inclusionAI/Ring-lite-rl-data huggingface dataset:
A man is 45 years older than his son. In 10 years, his age will be four times the age of his son. Additionally, the son's age will double in 15 years. What is the present age of the son?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
24 people participate in a training competition consisting of 12 rounds. After each round, every participant receives a certain score \( a_k \) based on their ranking \( k \) in that round, where \( a_{k} \in \mathbb{N}_+, k = 1, 2, \ldots, n, a_1 > a_2 > \cdots > a_n \). After all the rounds are completed, the overall ranking is determined based on the total score each person has accumulated over the 12 rounds. Find the smallest positive integer \( n \) such that no matter the ranking in the penultimate round, at least 2 participants have the potential to win the championship.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Given that there are 20 cards numbered from 1 to 20 on a table, and Xiao Ming picks out 2 cards such that the number on one card is 2 more than twice the number on the other card, find the maximum number of cards Xiao Ming can pick.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
A company pays a certain percentage as dividend to its investors. An investor buys Rs. 60 shares and gets 25% on investment. The investor bought the shares at Rs. 30. What is the dividend percentage paid by the company?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12.5\%}
Let $ABC$ be a triangle with $AB = 13$, $BC = 14$, $CA = 15$. Company $XYZ$ wants to locate their base at the point $P$ in the plane minimizing the total distance to their workers, who are located at vertices $A$, $B$, and $C$. There are $1$, $5$, and $4$ workers at $A$, $B$, and $C$, respectively. Find the minimum possible total distance Company $XYZ$'s workers have to travel to get to $P$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{69}
A pedestrian and a cyclist set off from point $A$ to point $B$ simultaneously. At point $B$, the cyclist turns back and meets the pedestrian 20 minutes after starting. Without stopping, the cyclist continues to point $A$, turns around, and catches up with the pedestrian 10 minutes after their first meeting. How long will it take for the pedestrian to travel from $A$ to $B$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
If "Labor Day" is on Monday, then "National Day" is on what day of the week?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Sunday}
In the TV show "Dad, Where Are We Going?", five dads each bring one child (son or daughter) to experience rural life. One day, the village chief arranges for one dad to take three kids to complete a certain task, and at least one girl (among the 5 kids, there are 3 boys and 2 girls) must be chosen. Kimi (a boy) says, "If my dad goes, I'll go; if my dad doesn't go, I won't go." Stone (a boy) is angry with his dad and says, "If my dad goes, I won't go; if my dad doesn't go, I'll go." The others have no objections. How many possible selections are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
A natural number greater than 1 is defined as nice if it is equal to the product of its distinct proper divisors. A number \( n \) is nice if:
1. \( n = pq \), where \( p \) and \( q \) are distinct prime numbers.
2. \( n = p^3 \), where \( p \) is a prime number.
3. \( n = p^2q \), where \( p \) and \( q \) are distinct prime numbers.
Determine the sum of the first ten nice numbers under these conditions.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{182}
Let $a$, $b$, and $c$ be positive integers with $a\ge$ $b\ge$ $c$ such that
$a^2-b^2-c^2+ab=2011$ and
$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.
What is $a$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{253}
Given that the angle between the unit vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ is $60^{\circ}$, and $\overrightarrow{a}=2\overrightarrow{e_{1}}-\overrightarrow{e_{2}}$, find the projection of $\overrightarrow{a}$ in the direction of $\overrightarrow{e_{1}}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{3}{2}}
A sphere is circumscribed around a right parallelepiped, which has base diagonals equal to \(a\) and \(b\). Determine the entire surface area of the parallelepiped.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3ab}
Azar and Carl play a game of tic-tac-toe. Azar places an $X$ in one of the boxes in a $3$-by-$3$ array of boxes, then Carl places an $O$ in one of the remaining boxes. After that, Azar places an $X$ in one of the remaining boxes, and so on until all boxes are filled or one of the players has three of their symbols in a row—horizontal, vertical, or diagonal—whichever comes first, in which case that player wins the game. Suppose the players make their moves at random, rather than trying to follow a rational strategy, and that Carl wins the game when he places his third $O$. How many ways can the board look after the game is over?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{148}
A certain factor and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ). The smallest possible positive value of n is 75. What is the other factor?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
In a 6 by 6 grid, each of the 36 small squares measures 1 cm by 1 cm and is shaded. Six unshaded circles are placed on top of the grid. One large circle is centered at the center of the grid with a radius equal to 1.5 cm, and five smaller circles each with a radius of 0.5 cm are placed at the center of the outer border of the grid. The area of the visible shaded region can be written in the form $C-D\pi$ square cm. What is the value of $C+D$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{39.5}
Suppose \( a_{i}, b_{i} (i=1,2,\ldots,n) \) are rational numbers, such that for any real number \( x \), the following holds:
\[ x^{2}+x+4=\sum_{i=1}^{n}\left(a_{i} x+b_{i}\right)^{2}. \]

