Copyright (c) 1960 Martin Gardner

The game is played on a NxN square. The board starts empty

  • MOVE - Each player drops a stone into an empty cell, which does not form a square with 3 other placed stones of the same color.
    • Squares are not just formed by orthogonal lines, they can make any slope with the board edge.
  • GOAL - Wins the player that moved the last stone.
An example

White cannot play at [1] since it would form a square with c5,e4 and d2 stones.

Black cannot also play there since it would form a black square with b5, d5 and d3.

Gardner, on his legendary Scientific American articles, states that if the board size is even (like the 8x8 Chess board), the game is a win for the 2nd player. Why? He just needs to mirror what the 1st player is doing, until his opponent is out of legal moves. There are two ways to remedy this:

1) Play on odd sized boards, with a center cell where the 2nd player cannot continue to use the mirror strategy.

2) Each player moves twice (except for the first move of the first player). This version, called DM Hip was designed by Mark Thompson and is presented at his website.