Epoch

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 stratgies 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.

題意

我在和我的朋友玩拿石頭遊戲，一次可以拿1~3顆，誰能拿到最後一顆就獲勝了

想法

一開始想用遞迴的方式做

若剩下1~3顆就 return true

4顆就 return false

若大於4顆就遞迴n-1 n-2 n-3

但這個方法好像行不通，所以改列出一下獲勝及失敗的數字

1 win

2 wiin

3 win

4 lose

5 win

6 win 

7 win

8 lose

...

好像發現只要是4的倍數都會失敗

因此只要判斷他是不是4的倍數就可以解開了