inclusionAI/Ring-lite-rl-data huggingface dataset:
Given that $| \overrightarrow{a}|=6$, $| \overrightarrow{b}|=3$, and $\overrightarrow{a} \cdot \overrightarrow{b}=-12$, find the projection of vector $\overrightarrow{a}$ onto vector $\overrightarrow{b}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4}
Given the set \( S = \{1, 2, \cdots, 1000\} \), a subset \( A \) of \( S \) with 201 elements is called a "good subset" if the sum of the elements in \( A \) is divisible by 5. Find the number of all good subsets of \( S \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{5} \binom{1000}{201}}
In a court-mandated traffic class, there are a certain number of drunk drivers, 3 less than 7 times that many speeders, and twice the number of drunk drivers who are seatbelt violators. If there are 105 students total, how many drunk drivers are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
If $\overrightarrow{a}=(2,-1),\overrightarrow{b}=(t,3)$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse, then the range of real number $t$ is ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty, -6) \cup (-6, \frac{3}{2})}
A set of positive integers is called [i]fragrant[/i] if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements.  Let $P(n)=n^2+n+1$.  What is the least possible positive integer value of $b$ such that there exists a non-negative integer $a$ for which the set $$\{P(a+1),P(a+2),\ldots,P(a+b)\}$$ is fragrant?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Given the general term formula of the sequence ${a_n} = -n + t$ and the general term formula of the sequence ${b_n} = {2^n}$, the sequence ${c_n}$ satisfies ${c_n} = \frac{{{a_n} + {b_n}}}{2} + \frac{{\left| {{a_n} - {b_n}} \right|}}{2}$. It is also known that ${c_n} \geqslant {c_3}(n \in {N^*})$, find the range of values of the real number $t$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[10, 19]}
9. Given that $A B C D$ is a tetrahedron, and each edge is colored red or blue with equal probability, the probability that point $A$ can reach point $B$ through the red edges of the tetrahedron $A B C D$ is $\qquad$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{4}}
How many positive integers $N$ in the segment $\left[10, 10^{20} \right]$ are such that if all their digits are increased by 1 and then multiplied, the result is $N+1$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{171}
已知 $n$ 为正整数, 使得存在正整数 $x_{1}$, $x_{2}, \cdots, x_{n}$ 满足
$x_{1} x_{2} \cdots x_{n}\left(x_{1}+x_{2}+\cdots+x_{n}\right)=100 n$.
求 $n$ 的最大可能值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9702}
If two functions $y=f(x)$ and $y=g(x)$ always satisfy $f(x)g(x) \geqslant 0$ over the same domain, then these two functions are called "harmonious functions". Given $f(x)=ax-20$ and $g(x)=\lg \left(\frac{x}{a}\right)$ ($a\in \mathbf{R}$) are harmonious functions over $x\in N^{*}$, the range of values for $a$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[4,5]}
Determine all real numbers  $a$  for which the system of equations
\begin{align*}
3x^2+2y^2+2z^2&=a
4x^2+4y^2+5z^2&=1-a
\end{align*}
has at least one solution  $(x,y,z)$  in the real numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\left[ \frac{2}{7}, \frac{3}{7} \right]}
4. Sharik and Matroskin are skiing on a circular track, half of which is an uphill climb and the other half is a downhill descent. Their speeds on the climb are the same and four times slower than their speeds on the descent. The minimum distance by which Sharik lags behind Matroskin is 4 km, and the maximum distance is 13 km. Find the length of the track.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Given the sequence $\{a_n\}$, where $a_1=1$ and $a_{n+1}=3a_n+1$ for $n\in\mathbb{N}_+$, and let $b_n= \frac{n}{(3^n-1)\cdot2^{n-2}}\cdot a_n$, $T_n$ is the sum of the first $n$ terms of $\{b_n\}$. If the inequality $2^n\lambda < 2^{n-1}T_n+n$ holds for all $n\in\mathbb{N}_+$, then the range of the real number $\lambda$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty,1)}
Calculate the limit:

