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Tchuka Ruma Solitaire

Student Symposium

Student Symposium will take place on Thursday, April 19. The Student Symposium schedule is available online.

Paul J. Campbell, Beloit College
Darrah P. Chavey, Beloit College

UMAP Journal, 16(4), (1995), pp. 343-365.


We analyze the game of Tchuka Ruma, a solitaire version of the Mancala family. Although the original game begins with 4 pits and 2 stones in each pit, we look at variations with any number of pits and stones per pit. We show that certain configurations are unwinnable, and these account for all of the forced losses that extensive computer calculation is able to find, except for certain "sporadic" examples that occur with only 2 pits. We investigate the cultural origins of the game, and related games, including the contexts in which the game was played. Evidence is presented that, while not conclusive, indicates that the game has a Malaysian or Indonesian origin.


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This work has been cited by the following papers (that I know of):

Broline, Duane M., and Daniel E. Loeb, 1995, "The Combinatorics of Mancala-Type Games: Ayo, Tchoukaillon, and1/π", in: The UMAP Journal, 16(1), 21-36.

Donkers, J., Uiterwijk, J., and Voogt, A. de, 2002, "Mancala Games – Topics in Artificial Intelligence and Mathematics" in: Step by Step. Proceedings of the 4th Colloquium, Board Games in Academia, (ed. J. Retschitzki, R. Haddad-Zubel), Editions Universitaires, Fribourg, Switzerland.

Dorée, Suzanne, 2008, "Bulgarian Solitaire", in: Resources For Teaching Discrete Mathematics, (ed. by Brian Hopkins).

van den Herik, H. Jaap, Jos W.H.M. Uiterwijk, and Jack van Rijswijck, 2002, "Games solved: Now and in the future" in: Artificial Intelligence, 134, pp. 277–311.