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.

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.

Tag: 

Brainteaser

Similar Problems: 

Flip Game II

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Brainstorming:
1 stone, I win.
2 stones, I win.
3 stones, I win.
4 stones, I lose.
5 stones, I can take 1 stone to force you into 4 stones situation. I win.
6 stones,

I can take 2 stones to force you into 4 stones situation. I win.
7
stones, I can take 3 stones to force you into 4 stones situation. I win.

8
stones, whatever number I took for the first round, you can take 1/2/3 stones to force me into 4 stones situation. I lose.
9
stones, I can take 1 stone to force you into 8 stones situation. I win.
...
From
the above situation, we can figure out:
If
the number of stones is multiple by 4, I lose. Otherwise I win.
/**
* @param {number} n
* @return {boolean}
*/
var canWinNim = function(n) {
return n%4 !== 0;
};