Here’s a little problem that Halyun brought up in group meeting today — a little googling showed that it’s a Putnam prep problem, but I won’t hold that against it. The problem is “Determinant Tic-Tac-Toe.” This is like regular Tic-Tac-Toe except that Player One puts a “1” in the square and Player Two puts a “0.” The grid forms a 3×3 matrix (call it ), and Player Two wants to make , whereas Player One wants to make . Player One gets to move first. Is there a winning strategy for either player? What if both players can place arbitrary real numbers? What about a general grid?