Date: Mar 19, 2004 5:14 PM
Author: Jonathan Welton
Subject: Re: Hex Win Proof?

> w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote in message news:<716e06f5.0403181938.72a82f90@posting.google.com>...

> > It is an old theorem that in Hex, once the board has been completely

> > filled in with two colours, there *must* be a winning path for one

> > or other of them.

> >

> > Now, I can prove this easily enough mathematically, but I'm wondering if

> > there is a simple proof, or proof outline, that would be understandable

> > and reasonably convincing to the intelligent layman.

> >

> > Can anyone help out please?

>

Neither of the proofs (which are basically the same) posted so far is

correct. Both would apparently conclude that a winning path would be

formed on a squared board, whereas this is not the case - a squared

board could end in a draw.

An actual proof must use the hex nature of the board or,

alternatively, that 3 cells meet at each vertex. A proof is given in

Cameron Browne's book Hex Strategy, but whether it would convince an

intelligent layman is not clear.

Maybe a simpler proof could be achieved by induction?

Jonathan Welton