Newsgroups: rec.games.abstract, rec.puzzles
From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: 1996/12/11
Subject: Re: Toe-Tac-Tic problem?

pcis...@nyx10.cs.du.edu (Paul Ciszek) writes:

> I seem to remember something about the 3x3x3 version of tic tac toe
> being unsolved if the players play to "lose", i.e. force the other
> into a row of 3.  Is this the case?  If so, we have a remarkably
> simple game that could still be a intellectual challange.

As I wrote yesterday,

: The first player has an easy win: Play the center, then play opposite
: the second player.  Draw is impossible, and the first player won't
: make three in a row before the second player does.

Having seen a couple of followups claiming draws, let me reiterate
that I am speaking of 3x3x3 three-dimensional tic-tac-toe, where there
are 27 different places to move and 49 possible rows of three.  I base
my claim on a program that enumerated the 8192 different ways of
placing two different markers at the ends of each diameter of the
cube, and found that each such arrangement creates at least two threes
of each color among the 36 non-central rows.  If you really think you
have a counterexample, please e-mail a copy to Hoey@AIC.NRL.Navy.Mil
to be very sure it gets here.

In fact, I haven't found any way of filling the board with black and
white markers without making three in a row, even if we drop the
requirement that there be 14 of one color and 13 of the other.  I'd
like to know what the minimum number of threes is.

In case my open problem was unclear: I don't know the outcome if
two-in-a row is considered a "check" that must be blocked, and the
object is to be checkmated.  That might be an interesting game on a
three-dimensional 3x3x3 board.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil