ is inscribed in a circle. From the vertex $C$ of the right angle, a chord $CM$ is drawn, intersecting the hypotenuse at point $K$. Find the area of triangle $ABM$ if $BK: AB = 3:4$, $BC=2\\sqrt{2}$, $AC=4$. Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "\\frac{36}{19} \\sqrt{2}"
} | {
"split": "train",
"index": 1605,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A month with $31$ days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 1606,
"solution": "To solve this problem, we need to determine how many days of the week could be the first day of a month with 31 days such that the number of Mondays and Wednesdays in that month are equal.\n\n1. **Understanding the Weekday Distribution:**\n A month with 31 days sp... |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\left\\{a_{n}\\right\\}$ with its sum of the first $n$ terms $S_{n}$ satisfying $2 S_{n}-n a_{n}=n$ for $n \\in \\mathbf{N}^{*}$, and $a_{2}=3$:\n1. Find the general term formula for the sequence $\\left\\{a_{n}\\right\\}$.\n2. Let $b_{n}=\\frac{1}{a_{n} \\... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 1607,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. Given $a^{2}-c^{2}=b^{2}- \\frac {8bc}{5}$, $a=6$, $\\sin B= \\frac {4}{5}$.\n\n(I) Find the value of $\\sin A$;\n\n(II) Find the area of $\\triangle ABC$. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\frac {168}{25}"
} | {
"split": "train",
"index": 1608,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(The 2018 Anqing City, Anhui Province, China, High School Second Mock Exam) Given that the focus of the parabola $x^{2}=4y$ is $F$, points $A$ and $B$ are on the parabola, and satisfy $\\overrightarrow{AF}=λ\\overrightarrow{FB}$. If $|\\overrightarrow{AF}|=\\frac{3}{2}$, then t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 1609,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the probability that in a family where there is already one child who is a boy, the next child will also be a boy. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"split": "train",
"index": 1610,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define a $\\it{good\\ word}$ as a sequence of letters that consists only of the letters A, B, C, and D — some of these letters may not appear in the sequence — where A is never immediately followed by B or D, B is never immediately followed by C, C is never immediately followed... | math | {
"style": "rule",
"ground_truth": "512"
} | {
"split": "train",
"index": 1611,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $10 \\cdot \\left(\\frac{1}{2} + \\frac{1}{5} + \\frac{1}{10}\\right)^{-1}?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{25}{2}"
} | {
"split": "train",
"index": 1612,
"solution": "1. **Simplify the expression inside the parentheses**: \n We start by adding the fractions inside the parentheses:\n \\[\n \\frac{1}{2} + \\frac{1}{5} + \\frac{1}{10}\n \\]\n To add these fractions, we need a common denominator. The least common multiple (... |
deepscaler | [
{
"role": "user",
"content": "Given \\( x_{i} \\in \\{-1,1\\}, i=1,2,\\cdots,2021 \\), and \\( x_{1}+x_{2}+\\cdots+x_{k} \\geq 0 \\) for \\( k=1,2,\\cdots,2020 \\), with \\( x_{1}+x_{2}+\\cdots+x_{2021}=-1 \\). How many ordered arrays \\( (x_{1}, x_{2}, \\cdots, x_{2021}) \\) are there? Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1011} \\binom{2020}{1010}"
} | {
"split": "train",
"index": 1613,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be a three-term arithmetic series where all the terms are positive, such that $abc = 64.$ Find the smallest possible value of $b.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1614,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all the odd divisors of $360$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "78"
} | {
"split": "train",
"index": 1615,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial\n$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 1616,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Positive integers $a$, $b$, $c$, and $d$ satisfy $a > b > c > d$, $a + b + c + d = 2020$, and $a^2 - b^2 + c^2 - d^2 = 2024$. Find the number of possible values of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "503"
} | {
"split": "train",
"index": 1617,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A man travels $m$ feet due north at $2$ minutes per mile. He returns due south to his starting point at $2$ miles per minute. The average rate in miles per hour for the entire trip is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 1618,