Find the minimum possible value of \( n \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
The function relationship between the total cost $y$ (in ten thousand yuan) of a certain product and the output $x$ (in units) is $y=3000+20x-0.1x^{2}$ ($0<x<240$, $x\in \mathbb{N}^{+}$). If the selling price per unit of the product is 25 thousand yuan, then the minimum output at which the producer does not incur losses (sales revenue is not less than total cost) is ____ units.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{150 \text{ units}}
In a cylinder with a base radius of 6, there are two spheres each with a radius of 6, and the distance between their centers is 13. If a plane is tangent to both spheres and intersects the cylindrical surface, forming an ellipse, what is the sum of the lengths of the major and minor axes of this ellipse? ( ).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
从正九边形中任取三个顶点构成三角形, 则正九边形的中心在三角形内的概率为 $\qquad$.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
## Problem Statement

Calculate the definite integral:

$$
\int_{0}^{\arcsin (3 / \sqrt{10})} \frac{2 \tan x-5}{(4 \cos x-\sin x)^{2}} d x
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{9}{4}-\ln16}
设正数X,y,Z,a,0,c满足cy+bz=a,az+cx=b,bx+ay=c,

求函数$f ( x , y , z ) = \frac { x ^ { 2 } } { 1 + x } + \frac { y ^ { 2 } } { 1 + y } + \frac { z ^ { 2 } } { 1 + z }$的最小值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{f(x,y,z)的最小值为$\frac { 1 } { 2 }$}
Cyclic pentagon $ABCDE$ has a right angle $\angle ABC=90^{\circ}$ and side lengths $AB=15$ and $BC=20$. Supposing that $AB=DE=EA$, find $CD$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
A, B, and C are partners in a business. A is a working partner, while B and C are sleeping partners. A invests Rs. 5000, B invests Rs. 1000, and C invests Rs. 7000. A receives 12% of the total profit for managing the business, while the remaining profit is divided in the following ratio: A's capital: 35%, B's capital: 25%, C's capital: 40%. Out of a total profit of Rs. 16,500, find the money received by A.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7,062}
On each of the lines \( y=0 \) and \( y=2 \), there are 64 points marked with abscissas \( 1, 2, 3, \ldots, 64 \). In how many ways can three points be chosen from the 128 marked points so that they form the vertices of a right triangle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8420}
Adam, Barney, Carrie, and Jerrie are participating in a sit-up competition. Here are their respective performance profiles:

- Adam can perform 40 sit-ups in the first minute, but his stamina decreases after each break, so he loses 8 sit-ups capacity per minute after each one-minute break.
- Barney can perform 45 sit-ups in one minute. Then he takes a 45-second break before starting again.
- Carrie can do twice as many sit-ups per minute as Barney can. However, after two minutes, she needs a 90-second break.
- Jerrie can do 5 more sit-ups per minute than Carrie can do. But Jerrie takes an extra 20-second break after every minute.

During the competition, Adam performs sit-ups for three rounds with two minutes of rest between each round. Barney does sit-ups for five rounds with one 45-second break between them. Carrie does sit-ups for four rounds, with one 90-second break after two rounds. Jerrie performs sit-ups for six rounds, taking a 20-second break after each round.

What would be the combined total number of sit-ups performed by all of them in the competition?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1251}
The surface of a clock is circular, and on its circumference, there are 12 equally spaced points representing the hours. Calculate the total number of rectangles that can have these points as vertices.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
Given a sequence $\{a_n\}$, where $a_{n+1} + (-1)^n a_n = 2n - 1$, find the sum of the first 12 terms of the sequence $\{a_n\}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{78}
Four girls — Mary, Alina, Tina, and Hanna — sang songs in a concert as trios, with one girl sitting out each time. Hanna sang 7 songs, which was more than any other girl, and Mary sang 4 songs, which was fewer than any other girl. Calculate the total number of songs these trios sang.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
How can we evaluate the following integral:
$$ \int_0^1 \frac{\tan^{-1}(x)}{x+1}dx $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\(\frac{\pi}{8}\ln(2)\)}
A man buys 1 liter of milk for 12 rs, mixes it with 20% water, and sells it for a certain price. The percentage of gain is 50%. What is the selling price of the milk?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
The security gate at a storage facility requires a 6-digit lock code. If the lock code must consist only of digits from 1 through 9, inclusive, with no repeated digits, and the first, third, and fifth digits of the code must be even, how many lock codes are possible?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1440}
Find the expected degree of the root of binary trees using probability generating functions.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Calculate the limit as $n$ approaches infinity for the following integral:

