Introduction

An enthusiastic group of puzzlers, magicians, and mathematical game buffs held weekend gatherings in Atlanta in January or February of 1993, 1996, 1998, and 2000. These meetings, which honor Martin Gardner, the well-known author and former Scientific American games columnist, are now called “Gatherings for Gardner”. A collection of papers presented at the earlier gatherings was published by [?]. The problems shown in Figure 1 were presented at the fourth such gathering in February 2000. The problem statement appears in [?]. The present paper presents solutions to the problems that appeared in “Four Games for Gardner” for Gathering for Gardner IV. The solutions require some background in combinatorial game theory and thermography, topics with which the readers of this volume are assumed to be familiar.

Superficially, in Figure 1 there appears to be one problem in each of four different well-known games: Go, Domineering, checkers and chess. In each of the four games, the reader is to play white (horizontal in domineering). But lurking below the surface is a more interesting and much deeper problem which occurs if we play the sum of all four games added together.

There may be disputes about how to interpret the rules. Do they matter? In Go, purists might quibble over whether to use the North American, Chinese, or Japanese version of the superko rule. (As in nearly all Go positions, it makes no difference here.)