ABSTRACT
We begin with a brief discussion of the game of Hex, discovered about 30 years ago. Two players, White and Black, play on a board consisting of n rows and columns of hexagons arranged in a rhombus. The 4 × 4 hexboard is illustrated in Figures 1, 2, 3, 4, and 5. White plays first and places a white marker in some hex (hexagon). Then Black places a black marker in another hex. White and Black continue to take turns, each placing a marker of his color in an unoccupied hex. White wins if he joins the top edge of the hexboard to the bottom edge with a chain of adjacent hexes containing white markers. (Two hexes are adjacent if they have a common side.) Similarly, Black wins if he forms a black chain joining the left and right edges. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315224169/bc8ae104-41e9-4605-a352-2689f2cb97f2/content/fig19_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <italic>Q</italic> <sub>1</sub>. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315224169/bc8ae104-41e9-4605-a352-2689f2cb97f2/content/fig19_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <italic>Q</italic> <sub>2</sub>. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315224169/bc8ae104-41e9-4605-a352-2689f2cb97f2/content/fig19_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <italic>Q</italic> <sub>3</sub>. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315224169/bc8ae104-41e9-4605-a352-2689f2cb97f2/content/fig19_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315224169/bc8ae104-41e9-4605-a352-2689f2cb97f2/content/fig19_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
