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.
啊,这个是个数学问题,赢的要点就是,在你的对手最后一次拿的时候,石头要是4个, 这时无论他拿1、2、3个,你都有石头拿。要保证这一点,你需要保证每次你拿完时石头的个数是4的倍数。那就意味着一开始石头的数目不是4的倍数。
/**
* @param {number} n
* @return {boolean}
*/
var canWinNim = function(n) {
return (n%4===0) ? false : true;
};