Cram | Topological Games

The players take turns linking pairs of dots on a grid. The first player unable to move loses.

History

The game was originally proposed by Geoffrey Mott-Smith who called it Plugg, and was described by Martin Gardner as the game Cram in "Mathematical Games: Cram, Crosscram and Quadraphage: New Games having Elusive Winning Strategies." Scientific American 230, 106-108, Feb. 1974.
It is related to the game Domineering, which is identical except that one player can only make vertical moves and the other player can only make horizontal moves.

Description

The game is played on a matrix of dots.
The players take turns in linking a pair of adjacent dots with a horizontal or vertical link. No dot can be linked more than once.
In the normal game the first player unable to move loses.
Alternatively, in the misère version, the first player who cannot move wins.

Strategy

Normal Cram has a simple winning strategy on boards with an even side. On an even-by-even grid the second player can win by making a symmetric copy of each of the first player's moves. On an even-by-odd grid the first player can win by making the first move on the centre two squares, and thereafter making a symmetric copy of each of the second player's moves.

Tags: Pencil and Paper games,topological games