[Leetcode] 292. Nim Game

题目：
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:

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?

思路：如果最后你一定会赢的是，需要在倒数第二轮取数后，剩余的stones的个数为4个，这样无论对手取1-3中的几个，最后你都会赢。
接着考虑你如何才能使stones剩余个数为4，即在你取的时候stone的个数是5~7个，如果是8个的时候，无论你怎么取，剩余的stones的数量都不会是4，所以在你取的时候如果是8个stones你就不会赢，以此类推，最终可以得，如果在你取的时候stones的个数是4的倍数，你就可能不会赢，如果你能保证你取完后，stones的个数是4的倍数，你最终会赢。

代码实现：

public class Solution {    public boolean canWinNim(int n) {        return (n%4)!=0;    }}