"solution": "To find the average rate in miles per hour for the entire trip, we need to calculate the total distance traveled and the total time taken, and then use the formula for average speed:\n\n\\[\n\\text{Average speed} = \\frac{\\text{Total distance}}{\\text{Total time}}\... |
deepscaler | [
{
"role": "user",
"content": "What is the value of $K$ in the equation $16^3\\times8^3=2^K$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 1619,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the limit of the ratio of an infinite decreasing geometric series \\(\\{a_{n}\\}\\) satisfies \\(\\lim _{n \\rightarrow \\infty} \\frac{a_{1} + a_{4} + a_{7} + \\cdots + a_{3n-2}}{a_{1} + a_{2} + \\cdots + a_{n}} = \\frac{3}{4}\\), find the common ratio of the series. Let... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{21} - 3}{6}"
} | {
"split": "train",
"index": 1620,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The arithmetic progressions $\\{2, 5, 8, 11, \\ldots\\}$ and $\\{3, 10, 17, 24, \\ldots \\}$ have some common values. What is the largest value less than 500 that they have in common? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "479"
} | {
"split": "train",
"index": 1621,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ be a multiple of $7200$. Determine the greatest common divisor of $g(x) = (5x+3)(11x+2)(17x+5)(4x+7)$ and $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 1622,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a cube PQRSTUVW with a side length s. Let M and N be the midpoints of edges PU and RW, and let K be the midpoint of QT. Find the ratio of the area of triangle MNK to the area of one of the faces of the cube. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 1623,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$, $B$ and $C$ be three distinct points on the graph of $y=x^2$ such that line $AB$ is parallel to the $x$-axis and $\\triangle ABC$ is a right triangle with area $2008$. What is the sum of the digits of the $y$-coordinate of $C$? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 1624,
"solution": "1. **Identify the Geometry of the Problem**: Given that $A$, $B$, and $C$ are on the graph $y = x^2$, and $AB$ is parallel to the $x$-axis, we know that $A$ and $B$ have the same $y$-coordinate. Since $\\triangle ABC$ is a right triangle with area $2008$, we need to... |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)$ is defined on $\\mathbb{R}$ and is not identically zero, and for any real numbers $x$, $y$, it satisfies: $f(2)=2$, $f(xy)=xf(y)+yf(x)$, $a_{n}= \\dfrac {f(2^{n})}{2^{n}}(n\\in\\mathbb{N}^{*})$, $b_{n}= \\dfrac {f(2^{n})}{n}(n\\in\\mathbb{N}^{*})$... | math | {
"style": "rule",
"ground_truth": "(2)(3)(4)"
} | {
"split": "train",
"index": 1625,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "It is given that \\( k \\) is a positive integer not exceeding 99. There are no natural numbers \\( x \\) and \\( y \\) such that \\( x^{2} - k y^{2} = 8 \\). Find the difference between the maximum and minimum possible values of \\( k \\). Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 1626,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a regular tetrahedron with edge length $2\\sqrt{6}$, the total length of the intersection between the sphere with center $O$ and radius $\\sqrt{3}$ and the surface of the tetrahedron is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\sqrt{2}\\pi"
} | {
"split": "train",
"index": 1627,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest real number \\(\\lambda\\) such that for the real coefficient polynomial \\(f(x) = x^3 + ax^2 + bx + c\\) with all non-negative real roots, it holds that \\(f(x) \\geqslant \\lambda(x - a)^3\\) for all \\(x \\geqslant 0\\). Additionally, determine when the equa... | math | {
"style": "rule",
"ground_truth": "-1/27"
} | {
"split": "train",
"index": 1628,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When studying the traffic situation in a certain city, road density refers to the number of vehicles passing through a certain section of road divided by time, and vehicle density is the number of vehicles passing through a certain section of road divided by the length of that ... | math | {
"style": "rule",
"ground_truth": "\\frac{28800}{7}"
} | {
"split": "train",
