Given this tic-tac-toe position, as played by two expert players, who went first and where? Also, which was the last "move"?

 X | O | O 
---+---+---
   |   | X
---+---+---
   | X | O

(An expert player is a player who would never play in such a way that would allow his opponent to win, and who would also try to get the possible best result.)

Read the comment titled "first step or two."  It shows why the first player could NOT have played in the corner first, and why the second player had to play on an adjacent corner or the opposite side.

So far, I have proved that the first move is on a side, and that the second move is accross or next to the first.

I just noticed something I missed earlier.  O can't have moved last, because then X would go West and force a win after the first six moves shown.  Expert's never win against each other.  I can't believe I missed that... duh!  Therefore, O has to go first, on the top.

There seem to be a few combinations left.  Followin A's idea, I'm going to refer to the spaces with logistic terms like south, north, west, middle, etc.  The moves are listed in columns, each column a separate possibility. I'll add an "-" if I find that the combination is impossible, then include the moves that would force the win.

N  N  N  N  N  N
NW NW NW S  S  S
NE SE SE NE SE SE
-  E  S  NW NW E
SW -  NE SE NE -
W  S  E  E  E  NW
SE

There are still three combinations left, and I'm not sure if I can disprove any of them.  More importantly though, I have enough information to answer the question!

The first move was O's on the top.  The last move was X's on the right.

That's a nice AHA! feeling there.

Posted by Tristan on 2004-05-08 13:56:46