Nim Game

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： 容易知道当石头的数目是4的倍数时，先手肯定会输，只要后手使得自己拿下的石头后，剩下的石头的数目是4的倍数，后手就会赢。

当石头的数目不是4的倍数时，先手先拿石头后，剩下的数目是4的倍数肯定后手会输。

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