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

 Messages: [ Previous | Next ]
 Chan-Ho Suh Posts: 425 Registered: 12/10/04
Re: Hex Win Proof?
Posted: Mar 20, 2004 4:35 AM

In article <Xns94B1B0DB1B331webmastertbrauchcom@63.223.5.95>, Tim
Brauch <RnEeMwOs.pVoEst@tbrauch.cNOoSPAMm> wrote:

> j_welton@hotmail.com (Jonathan Welton) wrote in
>

> > 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

>
> I wasn't assuming a square board, I was imagining the board set up like
> a parallelogram. At least, that is how I orientate the board when I
> play. Then red goes top to bottom and blue goes left to right (red and
> blue because the board I made uses poker chips).
>

What Jonathan is trying to point out is that you aren't using the fact
that there are hexagons. If you took a checkerboard and squished it to
form a parallelogram (with angles not 90 degrees), then you would have
a board where every piece of the board looked like a little
parallelogram (instead of a hexagon). Clearly we can color this
checkerboard without a winning path by the usual checkerboard coloring.
[I'm not considering two parallelograms that touch only in a corner to
be part of a path]

Your proof attempt makes no use of the specifics of the Hex board, and
so would apply to any board like the one above.
.

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