292. Nim Game 难度：easy

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：

题目要求桌子上给定n个石头，我先取，一次可以取1~3个，双方轮流着取，问我是否能拿走最后一个石头。这题目相当于一道找规律的题目，我们发现当我们取倒数第二次的时候，如果桌子上能只剩下4个石头的话，我们肯定能赢，于是题目问n个石头时候相当于问n - 4个石头的时候，然后我们很轻易能知道当只有1、2、3个石头的时候是肯定能赢的，有4个石头的时候肯定会输，于是8、12、16等等能整除4的个数的石头都肯定会输，所以题目就变成问所给的数能否整除4。接下来的程序就非常简单了。

程序：

class Solution {public:    bool canWinNim(int n) {        return (bool)(n % 4);    }};