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Topic: Hex Win Proof?
Replies: 41   Last Post: Mar 24, 2004 6:39 PM

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 Jonathan Welton Posts: 1 Registered: 12/13/04
Re: Hex Win Proof?
Posted: Mar 19, 2004 5:14 PM

> 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

Date Subject Author
3/18/04 Bill Taylor
3/18/04 Tim Brauch
3/19/04 Brian Chandler
3/19/04 Jonathan Welton
3/19/04 Tim Brauch
3/19/04 Richard Henry
3/20/04 Chan-Ho Suh
3/21/04 Arthur J. O'Dwyer
3/19/04 Bob Harris
3/19/04 Tim Smith
3/19/04 Dvd Avins
3/20/04 Nate Smith
3/20/04 Chan-Ho Suh
3/20/04 G. A. Edgar
3/19/04 Richard Henry
3/19/04 Steven Meyers
3/20/04 Nate Smith
3/20/04 Larry Hammick
3/20/04 Tim Smith
3/21/04 Steven Meyers
3/22/04 Torben Mogensen
3/22/04 Chan-Ho Suh
3/22/04 Torben Mogensen
3/22/04 Chan-Ho Suh
3/23/04 Torben Mogensen
3/23/04 Robin Chapman
3/23/04 Chan-Ho Suh
3/24/04 Robin Chapman
3/24/04 Tim Smith
3/24/04 Robin Chapman
3/24/04 Tim Smith
3/24/04 Jon Haugsand
3/22/04 Andrzej Kolowski
3/23/04 Alexander Malkis
3/23/04 Chan-Ho Suh
3/23/04 Dr. Eric Wingler
3/24/04 Danny Purvis
3/24/04 Danny Purvis