"index": 1629,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The longest side of a right triangle is 5 meters and the shortest side is 3 meters. What is the area of the triangle in square meters? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 1630,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A solid cube of side length \\(4 \\mathrm{~cm}\\) is cut into two pieces by a plane that passed through the midpoints of six edges. To the nearest square centimetre, the surface area of each half cube created is: Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"split": "train",
"index": 1631,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 20 cards, each with a number from 1 to 20. These cards are placed in a box, and 4 people each draw one card without replacement. The two people who draw the smaller numbers form one group, and the two people who draw the larger numbers form another group. If two peopl... | math | {
"style": "rule",
"ground_truth": "7/51"
} | {
"split": "train",
"index": 1632,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(1) Point $P$ is any point on the curve $y=x^{2}-\\ln x$. The minimum distance from point $P$ to the line $x-y-4=0$ is ______.\n\n(2) If the tangent line to the curve $y=g(x)$ at the point $(1,g(1))$ is $y=2x+1$, then the equation of the tangent line to the curve $f(x)=g(x)+\\l... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 1633,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles with radii $\\sqrt{5}$ and $\\sqrt{2}$ intersect at point $A$. The distance between the centers of the circles is 3. A line through point $A$ intersects the circles at points $B$ and $C$ such that $A B = A C$ (point $B$ does not coincide with $C$). Find $A B$. Let's... | math | {
"style": "rule",
"ground_truth": "\\frac{6\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 1634,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A person who left home between 4 p.m. and 5 p.m. returned between 5 p.m. and 6 p.m. and found that the hands of his watch had exactly exchanged place, when did he go out ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4:26.8"
} | {
"split": "train",
"index": 1635,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Amelia and Blaine are playing a modified game where they toss their respective coins. Amelia's coin lands on heads with a probability of $\\frac{3}{7}$, and Blaine's lands on heads with a probability of $\\frac{1}{3}$. They begin their game only after observing at least one hea... | math | {
"style": "rule",
"ground_truth": "\\frac{21609}{64328}"
} | {
"split": "train",
"index": 1636,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the parametric equations of curve $C_{1}$ are $\\left\\{{\\begin{array}{l}{x=1+t\\cos\\alpha}\\\\{y=t\\sin\\alpha}\\end{array}}\\right.$ ($t$ is the parameter, $0\\leqslant \\alpha\\ \\ \\lt \\pi$). Taking the origin $O$ as the pole and... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 1637,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Unit circle $\\Omega$ has points $X, Y, Z$ on its circumference so that $X Y Z$ is an equilateral triangle. Let $W$ be a point other than $X$ in the plane such that triangle $W Y Z$ is also equilateral. Determine the area of the region inside triangle $W Y Z$ that lies outside ... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{3}-\\pi}{3}"
} | {
"split": "train",
"index": 1638,
"solution": "Let $O$ be the center of the circle. Then, we note that since $\\angle W Y Z=60^{\\circ}=\\angle Y X Z$, that $Y W$ is tangent to $\\Omega$. Similarly, $W Z$ is tangent to $\\Omega$. Now, we note that the circular segment corresponding to $Y Z$ is equal to $\\frac{1... |
deepscaler | [
{
"role": "user",
"content": "Each day Walter gets $3$ dollars for doing his chores or $5$ dollars for doing them exceptionally well. After $10$ days of doing his chores daily, Walter has received a total of $36$ dollars. On how many days did Walter do them exceptionally well? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 1639,
"solution": "1. Let $b$ be the number of days Walter does his chores but doesn't do them well, and let $w$ be the number of days he does his chores exceptionally well.\n\n2. We know that Walter works for $10$ days, so we have the equation:\n \\[\n b + w = 10\n \\]\n\n3. We... |
deepscaler | [
{
"role": "user",
