Re: [math-fun] Games of Ramsey and van der Waerden

A simple pairing strategy guarantees Player 2 a win or draw in the Game of Toral Squares. On a 2k x j torus, Player 2 answers (a,b) with (a+k,b). - Scott

David asks:

Who wins in the

Game of Squares: Players take turns placing a marker of their own color (say white or black) on the vertices of an 8x8 square grid until there is some square (tilted or not) with all four vertices having the same-colored markers on them. The player whose color it is loses.

Same question for the slightly more symmetrical

Game of Toral Squares: Same game but on the 64 vertices of GxG, where G is a regular octagon.