$$\lim_{n\to\infty}n\int_0^1 nx^{n-1}\left(\frac{1}{1+x}-\frac{1}{2}\right)\,dx$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/4}
Given a rectangle with a length of 8 and a width of 4, it is folded along a diagonal and pressed flat. Find the area of the overlapping part (grey triangle).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Five different products, A, B, C, D, and E, are to be arranged in a row on a shelf. Products A and B must be placed together, while products C and D cannot be placed together. How many different arrangements are possible?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
Find the set of values of the parameter \(a\) for which the discriminant of the equation \(a x^{2} + 2x + 1 = 0\) is 9 times the square of the difference of its two distinct roots.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-3}
Let $G = \mathbb{Z}/30\mathbb{Z} \oplus \mathbb{Z}$ and $H = \mathbb{Z}/15\mathbb{Z} \oplus \mathbb{Z}/7\mathbb{Z}$ be abelian groups. Determine the number of group homomorphisms from $G$ to $H$, i.e., find the number of elements in $\text{Hom}_{\mathbb{Z}}(G, H)$. \(\text{Hom}_{\mathbb{Z}}(G, H)\)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1575}
Points \( M \), \( N \), and \( K \) are located on the lateral edges \( A A_{1} \), \( B B_{1} \), and \( C C_{1} \) of the triangular prism \( A B C A_{1} B_{1} C_{1} \) such that \( \frac{A M}{A A_{1}} = \frac{3}{7} \), \( \frac{B N}{B B_{1}} = \frac{2}{5} \), and \( \frac{C K}{C C_{1}} = \frac{4}{9} \). Point \( P \) lies within the prism. If the volume of the prism is 40, find the maximum possible volume of the pyramid \( M N K P \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
In a psychology experiment, an image of a cat or an image of a dog is flashed briefly onto a screen and then Anna is asked to guess whether the image showed a cat or a dog. This process is repeated a large number of times with an equal number of images of cats and images of dogs shown. If Anna is correct 95% of the time when she guesses "dog" and 90% of the time when she guesses "cat", determine the ratio of the number of times she guessed "dog" to the number of times she guessed "cat".
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8:9}
A positive integer $k$ is said to be \textit{good} if there exists a partition of $\{1, 2, 3, \ldots, 20\}$ into disjoint proper subsets such that the sum of the numbers in each subset of the partition is $k$. How many \textit{good} numbers are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
24. In a $100 \times 100$ square table, some cells are shaded. Each shaded cell is the only shaded cell either in its column or in its row. What is the maximum number of cells that can be shaded?

## 10th grade
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{198}
A palindrome is an integer that reads the same forward and backward, such as 1221. What percent of the palindromes between 1000 and 2000 contain at least one digit 7?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10\%}
If the maximum value of the function $f(x) = |a\sin x + b\cos x - 1| + |b\sin x - a\cos x|$ is $11$, then $a^{2} + b^{2} =$ ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
Evaluate $\lfloor 3.998 \rfloor + \lceil 7.002 \rceil$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Positive integers $a$, $b$, and $c$ satisfy the equation:
\[
\frac{ab}{a - b} = c
\]
What is the largest possible value of $a + b + c$ that does not exceed 99?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{99}
Given $A \subseteq \{1, 2, \cdots, 2000\}$, and the absolute value of the difference between any two numbers in $A$ is not equal to 4 or 7, find the maximum value of $|A|$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{910}
Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=|\overrightarrow{b}|=2$, and $\overrightarrow{b} \perp (2\overrightarrow{a}+ \overrightarrow{b})$, calculate the angle between vector $\overrightarrow{a}$ and $\overrightarrow{b}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{2\pi}{3}}
A board with dimensions $2018 \times 2018$ is divided into unit cells of size $1 \times 1$. In some cells of the board, black chips are placed, and in others, white chips are placed (each cell contains at most one chip). 

First, we remove all black chips from columns that contain white chips. Then, we remove all white chips from rows that contain black chips. 