"content": "Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. 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": 1640,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that point $P(-4,3)$ lies on the terminal side of angle $\\alpha$, find the value of $$\\frac{3\\sin^{2}\\frac{\\alpha}{2}+2\\sin\\frac{\\alpha}{2}\\cos\\frac{\\alpha}{2}+\\cos^{2}\\frac{\\alpha}{2}-2}{\\sin(\\frac{\\pi}{2}+\\alpha)\\tan(-3\\pi+\\alpha)+\\cos(6\\pi-\\alph... | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 1641,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $BCD$, $\\angle CBD=\\angle CDB$ because $BC=CD$. If $\\angle BCD=80+50+30=160$, find $\\angle CBD=\\angle CDB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1642,
"solution": "$\\angle CBD=\\angle CDB=10$"
} |
deepscaler | [
{
"role": "user",
"content": "The number $(2^{48}-1)$ is exactly divisible by two numbers between $60$ and $70$. These numbers are Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63,65"
} | {
"split": "train",
"index": 1643,
"solution": "To solve the problem, we need to find the factors of $2^{48} - 1$ that lie between $60$ and $70$. We start by factoring $2^{48} - 1$ using the difference of squares repeatedly.\n\n1. **Factorization using difference of squares:**\n \\[\n 2^{48} - 1 = (2^{24} - 1... |
deepscaler | [
{
"role": "user",
"content": "If a sequence $\\{a_n\\}$ satisfies $$\\frac {1}{a_{n+1}}- \\frac {1}{a_{n}}=d$$ (where $n\\in\\mathbb{N}^*$, $d$ is a constant), then the sequence $\\{a_n\\}$ is called a \"harmonic sequence\". Given that the sequence $\\{\\frac {1}{x_{n}}\\}$ is a \"harmonic sequence\", and $... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 1644,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Person A and person B each have a certain number of books. If person A gives 10 books to person B, then the total number of books between the two of them will be equal. If person B gives 10 books to person A, then the number of books person A has will be twice the number of boo... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 1645,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $A$ and $B$ such that\n\\[\\frac{5x+2}{x^2-7x-30}=\\frac{A}{x-10}+\\frac{B}{x+3}.\\]Write your answer in the form $(A,B)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(4,1)"
} | {
"split": "train",
"index": 1646,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Zhang Qiang rides a bike starting from bus stop $A$, traveling along the bus route at 250 meters per minute. After some time, a bus also departs from stop $A$, traveling at 450 meters per minute, but it needs to stop at a station for 1 minute every 6 minutes. If the bus catches... | math | {
"style": "rule",
"ground_truth": "2100"
} | {
"split": "train",
"index": 1647,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ , $b$ , $c$ be positive reals for which\n\\begin{align*}\n (a+b)(a+c) &= bc + 2 \n (b+c)(b+a) &= ca + 5 \n (c+a)(c+b) &= ab + 9\n\\end{align*}\nIf $abc = \\frac{m}{n}$ for relatively prime positive integers $m$ and $n$ , compute $100m+n$ .\n\n*Proposed by E... | math | {
"style": "rule",
"ground_truth": "4532"
} | {
"split": "train",
"index": 1648,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The vertex of a parabola is \\( O \\) and its focus is \\( F \\). When a point \\( P \\) moves along the parabola, find the maximum value of the ratio \\( \\left|\\frac{P O}{P F}\\right| \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 1649,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of 81 points $(x, y)$ such that $x$ and $y$ are integers from $-4$ through $4$ . Let $A$ , $B$ , and $C$ be random points chosen independently from $S$ , with each of the 81 points being equally likely. (The points $A$ , $B$ , and $C$ do... | math | {
"style": "rule",
"ground_truth": "\\frac{200}{3}"
} | {
"split": "train",
"index": 1650,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y^2 = 4x$ whose directrix intersects the x-axis at point $P$, draw line $l$ through point $P$ with the slope $k (k > 0)$, intersecting the parabola at points $A$ and $B$. Let $F$ be the focus of the parabola. If $|FB| = 2|FA|$, then calculate the length of s... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{17}}{2}"
} | {
"split": "train",
"index": 1651,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, point $A$ is at $(1, 1)$, point $B$ is at $(4, 2)$, and point $C$ is at $(-4, 6)$.\n(1) Determine the equation of the line where the median to side $BC$ lies;\n(2) Determine the length of the altitude to side $BC$ and the area of triangle $ABC$. Let's think s... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1652,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = x + 1 + |3 - x|$, where $x \\geq -1$.\n1. Find the solution set for the inequality $f(x) \\leq 6$.\n2. If the minimum value of $f(x)$ is $n$, and the positive numbers $a$ and $b$ satisfy $2nab = a + 2b$, find the minimum value of $2a + b$. Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{8}"
} | {
"split": "train",
"index": 1653,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y^{2}=4x$ and the circle $E:(x-4)^{2}+y^{2}=12$. Let $O$ be the origin. The line passing through the center of circle $E$ intersects the circle at points $A$ and $B$. The lines $OA$ and $OB$ intersect the parabola at points $P$ and $Q$ (points $P$ and $Q$ ar... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{16}"
} | {
"split": "train",
"index": 1654,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lateral face of a regular triangular pyramid \\( SABC \\) is inclined to the base \\( ABC \\) at an angle \\(\\alpha = \\arctan \\frac{3}{4}\\). Points \\( M, N, K \\) are the midpoints of the sides of the base \\( ABC \\). The triangle \\( MNK \\) forms the lower base of a... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1655,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many numbers of the form $\\overline{a b c d a b c d}$ are divisible by 18769? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 1656,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest \\(k\\) such that for any arrangement of 3000 checkers in a \\(2011 \\times 2011\\) checkerboard, with at most one checker in each square, there exist \\(k\\) rows and \\(k\\) columns for which every checker is contained in at least one of these rows or column... | math | {
"style": "rule",
"ground_truth": "1006"
} | {
"split": "train",
"index": 1657,
"solution": "If there is a chip in every square along a main diagonal, then we need at least 1006 rows and columns to contain all these chips. We are left to show that 1006 is sufficient. Take the 1006 rows with greatest number of chips. Assume without loss of generality they ar... |
deepscaler | [
{
"role": "user",
"content": "The clock shows $00:00$, with both the hour and minute hands coinciding. Considering this coincidence as number 0, determine after what time interval (in minutes) they will coincide for the 21st time. If the answer is not an integer, round the result to the nearest hundredth. L... | math | {
"style": "rule",
"ground_truth": "1374.55"
} | {
"split": "train",
"index": 1658,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $k$ be a natural number. For which value of $k$ is $A_k = \\frac{19^k + 66^k}{k!}$ maximized? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 1659,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The expression $\\frac{k^{2}}{1.001^{k}}$ reaches its maximum value with which natural number $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2001"
} | {
"split": "train",
"index": 1660,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that 3 people are to be selected from 5 girls and 2 boys, if girl A is selected, determine the probability that at least one boy is selected. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 1661,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a regular quadrilateral pyramid $S-ABCD$ with side edges of length $4$ and $\\angle ASB = 30^\\circ$, a plane passing through point $A$ intersects the side edges $SB$, $SC$, and $SD$ at points $E$, $F$, and $G$ respectively. Find the minimum perimeter of the cross-section... | math | {
"style": "rule",
"ground_truth": "4\\sqrt{3}"
} | {
"split": "train",
"index": 1662,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a right triangle \\( ABC \\) with legs \\( AC = 3 \\) and \\( BC = 4 \\). Construct triangle \\( A_1 B_1 C_1 \\) by successively translating point \\( A \\) a certain distance parallel to segment \\( BC \\) to get point \\( A_1 \\), then translating point \\( B \\) parall... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1663,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x)=\\ln x$, $g(x)= \\frac {1}{3}x^{3}+ \\frac {1}{2}x^{2}+mx+n$, and line $l$ is tangent to both the graphs of $f(x)$ and $g(x)$ at point $(1,0)$.\n1. Find the equation of line $l$ and the expression for $g(x)$.\n2. If $h(x)=f(x)-g′(x)$ (where $g′(x)$ is the derivative... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{4}- \\ln 2"
} | {
"split": "train",
"index": 1664,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, the equilateral triangle has a base of $8$ m. What is the perimeter of the triangle? [asy]\nsize(100);\ndraw((0,0)--(8,0)--(4,4*sqrt(3))--cycle);\nlabel(\"8 m\",(4,0),S);\ndraw((4,-.2)--(4,.2));\ndraw((1.8,3.5)--(2.2,3.3));\ndraw((6.3,3.5)--(5.8,3.3));\n[/asy] L... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 1665,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the Cartesian plane, find the number of integer coordinate points (points where both x and y are integers) that satisfy the following system of inequalities:\n\\[\n\\begin{cases}\ny \\leq 3x, \\\\\ny \\geq \\frac{1}{3}x, \\\\\nx + y \\leq 100.\n\\end{cases}\n\\] Let's think ... | math | {
"style": "rule",
"ground_truth": "2551"
} | {
"split": "train",
"index": 1666,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the length of the chord intercepted by the line given by the parametric equations $x = 1 + \\frac{4}{5}t$, $y = -1 - \\frac{3}{5}t$ and the curve $ρ = \\sqrt{2}\\cos\\left(θ + \\frac{π}{4}\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{5}"
} | {
"split": "train",
"index": 1667,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A scanning code consists of a $7 \\times 7$ grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of $49$ squares. A scanning code is called $\\textit{symmetric}$ if its look does not cha... | math | {
"style": "rule",
"ground_truth": "1022"
} | {
"split": "train",
"index": 1668,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many positive integers $n$ does $1+2+\\cdots+n$ evenly divide $6n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 1669,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $\\frac{2+4+6}{1+3+5} - \\frac{1+3+5}{2+4+6}$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{12}"
} | {
"split": "train",
"index": 1670,
"solution": "1. **Calculate the sums in the numerators and denominators:**\n - The sum of the numerators in the first fraction: $2 + 4 + 6 = 12$.\n - The sum of the denominators in the first fraction: $1 + 3 + 5 = 9$.\n - The sum of the numerators in the second fraction: $... |
deepscaler | [
{
"role": "user",
"content": "What integer $n$ satisfies $0 \\leq n < 151$ and $$100n \\equiv 93 \\pmod {151}~?$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 1671,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f\\left( x \\right)={e}^{x}\\left( {x}^{2}+x+1 \\right)$,\n\n(1) Find the monotonic intervals of the function $f\\left( x \\right)$\n\n(2) Find the extreme values of the function $f(x)$ Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{e}"
} | {
"split": "train",
"index": 1672,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the seventh element in Row 20 of Pascal's triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "38760"
} | {
"split": "train",
"index": 1673,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a sequence $\\{a_n\\}$ where the sum of the first $n$ terms, $S_n$, satisfies $S_n = 2a_n - a_1$, and $a_1$, $a_2 + 1$, $a_3$ form an arithmetic sequence.\n\n(1) Find the general formula for the sequence $\\{a_n\\}$.\n(2) Let $b_n = \\log_2 a_n$ and $c_n = \\frac{3}{b_... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1674,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCDEF$ be a regular hexagon. Let $P$ be the circle inscribed in $\\triangle BDF$. Find the ratio of the area of circle $P$ to the area of rectangle $ABDE$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi \\sqrt{3}}{12}"
} | {
"split": "train",
"index": 1675,
"solution": "Let the side length of the hexagon be $s$. The length of $BD$ is $s \\sqrt{3}$, so the area of rectangle $ABDE$ is $s^{2} \\sqrt{3}$. Equilateral triangle $BDF$ has side length $s \\sqrt{3}$. The inradius of an equilateral triangle is $\\sqrt{3} / 6$ times the lengt... |
deepscaler | [
{
"role": "user",
"content": "A radio system consisting of 1000 components (each with a failure rate of $\\lambda_{i} = 10^{-6}$ failures/hour) has been tested and accepted by the customer. Determine the probability of the system operating without failure over the interval $t_{1} < (t = t_{1} + \\Delta t) <... | math | {
"style": "rule",
"ground_truth": "0.367879"
} | {
"split": "train",
