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From: lee@ukma.UUCP (Carl Lee)
Newsgroups: net.puzzle
Subject: Re: Inverse Tic-Tac-Toe
Message-ID: <2774@ukma.UUCP>
Date: Sat, 1-Mar-86 14:55:10 EST
Article-I.D.: ukma.2774
Posted: Sat Mar  1 14:55:10 1986
Date-Received: Sun, 2-Mar-86 02:37:17 EST
Organization: U of Kentucky, Mathematical Sciences, Lexington KY
Lines: 48
Keywords: tic-tac-toe

>        All good net.puzzlers know that a good tic-tac-toe player will
>always either win or tie a game regardless of whether or not he makes
>the first move.  Two perfect tic-tac-toe players will always end the
>game in a draw.
>
>        Suppose we keep the same rules of playing (3x3 board, alternating
>turns, etc.), but change the requirements for winning.  The winner of
>the game is the player who forces his OPPONENT to occupy three squares
>in a row.
>
>        Is there any strategy which will always permit a player to win?
>If so, which one (first or second)?  Or, will two perfect "toe-tac-tic"
>players always end the game in a draw?
>
>                                -- Chris
>
>PS - My thanks to math whiz Alan Murray, who co-invented this puzzle with
>me.  (It may have been done before, but I haven't heard about it).

Martin Gardner writes in chapter four of his book The Scientific American
Book of Mathematical Puzzles and Diversions:

"Many delightful versions of ticktacktoe do not, however, make use of moving
counters.  For example:  toetacktick (a name supplied by reader Mike Shodell,
of Great Neck, New York).  This is played like the usual game except that the
first player to get three in a row loses.  The second player has a decided
advantage.  The first player can force a draw only if he plays first in the
center.  Thereafter, by playing symmetrically opposite the second player,
he can insure the draw."

"In recent years several three-dimensional ticktacktoe games have been
marketed.  They are played on cubical boards, a win being along any
orthogonal or diagonal row as well as on the four main diagonals of the cube.
On a 3 x 3 x 3 cube the first player has an easy win.  Curiously, the game
can never end in a draw because the first player has fourteen plays and it 
is impossible to make all fourteen of them without scoring."

So, what about playing 3 x 3 x 3 tic-tac-toe, where the first to get three
in a row loses, since there can be no tie?

Carl W. Lee
Department of Mathematics
University of Kentucky
Lexington, KY 40506

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