Let $W$ be the number of remaining white chips, and $B$ be the number of remaining black chips on the board. Define $A = \min\{W, B\}$. Determine the maximum value of $A$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1018081}
A positive integer $n$ is infallible if it is possible to select $n$ vertices of a regular 100-gon so that they form a convex, non-self-intersecting $n$-gon having all equal angles. Find the sum of all infallible integers $n$ between 3 and 100, inclusive.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{262}
How many coefficients in the binomial expansion of $(x+1)^{65}$ are not divisible by $65$? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
求最小的实数 C，使得对任意正实数 a_1, a_2, a_3, a_4, a_5（允许相同），总可以选择不同的下标 i,j,k,l，满足 \left|\df{a_i}{a_j}-\df{a_k}{a_l}\right|\leq C.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{3}
Given a convex n-gon, circles are drawn with each of its sides as diameters, ensuring that the n-gon can be completely covered by these n circles. Determine the maximum value of n for which this is possible. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
After a storm deposits 115 billion gallons of water into the city reservoir, the reservoir is 80% full. The original contents of the reservoir totaled some gallons. The reservoir was approximately 54.44444444444444% full before the storm. What is the total capacity of the reservoir?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{450}
Mr. Rocky went to the market to sell his handmade crafts on a particular week. He was selling jewelry at $30 each and paintings at $100 each. However, he realized the income from the sales wasn't worth the labor and materials he had used, so he decided to increase the price of jewelry by $10 each and the cost of each painting by 20%. A 6% sales tax was applied to each jewelry item and an 8% sales tax was applied to each painting. Mr. Rocky also decided to offer a 10% discount on the total price if a buyer purchases more than one piece of jewelry, at least three paintings and spends a minimum of $800. Calculate the total price a buyer who takes two pieces of jewelry and five paintings would pay after applying the sales tax and the discount.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$732.80}
How many squares of side at least $8$ have their four vertices in the set $H$, where $H$ is defined by the points $(x,y)$ with integer coordinates, $-8 \le x \le 8$ and $-8 \le y \le 8$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{285}
Given the sequence $\{n(n+4)\left(\frac{2}{3}\right)^{n}\}$, find the value of $k$ such that the $k$-th term is the largest term in the sequence. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
In parallelogram  $ABCD$ ,  $AC=10$  and  $BD=28$ . The points  $K$  and  $L$  in the plane of  $ABCD$  move in such a way that  $AK=BD$  and  $BL=AC$ . Let  $M$  and  $N$  be the midpoints of  $CK$  and  $DL$ , respectively. What is the maximum walue of  $\cot^2 (\tfrac{\angle BMD}{2})+\tan^2(\tfrac{\angle ANC}{2})$  ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
A screenwriter is collaborating with James Nesbitt on a new movie project. They need to write 120 pages of the script. The screenwriter wants to write 3 pages every day, while James suggests writing 5 pages on weekends. If the screenwriter follows this plan and writes every day, how many weekends will it take them to complete the script?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
A 16-step path is to go from $( -4, -4)$ to $(4,4)$ with each step increasing either the $x$-coordinate or the $y$-coordinate by 1. Find the number of such paths that stay outside or on the boundary of the square $-2 \le x \le 2$, $-2 \le y \le 2$ at each step.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1698}
Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=1$ and $(\overrightarrow{a} + \overrightarrow{b}) \perp \overrightarrow{b}$, calculate the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2\pi}{3}}
Given that $\alpha, \beta \in \{1, 2, 3, 4, 5\}$, find the total number of pairs $(\alpha, \beta)$ such that $\sin(\alpha) \cdot \cos(\beta) < 0$. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
There are ten cards, each with one of the digits from 0 to 9. They are arranged in a sequence to display the number 9072543681. If swapping the positions of two adjacent cards is considered one operation, what is the minimum number of operations needed to rearrange the original number into a number that is divisible by 99?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
John and Jane went out for a dinner and they ordered the same dish. John used a 10% discount coupon while Jane used a 15% discount coupon. Both were subjected to a varying tax rate, with John having to pay an 8% tax and Jane having to pay a 6% tax over the original price of the dish. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $1.00 more than Jane, what was the original price of the dish?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$10.81}
As shown in the diagram, \(ABCD\) is a square with side length \(6\). \(ADGH\) is a trapezoid, and points \(E\) and \(F\) are the midpoints of \(AD\) and \(GH\), respectively. It is given that \(HF = 6\), \(EF = 4\), and \(EF \perp GH\). Line segment \(HE\) is extended to intersect \(CD\) at point \(I\). A line segment \(IJ\) is drawn perpendicular to \(HA\). Find the length of \(IJ\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3.6}
Each term of a sequence of natural numbers is obtained from the previous term by adding to it its largest digit. What is the maximal number of successive odd terms in such a sequence?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
What is the largest area of the projection of a rectangular parallelepiped with edges \(a\), \(b\), and \(c\) onto a plane?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2}}}
求下述反三角式子的和：

$\arcsin \frac { \sqrt { 3 } } { 2 } + \arcsin \frac { \sqrt { 8 } - \sqrt { 3 } } { 6 } + \arcsin \frac { \sqrt { 1 5 } - \sqrt { 8 } } { 1 2 } +$

$\cdots + \arcsin \frac { \sqrt { ( n + 1 ) ^ { 2 } - 1 } - \sqrt { n ^ { 2 } - 1 } } { n ( n + 1 ) } ,$

