Mathematica Plays Games!

Robert Cowen
Queens College, CUNY

Everyone likes to play games, and a lot can be learned in the classroom from studying strategies for playing them. We consider here the game of Cram, which is played on a rectangular "checker" board. Players take turns placing "dominoes," each of which covers two squares. The last player who can place a domino wins. This game is an example of a Two-Person Impartial game. There is an algorithm for playing such a game which gives a winning strategy, and we describe the algorithm and show how it can be easily implemented in Mathematica and how the game positions can be effectively displayed. We also show how to compute which player wins on the five by five board, which was mentioned as an unsolved problem in Martin Gardner's column in Scientific American in 1974.