$$\lim_{n \to \infty} \int_0^3 \sin\left(\frac{\pi}{3} \sin\left(\frac{\pi}{3} \sin \left(\frac{\pi}{3} \dots \sin\left(\frac{\pi}{3} x\right) \dots \right)\right)\right)dx$$

where the sine function is applied $n$ times.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3/2}
How many sequences of $0$s and $1$s of length $19$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s? Find the number of such sequences.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{65}
All dwarves are either liars or knights. Liars always lie, while knights always tell the truth. Each cell of a $4 \times 4$ board contains one dwarf. It is known that among them there are both liars and knights. Each dwarf stated: "Among my neighbors (by edge), there are an equal number of liars and knights." How many liars are there in total?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
已知复数 $z_{1} 、 z_{2}$ 满足 $\left|z_{1}\right|<1$, $\left|z_{2}\right|<1, z_{1}+z_{2}$ 为实数，且 $z_{1}+z_{2}+z_{1} z_{2}=0$ 。求 $z_{1} z_{2}$ 的取值范围。请给出区间端点的倒数的和。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1}
Let \( A \) be the \( 2n \times 2n \) matrix whose diagonal elements are all \( x \) and whose off-diagonal elements \( a_{ij} = a \) for \( i + j \) even, and \( b \) for \( i + j \) odd. Find \( \lim_{x \to a} \frac{\det(A)}{(x - a)^{2n - 2}} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n^2 (a^2 - b^2)}
In preparation for a game of Fish, Carl must deal $48$ cards to $6$ players. For each card that he deals, he runs through the entirety of the following process:

1. He gives a card to a random player.
2. A player $Z$ is randomly chosen from the set of players who have at least as many cards as every other player (i.e., $Z$ has the most cards or is tied for having the most cards).
3. A player $D$ is randomly chosen from the set of players other than $Z$ who have at most as many cards as every other player (i.e., $D$ has the fewest cards or is tied for having the fewest cards).
4. $Z$ gives one card to $D$.

He repeats steps $1-4$ for each card dealt, including the last card. After all the cards have been dealt, what is the probability that each player has exactly $8$ cards?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Two trains of length 180 m and another length are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In 22.998 seconds, they will be clear of each other from the moment they meet. What is the length of the second train?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{279.96}
Winwin won $50,000 in a lottery. The government imposes a progressive tax system: 
- 0% for the amount up to $10,000 
- 10% for the amount between $10,001 and $20,000 
- 20% for the amount between $20,001 and $50,000 

Additionally, there are multiple processing fees: 
- $5 for the standard processing 
- $200 for mandatory identity verification check 
- 2% administrative fee on the final amount she can take home 

How much was Winwin able to take home after the taxes and processing fees have been deducted?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$41,939.10}
Paul and Sara are playing a game with integers on a whiteboard, with Paul going first. When it is Paul's turn, he can pick any two integers on the board and replace them with their product; when it is Sara's turn, she can pick any two integers on the board and replace them with their sum. Play continues until exactly one integer remains on the board. Paul wins if that integer is odd, and Sara wins if it is even.

Initially, there are $2021$ integers on the board, each one sampled uniformly at random from the set $\{0, 1, 2, 3, \ldots, 2021\}$. Assuming both players play optimally, the probability that Paul wins is $\frac{m}{n}$, where $m, n$ are positive integers and $\gcd(m, n) = 1$. Find the remainder when $m + n$ is divided by $1000$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Samantha sleeps for some hours everyday. If today she woke up at 11 in the morning and went to bed at 7, how many hours does she sleep every day?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
On a line, there are blue and red points, with at least 5 red points. It is known that on any segment with endpoints at red points, containing a red point inside, there are at least 4 blue points. Additionally, on any segment with endpoints at blue points, containing 3 blue points inside, there are at least 2 red points. What is the maximum number of blue points that can be on a segment with endpoints at red points, that does not contain other red points?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
In square \( A B C D \), \( P \) and \( Q \) are points on sides \( C D \) and \( B C \), respectively, such that \( \angle A P Q = 90^\circ \). If \( A P = 4 \) and \( P Q = 3 \), find the area of \( A B C D \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{256}{17}}
In triangle $A B C$ where $A C = B C$ and $\angle A C B = 30^\circ$, point $D$ lies on side $B C$ such that $B D = 3$ and $D C = 6$. Find a point $P$ on side $A C$ such that the angle $D P C$ is 1.5 times the angle $A P B$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3 \sqrt{3}}
In the triangular pyramid \( SABC \) with vertex \( S \), the lateral edges are equal, and the sum of the dihedral angles at the edges \( SA \) and \( SC \) is \( 180^\circ \). Express the length of the lateral edge in terms of the sides \( a \) and \( c \) of triangle \( ABC \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{a^2 + c^2}}{2}}
Call a fraction $\frac{a}{b}$, not necessarily in the simplest form, special if $a$ and $b$ are positive integers whose sum is $15$. How many distinct integers can be written as the sum of two, not necessarily different, special fractions?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
A Tim number is a five-digit positive integer with the following properties:
1. It is a multiple of 15.
2. Its hundreds digit is 3.
3. Its tens digit is equal to the sum of its first three (leftmost) digits.