"index": 1676,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The minimum element of the set of positive integers $A_k$ is 1, the maximum element is 2007, and all elements can be arranged in ascending order to form an arithmetic sequence with a common difference of $k$. Then, the number of elements in the union $A_{17} \\cup A_{59}$ is __... | math | {
"style": "rule",
"ground_truth": "151"
} | {
"split": "train",
"index": 1677,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In some squares of a $2012\\times 2012$ grid there are some beetles, such that no square contain more than one beetle. At one moment, all the beetles fly off the grid and then land on the grid again, also satisfying the condition that there is at most one beetle standing in eac... | math | {
"style": "rule",
"ground_truth": "\\frac{2012^3}{4}"
} | {
"split": "train",
"index": 1678,
"solution": "\nIn a \\(2012 \\times 2012\\) grid, we place beetles such that no square contains more than one beetle. When the beetles fly off and land again, each beetle has a translation vector from its initial to its final position. We aim to find the maximum length of the su... |
deepscaler | [
{
"role": "user",
"content": "If $3 \\in \\{a, a^2 - 2a\\}$, then the value of the real number $a$ is __________. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 1679,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. The radius of the circumcircle is $1$, and it is given that $\\frac{\\tan A}{\\tan B} = \\frac{2c-b}{b}$. Find the maximum value of the area of $\\triangle ABC$. L... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 1680,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\frac{(2112-2021)^2}{169}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 1681,
"solution": "1. **Calculate the difference in the numerator**: \n \\[\n 2112 - 2021 = 91\n \\]\n This is the exact value, not an approximation.\n\n2. **Square the difference**:\n \\[\n (2112 - 2021)^2 = 91^2 = 8281\n \\]\n\n3. **Divide by the denominator**:\n \\[... |
deepscaler | [
{
"role": "user",
"content": "A regular polygon has interior angles of 160 degrees, and each side is 4 units long. How many sides does the polygon have, and what is its perimeter? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 1682,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four points are independently chosen uniformly at random from the interior of a regular dodecahedron. What is the probability that they form a tetrahedron whose interior contains the dodecahedron's center? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"split": "train",
"index": 1683,
"solution": "Situate the origin $O$ at the dodecahedron's center, and call the four random points $P_{i}$, where $1 \\leq i \\leq 4$. To any tetrahedron $P_{1} P_{2} P_{3} P_{4}$ we can associate a quadruple $\\left(\\epsilon_{(i j k)}\\right)$, where $(i j k)$ ranges over all c... |
deepscaler | [
{
"role": "user",
"content": "Let \\( S_1, S_2, \\ldots, S_{10} \\) be the first ten terms of an arithmetic progression (A.P.) consisting of positive integers. If \\( S_1 + S_2 + \\ldots + S_{10} = 55 \\) and \\( \\left(S_{10} - S_{8}\\right) + \\left(S_{9} - S_{7}\\right) + \\ldots + \\left(S_{3} - S_{1}\\... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1684,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $n$ such that $2^5 \\cdot 3^2 \\cdot n = 8!$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 1685,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\cos \\left(\\alpha- \\frac {\\beta}{2}\\right)=- \\frac {1}{9}$ and $\\sin \\left( \\frac {\\alpha}{2}-\\beta\\right)= \\frac {2}{3}$, with $0 < \\beta < \\frac {\\pi}{2} < \\alpha < \\pi$, find $\\sin \\frac {\\alpha+\\beta}{2}=$ ______. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac {22}{27}"
} | {
"split": "train",
"index": 1686,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all positive integers such that their expression in base $7$ digits is the reverse of their expression in base $16$ digits. Express your answer in base $10$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "58"
} | {
"split": "train",
"index": 1687,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Joy has $30$ thin rods, one each of every integer length from $1$ cm through $30$ cm. She places the rods with lengths $3$ cm, $7$ cm, and $15$ cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 1688,
"solution": "To determine the number of rods that can be chosen as the fourth rod to form a quadrilateral with the rods of lengths $3$ cm, $7$ cm, and $15$ cm, we need to ensure that the sum of the lengths of any three sides must be greater than the length of the fourth side. Th... |
