Spring 2010 Problem 6: Wild tic-tac-toe
Suppose you play tic-tac-toe on the usual three by three board with the following change: on your turn, you can mark either an X or an O. The winner is the first person to get three X's or three O's in a row. Unlike regular tic-tac-toe, this game (with optimal play) does not end in a draw. Who wins (the first or second player) and how?
Solution
While some people got close, no one had the winning strategy. The first player wins as follows: place an X in the center square. The second player must place an O elsewhere. The first player's move should be to place an O in the space opposite the first O. If that's a corner square, any play by the second player results in a win for the first player on the next move. If the second O is one the side, the second player immediately loses unless they play an O on the other side. The first player then ensures that all side spots have an O in them —- no matter how the second player plays, she loses.