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Solitaire Mancala Games and the Chinese Remainder Theorem

Brant Jones, Laura Taalman and Anthony Tongen
The American Mathematical Monthly
Vol. 120, No. 8 (October 2013), pp. 706-724
DOI: 10.4169/amer.math.monthly.120.08.706
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Page Count: 19
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Solitaire Mancala Games and the Chinese Remainder Theorem
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Abstract Mancala is a generic name for a family of sowing games that are popular all over the world. There are many two-player mancala games in which a player may move again if their move ends in their own store. In this work, we study a simple solitaire mancala game called Tchoukaillon that facilitates the analysis of “sweep” moves, in which all of the stones on a portion of the board can be collected into the store. We include a self-contained account of prior research on Tchoukaillon, as well as a new description of all winning Tchoukaillon boards with a given length. We also prove an analogue of the Chinese Remainder Theorem for Tchoukaillon boards, and give an algorithm to reconstruct a complete winning Tchoukaillon board from partial information. Finally, we propose a graph-theoretic generalization of Tchoukaillon for further study.

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