In mathematics and game theory, Bulgarian solitaire is a card game that was introduced by Martin Gardner. In the game, a pack of cards is divided into several piles. Then for each pile, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored). If is a triangular number (that is, for some ), then it is known that Bulgarian solitaire will reach a stable configuration in which the sizes of the piles are . This state is reached in moves or fewer. If is not triangular, no stable configuration exists and a limit cycle is reached.