題目

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.

Example:

Input: 4
Output: false 
Explanation: 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.

十分鐘思考

其實我沒有思考，感覺沒有思路，後來發現就是歸納證明問題。下次可以試試這個思路。本題目只要總數不可以被4整除，就能贏

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