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A Winning Opening in Reverse Hex

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. <italic>Q</italic> <sub>1</sub>. <italic>Q</italic> <sub>2</sub>. <italic>Q</italic> <sub>3</sub>.