Question

Two players Oh and Ex alternately choose points of a finite projective plane.
The first player (if any) to make a line in his/her chosen points is the winner.
Using the Erdos-Selfridge theorem, we can see that the game is a draw if the order of the projective plane is 5 or greater. The game is a trivial Oh win if the order is 2. Does Oh win if the order is 3 or 4?

Answer 1

See "Tic-Tac-Toe on a Finite Plane", Maureen T. Carroll and Steven T. Dougherty, Mathematics Magazine, Vol. 77, No. 4 (Oct., 2004), pp. 260-274. (Preprint here: http://academic.scranton.edu/faculty/carrollm1/tictac.pdf) The second player can force a draw on the 3-by-3 and 4-by-4 projective planes.