Nim Game

原题：

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

 

Hint:

 

1. If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?

 

翻译：

有一堆石头，你和你的朋友每人每次能拿1至3个，拿走最后一个石头的人胜利。假设你和你的朋友都非常聪明，都知道玩这个游戏的秘笈。现在给你石头的数量，由你先开始拿，如果你一定能赢返回true，否则返回false。

分析：

　　这道题首先要找获胜的方法。策略在于，每个人都取不到4个，假设自己后走，要保证每轮自己和对方取得数量的和是4，这样就能确保每轮完后都有4的倍数个石头被取走，但石头个数必须是4的倍数。所以如果我们先走的话，先把n除4的余数个石头拿走，这样不管怎样，到最后都会留4个下来，对方取a个你就取4-a个，就必赢了。

1 public class Solution2 {3     public bool CanWinNim(int n) 4     {5         return !(n%4==0);6     }7 }

LeetCode Q292 Nim Game(Easy)