# Some Remarks about a Hex Problem

• Claude Berge

## Abstract

The readers of Gardner’s rubric (see Scientific American: July 1957; October 1957; July 1975; December 1975) know the depth and the beauty of the game of Hex, launched almost simultaneously by Piet Hein in Denmark and by John Nash in America. This game is especially appealing to mathematicians. Two players play alternately by putting a peg in an empty hole of the lozenge board shown in Figure 1. The first player uses black pegs, and wins if he manages to construct a chain of black pegs connecting East to West; his opponent tries to construct a chain of white pegs connecting North to South. The best size for a board seems to be 14 × 14, and because a proof by contradiction shows that the first player has a winning strategy, his opponent can require him to put the first peg in a restricted area of the board. Of course, all kinds of handicaps can be used if the two players are not of equal strength, and the aesthetic interest of the game is nearly unchanged.

## Keywords

Restricted Area Winning Strategy Graph Isomorphism Equal Strength Good Size
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