A Combinatorial Problem Which Is Complete in Polynomial Space. The Game of Hex and the Brouwer Fixed-point Theorem. A. A few. It looks so simple to program. A. Hex is simple, but standard computer chess methods would be woefully inadequate.
Human players use several powerful reasoning techniques to analyse the game.
A good hex program must approximate these methods. That's what my thesis work is about. I don't know, maybe in a few months.