TIC-TAC-TOE

Tic-Tac-Toe

In this partially completed tic-tac-toe game, both players were experts (neither one ever afforded the other an opportunity to force a win.) What were the first and the last moves played?

Solution:

If O played last, then X can force a win by playing at 4. Since O is an expert, he would not have allowed this. Thus it was X that played last. Since each played has moved three times, this means that O went first.

The only non-losing reponse to a corner opening is to play in the middle. Since the middle is not taken, the opening move could not have been in a corner and must therefore have been at 2.

With that established, trial and error reveals only two possible orders in which the moves could have been played with neither playing giving the other a chance to force the win.
2,1,9,8,3,6 or 2,8,3,1,9,6.