Quantum Tic-Tac-Toe

End Games

This month's challenge is an end-game puzzle. X and O have maneuvered around the board without making a single cycle, and now it's move 9. X's last move will, of course, make a cycle that collapses the entire game. Can X win? Can X win regardless of which way the cycle collapses?

Move		X		O
1		3 - 8		1 - 6
3		1 - 8		2 - 9
5		4 - 6		7 - 9
7		5 - 8		7 - 4
9		?

Be sure to include your name and email address! We want to give credit to the person that sends the best solution.

Last month's challenge was to find the widest move spread, with X getting two three-rows or X and O both getting three-rows. The solutions to this challenge require cooperation between X and O, so they don't seem very "game-like." But that's OK, both players learn something about the game by figuring this challenge out.

The earliest that X can get three in a row, is move 5, and the latest is move 9. The earliest that O can get three in a row, is move 6, and the latest is move 8. Let's see what they can do together.

X and O can get three-rows on moves 6 and 9, if they play this way:

Move   X   O 1   1 - 2   4 - 5 3   2 - 3   5 - 6 5   7 - 8   8 - 6 7   9 - 8   9 - 3 9   9 - 3

Whichever way the cycle collapses, O will have a three-row ending with move 6, and X will have one ending with move 9. The move spread is 3. (Could you find a setup that gives X his three-row on move 5, while O gets hers on move 8?)

X can get two three-rows on moves 5 and 9, if O cooperates:

Move   X   O 1   1 - 2   1 - 4 3   2 - 3   2 - 5 5   3 - 6   5 - 7 7   6 - 9   7 - 8 9   9 - 3

When O collapses the cycle, if she makes move 5 real in square 3, then X gets three-rows across the top and down the right side, for a point-and-a-half, and the move spread is 4. But if she makes move 9 real in square three, X gets two points for two three-rows both ending with move 9. The move spread is zero...