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.

思路：

乍一看，好像没什么思路，则采用举例法来找规律。

若有4块石头，那么你一定会输；

若有5块石头，你可以先拿走1块石头，那么你的朋友就像有4块石头时你的情况一样；

若有6块石头，你可以先拿走2块石头，那么你的朋友就像有4块石头时你的情况一样；

若有7块石头，你可以先拿走3块石头，那么你的朋友就像有4块石头时你的情况一样。

若有8块石头，你拿走x块石头，你的朋友拿走4-x块石头，那么就像有4块石头一样，你一定会输。

因此找到规律，当石头的数量是4的倍数的时候，你一定会输。

代码：

public class Solution {
public boolean canWinNim(int n) {
if(n%4 == 0){
return false;
}else{
return true;
}
}
}