2011/12/15 by Brant Jones, Jones, Brant, Laura Taalman +3
Computer Science · Mathematics · #00A08 #05C57 #11Y55 #Algorithms and Data Compression #Artificial Intelligence in Games #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #math.CO #msc:00A08 #msc:05C57 #msc:11Y55
paper · pdf · doi:10.48550/arxiv.1112.3593
16 pages
arxiv created 2011/12/15 · openalex publication_date 2011/12/15 · arxiv updated 2011/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.