Tic-Tac-Toe on Designs
Tic-Tac-Toe on Designs
We consider playing the game of Tic-Tac-Toe on block designs BIBD($v, k, \lambda$) and transversal designs TD($k, n$). Players take turns choosing points and the first player to complete a block wins the game. We show that triple systems, BIBD($v, 3, \lambda$), are a first player win if and only …