From: cet1@cus.cam.ac.uk (Chris Thompson) Newsgroups: sci.math Subject: Re: Four in a row, is it solved? Date: 12 Jan 1998 00:27:50 GMT In article <695d3k$pqf$1@gannett.math.niu.edu>, Dave Rusin wrote: >In article <68lvg0$bj2$1@ubnnews.unisource.ch>, >Daniel Baechli wrote: >>My question is concerning Four in a row played >>on a 8x8 board in two dimensions or with a 4x4x4 >>board in three dimensions. >>The obligate question - is the optimal >>strategy determined for any of the two? > >I was hoping someone else would fill in details here. All I could find >was a comment suggesting the answers are known. What follows is an extract >of a post which was in turn quoting a previous post! which many layers deep becomes >> 3. 4x4x4 tic tac toe. Recently show to be a win for the first >> player. The strategy for doing it is rather involved. where of course the time to which "recently" is bound is not obvious. Just to point out that it can hardly be so described any longer: Oren Patashnik proved this in May 1977 (by his own account) and it was published in Mathematics Magazine Vol 53 No 4 (Sep 1980) pp 202-216. As regards the minimum square board in two dimensions in which (8-direction) 4-in-a-row is a first player win: it's a draw on a 5x5 board (see Winning Ways) but seems to be obviously a first player win on a 7x7 board [start by playing in the centre, of course: am I missing something?]. The difficult case would seem to be 6x6. Chris Thompson Email: cet1@cam.ac.uk