Leetcode 292. Nim Game

Question

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.

Solution

Cases of this game:

  1. When number of stone is 1 ~ 3 , you win.
  2. When number of stone is 4, you always lose
  3. when number of stone is 5 ~ 7 , you can take 1 ~ 3 stones. and your oppenent will start game with 4 , you win.

So If the number of stones is a mutiple of 4 , you always lose.

# @param {Integer} n
# @return {Boolean}
def can_win_nim(n)
return false if n % 4 == 0
return true
end
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