As mentioned in my previous post, here I will give several example of impartial game which turn out to be exactly equivalent to Nim Game.

Nimble
Given a line of squares labeled 0, 1, 2, …. Several coins are placed on some squares (it’s possible to have more than one coin on a single square). Two players take turns. One move consists of taking any one coin and moving it to any square to the left of it. It’s possible that the coin moved into a square already containing coins.

I’ll discuss a little bit about Nim Game. Felix said that he doesn’t understand about Nim Game so he asked me to write a blog. I don’t know whether he really doesn’t understand or he is just looking for a reason to make me write.

Nim is a two player combinatorial/mathematical game strategy. Given a number of piles which in each pile contains some numbers of stones. In each turn, player choose one pile and remove any number of stones (at least one) from that pile. In a normal play, player who cannot move is considered lose (ie., one who take the last stone is the winner). There is another variation where player who cannot move is considered as winning (misere play).