这里n为给定的正整数.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$ \arccos \frac { 1 } { n + 1 } .$}
In trapezoid $PQRS$, the parallel sides $PQ$ and $RS$ have lengths of 10 and 30 units, respectively, and the altitude is 18 units. Points $T$ and $U$ are the midpoints of sides $PR$ and $QS$, respectively. What is the area of quadrilateral $TURS$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{225}
Find the closed form for the sum $S = \frac {2}{3+1} + \frac {2^2}{3^2+1} + \cdots + \frac {2^{n+1}}{3^{2^n}+1}$ and express it in the form $1 - \frac{a^{n+b}}{3^{2^{n+c}}-1}$, where $a$, $b$, and $c$ are integers. Find $a+b+c$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Points $A$, $B$, and $C$ form an isosceles triangle with $AB = AC$. Points $M$, $N$, and $O$ are the midpoints of sides $AB$, $BC$, and $CA$ respectively. Find the number of noncongruent triangles that can be drawn using any three of these six points as vertices.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
If j is the least positive integer that is divisible by every integer from 10 to 15 inclusive, what is the result when j is divided by 26?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2310}
In a certain cleaning solution, the ratio by volume of bleach to detergent to water is 2 : 25 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled, and the ratio of detergent to water is halved. If the altered solution will contain 80 gallons of water, how many quarts of detergent will it contain? Note that 1 gallon equals 4 quarts.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{160}
ABCD is a cyclic quadrilateral with circumcenter $O$ and circumradius 7. The line segments $AB$ and $CD$ intersect at point $E$, while $DA$ and $CB$ intersect at point $F$. Given that $OE = 13$ and $OF = 14$, let $\cos\angle FOE = \frac{p}{q}$, where $p$ and $q$ are coprime integers. Find the sum $p + q$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
Let's call integer square-free if it's not divisible by  $p^2$  for any prime  $p$ . You are given a square-free integer  $n>1$ , which has exactly  $d$  positive divisors. Find the largest number of its divisors that you can choose, such that  $a^2 + ab - n$  isn't a square of an integer for any  $a, b$  among chosen divisors.

*(Proposed by Oleksii Masalitin)*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{k-1}}
For the sequence $\{a_n\}$, we have $a_1 = 5$ and $a_n = 2a_{n-1} + 2^{n} - 1$ for $n \ge 2$ and $n \in \mathbb{N}^*$. If there exists a real number $\lambda$ such that the sequence $\left\{ \frac{a_n + \lambda}{2^n}\right\}$ is an arithmetic progression, then find the value of $\lambda$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1}
the average runs scored by a batsman in 15 matches is 30 . in the next 20 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Given a quadratic function $f(x)=ax^{2}+2x+c$ $(x \in \mathbb{R})$ whose range is $[0, +\infty)$, find the minimum value of $\frac{a+1}{c} + \frac{c+1}{a}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Two fair octahedral dice, each with the numbers 1 through 8 on their faces, are rolled. Let $N$ be the remainder when the product of the numbers showing on the two dice is divided by 8. Find the expected value of $N$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{11}{4}}
Let $X,$ $Y,$ and $Z$ be points on the line such that $\frac{XZ}{ZY} = 3$. If $Y = (2, 6)$ and $Z = (-4, 8)$, determine the sum of the coordinates of point $X$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-8}
Right triangle $XY Z$ has right angle at $Y$ and $XY = 228$, $Y Z = 2004$. Angle $Y$ is trisected, and the angle trisectors intersect $XZ$ at $P$ and $Q$ so that $X$, $P$, $Q$,$Z$ lie on $XZ$ in that order. Find the value of $(PY + Y Z)(QY + XY )$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1370736}
In a hockey tournament, there are $n$ teams participating. Each team plays with every other team exactly once, where the winning team is awarded 2 points, a draw gives each team 1 point, and the losing team gets 0 points. What is the maximum point difference that can occur between teams that are ranked in consecutive positions?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n}
Trapezoid $ABCD$ has $\overline{AB}\parallel\overline{CD}, BC=CD=43$, and $\overline{AD}\perp\overline{BD}$. Let $O$ be the intersection of the diagonals $\overline{AC}$ and $\overline{BD}$, and let $P$ be the midpoint of $\overline{BD}$. Given that $OP=11$, the length of $AD$ can be written in the form $m\sqrt{n}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. What is $m+n$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{194}
Several oranges (not necessarily of equal mass) were picked from a tree. On weighing them, it turned out that the mass of any three oranges taken together is less than 5% of the total mass of the remaining oranges. What is the minimum number of oranges that could have been picked?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{64}
Given that $ \frac{\pi}{2} < \beta < \alpha < \frac{3\pi}{4} $, and $ \cos (\alpha - \beta) = \frac{12}{13} $, $ \sin (\alpha + \beta) = -\frac{3}{5} $. Find the value of $ \sin \alpha + \cos \alpha $.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3\sqrt{65}}{65}}
In the "Turn Back Difference" game, two polynomials $-m$ and $-n$ are operated on sequentially. The operation rule is: the polynomial added in each operation is the difference between the last polynomial obtained in the previous operation and the one before it. Calculate the sum of the polynomials obtained after the $2023$rd operation. Express your answer as a polynomial.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2n}
Let natural numbers \( k \) and \( n \) be coprime, where \( n \geq 5 \) and \( k < \frac{n}{2} \). A regular \((n ; k)\)-star is defined as a closed broken line formed by replacing every \( k \) consecutive sides of a regular \( n \)-gon with a diagonal connecting the same endpoints. For example, a \((5 ; 2)\)-star has 5 points of self-intersection, which are the bold points in the drawing. How many self-intersections does the \((2018 ; 25)\)-star have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48432}