# 【LeetCode】 292. Nim Game

## Description
> 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.

> 你在和朋友玩拈(尼姆)遊戲：有一堆石頭在桌上，每次你的回合可以拿走一到三顆石頭。誰拿走最後一顆石頭的就是贏家。你先手。
> 你們兩個都很聰明，一定會採取最佳策略。請寫一個程式，給予開場的石頭數量，判斷你是能夠贏得這場遊戲。

## Example:

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.

## Solution

* 當石頭為1~3顆，你可以直接拿光，你贏了。
* 當石頭為4顆，你不管拿幾顆，對手都可以拿光，你輸了。
* 當石頭為5~7顆，你都可以拿到剩4顆，你贏了。
* 當石頭為8顆，不管你拿幾顆，對手都可以拿到剩4顆，你輸了。
* 你可以發現，當石頭為`4`的倍數的時候，你會輸，反之則贏。

### Code

class Solution {
public:
    bool canWinNim(int n) {
        return (n % 4);
    }
};

###### tags: `LeetCode` `C++`