How many Tim numbers are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
Given that $f(x) = \log_{\frac{1}{2}}(x^2 - ax + 3a)$ is a decreasing function on the interval $[2,+\infty)$, find the range of the real number $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4 < a \leq 4}
Given a class with 21 students, such that at least two of any three students are friends, determine the largest possible value of k.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
The region $G$ is bounded by the ellipsoid $\frac{x^{2}}{16}+\frac{y^{2}}{9}+\frac{z^{2}}{4}=1$, and the region $g$ is bounded by this ellipsoid and the sphere $x^{2}+y^{2}+z^{2}=4$. A point is randomly chosen within the region $G$. What is the probability that it belongs to region $g$ (event $A$)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2}{3}}
Let $m$ and $n$ be positive integers such that $\gcd(m,n)=1$ and $$\sum_{k=0}^{2020} (-1)^k {{2020}\choose{k}}  \cos(2020\cos^{-1}(\tfrac{k}{2020}))=\frac{m}{n}.$$ Suppose $n$ is written as the product of a collection of (not necessarily distinct) prime numbers. Compute the sum of the members of this collection. (For example, if it were true that $n=12=2\times 2\times 3$, then the answer would be $2+2+3=7$.)

[i]Proposed by Ankit Bisain[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{209601}
Three bodies x, y, and z start moving around a circular track from the same point simultaneously in the same direction at speeds of 12 m/s, 20 m/s, and 36 m/s respectively. They meet for the first time after 120 seconds since they started moving. What is the length of the circular track?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{480}
Given the function $f(x)=\sin (2x-\frac{\pi }{6})$ whose graph is $C_{1}$, if the graph $C_{1}$ is translated to the left by $\frac{\pi }{4}$ units to obtain the graph $C_{2}$, then the interval where $C_{2}$ is monotonically decreasing on $\left[ 0,\pi \right]$ is.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\left[\frac{\pi}{12}, \frac{7\pi}{12}\right]}
焦点在 $x$ 轴上的椭圆 $\frac{x^2}{m} + \frac{y^2}{4-m} = 1$ 的离心率为 $\frac{6}{3}$，则 $m$ 的值为何？
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
In quadrilateral $ABCD$, let $AB = 7$, $BC = 11$, $CD = 3$, $DA = 9$, $\angle BAD = \angle BCD = 90^o$, and diagonals $\overline{AC}$ and $\overline{BD}$ intersect at $E$. The ratio $\frac{BE}{DE} = \frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{104}
Among all pairs of real numbers  $(x, y)$  such that  $\sin \sin x = \sin \sin y$  with  $-10 \pi \le x, y \le 10 \pi$ , Oleg randomly selected a pair  $(X, Y)$ .  Compute the probability that  $X = Y$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{20}}
A pentagon is obtained by joining, in order, the points \((0,0)\), \((1,2)\), \((3,3)\), \((4,1)\), \((2,0)\), and back to \((0,0)\). The perimeter of the pentagon can be written in the form \(a + b\sqrt{c} + d\sqrt{e}\), where \(a\), \(b\), \(c\), \(d\), and \(e\) are whole numbers. Find \(a+b+c+d+e\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Example 5 Suppose we have a $4 \times 4$ grid where each cell is colored differently. Each cell is filled with either 0 or 1, such that the product of the numbers in any two adjacent cells is 0. How many different ways are there to fill the grid with numbers?

(2007, Korean Mathematical Olympiad)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1234}
One day, Raviraj left home and cycled 20 km southwards, turned right and cycled some distance, turned right and cycled 20 km, and turned left and cycled 20 km. He will have to cycle 30 km to reach his home straight. How many kilometers did he cycle after the first turn?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Given that the greatest common divisor (GCD) of a pair of positive integers \((a, b)\) is 2015, find the minimum value of \(a+b\) such that \((a+b) \mid \left[(a-b)^{2016} + b^{2016}\right]\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10075}
Three of the four endpoints of the axes of an ellipse are, in some order, \[(-2, 4), \; (3, -2), \; (8, 4).\]Find the distance between the foci of the ellipse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \sqrt{11}}
A question from an old exam asks to find the number of groups of order 2014. Given that $2014 = 2 · 19 · 53$, how many groups of order 2014 are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}