Question

Formatted question description: https://leetcode.ca/all/292.html

 292	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:

 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.

Algorithm

List 1 to 10 cases as follows:

1 Win

2 Win

3 Win

4 Lost

5 Win

6 Win

7 Win

8 Lost

9 Win

10 Win

From this we can find the law, as long as it is a multiple of 4, we will definitely lose, so take the remainder of 4 to decide.

Code

Java

public class Nim_Game {

    class Solution {
        public boolean canWinNim(int n) {
            return (n % 4 != 0);
        }
    }
}

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