I'm designing some lessons on Game Theory, various versions to adapt to grades 1 through 9. In one of them I use the game of Hex to talk about games where we can prove some stuff about it even though its game tree is ridiculously huge. (For instance, that somebody always wins, that there is a winning strategy for player one even though we don't know what it is.)
I am wondering what board size would be appropriate so that a game can be played in about 15 minutes. The usual 11x11 is definitely too big.