Nim Game

Go to the battlefield

Instructions

You are playing the following Nim Game with your friend:

  • Initially, there is a heap of stones on the table.
  • You and your friend will alternate taking turns, and you go first.
  • On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
  • The one who removes the last stone is the winner.

Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false.

/**
 * @param {number} n
 * @return {boolean}
 */
var canWinNim = function (n) {}

Test Cases

t.false(canWinNim(4))
t.true(canWinNim(1))
t.true(canWinNim(2))

Solution

const canWinNim = function canWinNim(n) {
  return n % 4 !== 0
}

Discourse

这道题的核心点在于每次只能移动 1~3 个石头，由此可以推算出如果总数量为 4 的倍数，则后执行者一定在最终操作时移动所有的石头从而赢得比赛。因此只需要判断总数是否为 4 个倍数即可。