  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.
