Abstract. We explain some analytic methods that can be useful in solving Hex puzzles.

Introduction

Solving Hex puzzles can be both fun and challenging. In this paper – a puzzling companion to Hex and Combinatorics and Dead Cell Analysis in Hex and the Shannon Game, both written in tribute to Claude Berge – we illustrate some theoretical concepts that can be useful in this regard.

We begin with a quick review of the rules, history, and classic results of Hex. For an in depth treatment of these topics, see.

The parallelogram-shaped board consists of an m × n array of hexagonal cells. The two players, say Black and White, are each assigned a set of coloured stones, say black and white respectively, and two opposing sides of the board, as indicated in our figures by the four stones placed off the board. In alternating turns, each player places a stone on an unoccupied cell. The first player to connect his or her two sides wins.

In the fall of 1942 Piet Hein introduced the game, then called Polygon, to the Copenhagen University student science club Parenthesis. Soon after, he penned an article on the game for the newspaper Politiken. In 1948 John Nash independently reinvented the game in Princeton, and in 1952 he wrote a classified document on it for the Rand Corporation.