Here's the gamesmanship way of playing tic-tac-toe. Offer the opponent the numerical version and ask to move first or take your turn after the first draw. Choose 2 or 4 or 6 or 8 as your first move. If the opponent makes any move but 5 you win. Then you crow, "When was the last time you lost a game of tic-tac-toe?" ************************ 3-d tic-tac-toe with sides of length 3 is an obvious win for the first player. As I recall, with sides of length 4, it's still a win for the first paper. The length 4 version has an interesting symmetry.
From: "Thane Plambeck" <thane@best.com> Date: Thu, 3 Apr 2003 00:11:09 -0800
Martin Gardner (I think) once suggested playing tic tac toe by instead having the two players choose integers from the set 1,2,3,4,5,6,7,8,9, the first player to obtain a sum of fifteen winning. The magic square
2 9 4 7 5 3 6 1 8
then proves useful.
My question: does anyone know a way to make tic-tac-toe, or something like it, into an interesting game? My sons, 5 and 7, are always wanting to play it and I'm suffering. I'm too strong at dots and boxes to play them with enjoyment.
Here's a problem for an idle moment:
How many essentially different "cat" positions (ie, fully played-out draws) are there in tic-tac-toe with best play, if we regard two as the same under a rotation or reflection of the board?
Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm