NORTHCOTT's GAME

Copyright (c) ? ??

This game is played on an empty NxM square board (say 8x8). One black and one white stone are placed on each column of the board. This is a possible setup:

 
TURNS - At each turn, each player must move one of his stones, up or down any number of cells, without jumping or capturing the enemy stone.
GOAL - Wins the player that makes the last move
 
An example

It is Black move, and he is about to loose. Whatever he moves (on the d or g column) White can reply and cut all moving possibilities.

There are several applets that play Northcott's game. Check Martin Chlond's page and the great Interactive Mathematics Miscellany and Puzzles website about the game. These applets play the game perfectly. Why? Because this game is just another way to see the game of NIM.

However, it is always possible to change the rules, and get a new game that try to avoid this winning strategy. A possible rule change is to allow that N adjacent friendly stones (sharing the same row) can push N-1 enemy stones on that same row on a column adjacent to one of them, one row left or right ( la Abalone). If a stone is pushed off board, it is captured. Also, if some  stone, has an effect of a pushing, becomes isolated on a column, it is removed from board.

An example

This is the same position as before, but now, Black may move g3-g2, threatening to push f2,g2-h2, capturing two stones. The one pushed off board at h2, and the white stone on column f.

Another possibility was to push g2,f2-e2, and so moving the e2 stone to d2. In that way, the white stone at g5 is captured.