c# 编程题，请会的大佬直接留下代码，输入输出得一致

Question

Here is a wheel with 10 numbers:

Suppose that the wheel begins in the position above. We are given an integer N in the range 0 ≤ N ≤ 100. We will spin the wheel three times. On each of the three spins, the wheel will rotate counterclockwise by a number of positions randomly chosen (uniformly) from the integers 0 .. N. For example, if N = 3, then on each spin there is

• a 1/4 chance that it will not rotate
• a 1/4 chance that it will rotate by 1 position
• a 1/4 chance that it will rotate by 2 positions
• a 1/4 chance that it will rotate by 3 positions

What is the exact probability that after the 3 spins the wheel will end up in the same position in which it started, i.e. pointing to number 1?

Write a program that can answer this question. The program should read the integer N on a single line of standard input, and write the answer as a fraction in reduced form.

Sample input:

3

Output:

1/64

Explanation: When N = 3, the wheel cannot possibly make a complete rotation in 3 spins. So it will end up at the starting position only if it never moves. On each spin, the probability that it won't move is 1/4, so the probability that it never moves is

    (1/4)(1/4)(1/4) = 1/64

Sample input #2:

9

Output:

1/10

Explanation:

When N = 9, the wheel will be in a (uniformly) random position after every spin. Therefore after 3 spins (or any number of spins, for that matter), the probability that it will be pointing to the number 1 is 1/10.

Sample input #3:

7

Output:

13/128

Hint:

Consider every possible sequence of 3 spins, and count how many of them end at the starting position. The probability of ending at the starting position is this count divided by the number of possible sequences.

Answer 1

 因为题目的n比较小，是一百以内的，O(n^3)也只有10^6，所以暴力解就行了，一般不会超时。

using System;
namespace HelloWorldApplication
{
    class HelloWorld
    {
		static int gcd(int a, int b){
			if(b == 0)return a;
			return gcd(b, a%b);
		}
        static int Main(string[] args)
        {	
			
			int n = int.Parse(Console.ReadLine());
			//int n = 3;
			if(n == 0){
				Console.WriteLine("1");
				return 0;
			}
			int trueNum=0, allNum=0;
			for(int i = 0; i <= n; i++){
				for(int j = 0; j <= n; j++){
					for(int k = 0; k <= n; k++){
						int sum = i + j + k;
						if(sum % 10 == 0){
							trueNum++;
						}
						allNum++;
					}
				}
			}
			int ggcd = gcd(trueNum, allNum);
			trueNum /= ggcd;
			allNum /= ggcd;
			Console.WriteLine(trueNum+"/"+allNum);
			return 0;
        }
    }
}