Abstract
In the game of Bulgarian Solitaire, analyzed by Akin and Davis ( Amer. Math. Monthly 92 (1985), 237–250), a “position” consists of N “stones” divided among k non-empty piles in some fashion. Simple rules are then applied to move the stones to a succession of new positions. This present game, “Montreal Solitaire,” is similar, but with a different set of rules. One effect of the rule changes is to make the process reversible, and any given initial position is reached again after finitely many steps. Thus we have an example of a finite, cyclic automaton. A useful invariant, which helps compute many interesting properties of the game, including a count of the number of distinct positions, and much information on periods, is discussed.
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