From: qscgz@aol.com (QSCGZ)
Newsgroups: sci.math
Subject: Re: Four in a row, is it solved?
Date: 12 Jan 1998 13:53:23 GMT

rec.puzzles FAQ  says :


==> competition/games/go-moku.p <==
For a game of k in a row on an n x n board,  for what values of k and n is
there a win?  Is (the largest such) k eventually constant or does it increase
with n?

==> competition/games/go-moku.s <==
Berlekamp, Conway, and Guy's _Winning_Ways_ reports proof that the
maximum k is between 4 and 7 inclusive, and it appears to be 5 or 6.
They report:

. 4-in-a-row is a draw on a 5x5 board (C. Y. Lee), but not on a 4x30
    board (C. Lustenberger).

. N-in-a-row is shown to be a draw on a NxN board for N>4, using a
    general pairing technique devised by A. W. Hales and R. I. Jewett.

. 9-in-a-row is a draw even on an infinite board, a 1954 result of H. O.
    Pollak and C. E. Shannon. 

. More recently, the pseudonymous group T. G. L. Zetters showed that
    8-in-a-row is a draw on an infinite board, and have made some
    progress on showing infinite 7-in-a-row to be a draw.

Go-moku is 5-in-a-row played on a 19x19 go board.  It is apparently a
win for the first player, and so the Japanese have introduced several
'handicaps' for the first player (e.g., he must win with _exactly_
five: 6-in-a-row doesn't count), but apparently the game is still a win
for the first player.  None of these apparent results have been
proven.