An optimal bound on the number of moves for open Mancala

Alessandro Musesti; Maurizio Paolini; Cesco Reale

doi:10.1016/j.disc.2015.04.013

paper

An optimal bound on the number of moves for open Mancala

arXiv:1310.8088 · doi:10.1016/j.disc.2015.04.013

Abstract

We determine the optimal bound for the maximum number of moves required to reach a periodic configuration of open mancala (also called open owari), inspired by a popular African game. A mancala move can be interpreted as a map from the set of compositions of a given integer in itself, thus relating our result to the study of the corresponding finite dynamical system.