Sowing Games

Abstract:  . At the Workshop, John Conway and Richard Guy proposed the class of "sowing games", loosely based on the ancient African games Mancala and Wari, as an object of study in combinatorial game theory. This paper presents an initial investigation into two simple sowing games, Sowing and Atomic Wari. 1. Introduction Most well-studied combinatorial games can be classified into a few broad classes. Taking and Breaking: Games played with piles of chips, in which the basic move is to take some chips and/or split some piles. They include Nim, Kayles, Dawson's Chess, other octal and hexadecimal games. Higher-dimensional variants include Maundy Cake, Cutcake, Eatcake, and Chomp. Cutting and Coloring: Games played on (colored) graphs, in which the basic move is to cut out a small piece of the graph of the appropriate color, possibly changing other nearby pieces. They include Hackenbush, Col, Snort, Domineering, and Dots and Boxes. Sliding and Jumping: Games played with tokens on a grid-like boa...