deepscaler | [
{
"role": "user",
"content": "How many positive integers $n \\leq 2009$ have the property that $\\left\\lfloor\\log _{2}(n)\\right\\rfloor$ is odd? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "682"
} | {
"split": "train",
"index": 1689,
"solution": "We wish to find $n$ such that there is some natural number $k$ for which $2 k-1 \\leq \\log _{2} n<$ $2 k$. Since $n \\leq 2009$ we must have $k \\leq 5$. This is equivalent to finding the number of positive integers $n \\leq 2009$ satisfying $2^{2 k-1} \\leq n<2^{2... |
deepscaler | [
{
"role": "user",
"content": "Find the solutions to $z^4 = -4.$ Enter the solutions, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1 + i, 1 - i, -1 + i, -1 - i"
} | {
"split": "train",
"index": 1690,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( f(x) = x^{5} + a_{1} x^{4} + a_{2} x^{3} + a_{3} x^{2} + a_{4} x + a_{5} \\), and \\( f(m) = 2017m \\) for \\( m = 1, 2, 3, 4 \\), calculate \\( f(10) - f(-5) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "75615"
} | {
"split": "train",
"index": 1691,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Paula the painter had just enough paint for 30 identically sized rooms. Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for 25 rooms. How many cans of paint did she use for the 25 rooms? Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 1692,
"solution": "1. **Understanding the problem**: Paula initially had enough paint for 30 rooms, but after losing three cans, she could only paint 25 rooms. We need to find out how many cans she used for these 25 rooms.\n\n2. **Relating cans of paint to rooms**: The loss of three c... |
deepscaler | [
{
"role": "user",
"content": "\nLet \\( M \\) be a set composed of a finite number of positive integers,\n\\[ \nM = \\bigcup_{i=1}^{20} A_i = \\bigcup_{i=1}^{20} B_i, \\text{ where}\n\\]\n\\[ \nA_i \\neq \\varnothing, B_i \\neq \\varnothing \\ (i=1,2, \\cdots, 20)\n\\]\nsatisfying the following conditions:\... | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 1693,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a cube $ABCDEFGH$, the coordinates of vertices are set in a conventional cube alignment with $A(0, 0, 0)$, $B(2, 0, 0)$, $C(2, 0, 2)$, $D(0, 0, 2)$, $E(0, 2, 0)$, $F(2, 2, 0)$, $G(2, 2, 2)$, and $H(0, 2, 2)$. Let $M$ and $N$ be the midpoints of the segments $\\overline{EB}$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{17}{2304}"
} | {
"split": "train",
"index": 1694,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $L_1$ and $L_2$ be perpendicular lines, and let $F$ be a point at a distance $18$ from line $L_1$ and a distance $25$ from line $L_2$ . There are two distinct points, $P$ and $Q$ , that are each equidistant from $F$ , from line $L_1$ , and from line $L_2$... | math | {
"style": "rule",
"ground_truth": "210"
} | {
"split": "train",
"index": 1695,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the integers \\( a, b, c \\) that satisfy \\( a + b + c = 2 \\), and\n\\[ \nS = (2a + bc)(2b + ca)(2c + ab) > 200,\n\\]\nfind the minimum value of \\( S \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 1696,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C D$ be a convex quadrilateral such that $\\angle A B D=\\angle B C D=90^{\\circ}$, and let $M$ be the midpoint of segment $B D$. Suppose that $C M=2$ and $A M=3$. Compute $A D$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{21}"
} | {
"split": "train",
"index": 1697,
"solution": "Since triangle $B C D$ is a right triangle, we have $C M=B M=D M=2$. With $A M=3$ and $\\angle A B M=90^{\\circ}$, we get $A B=\\sqrt{5}$. Now $$A D^{2}=A B^{2}+B D^{2}=5+16=21$$ so $A D=\\sqrt{21}$."
} |
deepscaler | [
{
"role": "user",
"content": "A pizza parlor has six different toppings. How many different one- and two-topping pizzas can you order? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 1698,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Henry constructs a model involving four spherical clay pieces of radii 1 inch, 4 inches, 6 inches, and 3 inches. Calculate the square of the total volume of the clay used, subtracting 452 from the squared result, and express your answer in terms of $\\pi$. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "168195.11\\pi^2"
} | {
"split": "train",
"index": 1699,
"solution": ""
} |
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