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.

分析：尋找先手必勝的情況。由於雙方都足夠聰明，結果是可預知的：

1，2，3 先手必勝;

4　　　　 後手必勝;

5，6，7 先手必勝（通過讓對手得到只有四個石頭剩余的情況取勝）;

4　　　　 後手必勝;（無論怎樣都不可避免拿到只有四個石頭剩余的情況）;

思路：判斷是否為4的整數倍即可。

JAVACODE

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

Nim Game