Copyright (c) 2002 Walter Joris

This game is played on a 4x4 board:

SETUP - Black and White, alternating, drop eight friendly stones each.
TURN - During just four turns, each player shifts one row left/right, one column up/down or one of the two main diagonals, just by one cell. 
Every stone pushed out the board is removed from play.
GOAL - After those four turns (i.e., eight shifts), wins the player with more stones on board (or a draw if equal).
An example

Black's turn after the 7th push. In this position, Black has four possibilities to draw the game, push column 'a' or 'd' up, push the 3rd row left or the 2nd row right. 

This game is presented at 100 Strategic Games for Pen and Paper by Walter Joris. The original rules state that the players should write on a shared paper the sequence of those eight shifts before making them. So, the game has also a component of mental representation which adds an extra layer of depth to this game.