The combinatorics of Mancala-type games: Ayo, Tchoukaitlon, and 1/pi

1995/02/09 by Duane M. Broline, Broline, Duane M., Daniel E. Loeb +1
Mathematics · #90D05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:90D05

paper · pdf · doi:10.48550/arxiv.math/9502225

arxiv created 1995/02/09 · arxiv updated 2009/11/30

Abstract

Certain endgame considerations in the two-player Nigerian Mancala-type game Ayo can be identified with the problem of finding winning positions in the solitaire game Tchoukaitlon. The periodicity of the pit occupancies in s stone winning positions is determined. Given n pits, the number of stones in a winning position is found to be asymptotically bounded by n²/π.

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