Pretzel Solitaire as a Pastime for the Lonely Mathematician

Abstract

In general, playing solitaire card games is a rather sad form of amusing oneself. Starting from a random position of cards on the table, arranged in some predefined format, we have to try to find a sequence of legitimate moves that turn the position into some predescribed goal. The moves are usually irreversible, and therefore dead positions can result where no further move is possible. If we are fortunate enough to reach the goal, we get some feeling of satisfaction. If we run into a dead end, however, we usually feel sad. The reason for distress is not that luck was against us, but that we wonder whether the failure had been unavoidable. We are sad because we feel as though we may have spoiled the game. More often than not, we have forgotten the original position, and now it is impossible to retrace our steps. Failing to solve a solitaire problem is particularly humiliating if it is a game with complete information; that is, all of the cards are facing up.