The combinatorics of Mancala-type games: Ayo, Tchoukaitlon, and 1/pi
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 stone...
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| Zusammenfassung: | 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 $n^{2}/\pi$. |
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| DOI: | 10.48550/arxiv.math/9502225 |