The Memory Game

The memory game, or concentration, as it is sometimes called, is a popular card game played by children and adults around the world. Good memory is one of the qualities required in order to succeed in it. This however is not enough. When it is assumed that the players have perfect memory, the memory game can be seen as a game of strategy. The game is analysed under this assumption and the optimal strategy is found. It is simple and perhaps unexpected. In contrast to the simplicity of the optimal strategy, the analysis leading to its optimality proof is rather involved. It supplies an interesting example of concrete mathematics of the sort used in the analysis of algorithms. It is doubtful whether this analysis could have been carried out without resort to experimentation and a substantial use of automated symbolic computations.