Solitaire Mancala Games and the Chinese Remainder Theorem
2013; Taylor & Francis; Volume: 120; Issue: 8 Linguagem: Inglês
10.4169/amer.math.monthly.120.08.706
ISSN1930-0972
AutoresBrant Jones, Laura Taalman, Anthony Tongen,
Tópico(s)Constraint Satisfaction and Optimization
ResumoAbstractMancala 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. Additional informationNotes on contributorsBrant JonesBRANT JONES received his B.A. from Bard College in 1997 and his Ph.D. from the University of Washington in 2007. He currently teaches at James Madison University and conducts research in algebraic combinatorics. Beyond mathematics, he also has interests in bicycling and music (eclectically interpreted).Laura TaalmanLAURA TAALMAN received her B.S. from the University of Chicago in 1994 and her Ph.D. from Duke University in 2000. She currently teaches at James Madison University, and has authored two calculus textbooks and five Sudoku books. When not doing mathematics, she enjoys pencil puzzles, videogames, and road trips.Anthony TongenANTHONY TONGEN received his B.S. from the University of Pittsburgh and his Ph.D. from Northwestern University. He was a Fulbright scholar in Mexico for the 2012–2013 academic year, where he shared his joy of sowing games with students at the University of Colima. In Harrisonburg, he and his family enjoy an abundance of Christian community
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