I was teaching myself how to play the Hex board game by reading some books. I learned how to do 2x2 and 3x3 hex games by starting at the principal diagonal. I wanted to know what the winning strategy would be for player one (white) in a 4x4 Hex game starting from the principal diagonal.
Consider a 4x4 Hex.
Show that White has a winning strategy, starting anywhere on the principal diagonal that is in any of the hexagons 1,6, 11, or 16.
Here is what the setup would be:
Let the Hexagons be represented by numbers such as:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Let White have the first move. Let black have the second move.
White opens up at 6 (principal diagonal).