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

 Messages: [ Previous | Next ]
 Tim Brauch Posts: 201 Registered: 12/6/04
Re: Hex Win Proof?
Posted: Mar 18, 2004 11:03 PM

w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote in

> 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?
>

Here's what I'm thinking...

Suppose you have red going top-bottom and blue going left-right. If red
does not win, then there must be a path that divides the board into to
pieces, a top and a bottom piece. Red cannot be in any position in that
path, so it must be blue. Thus blue wins. Rotate pi/2 and switch colors.
QED

- Tim

--
Timothy M. Brauch
Department of Mathematics
Wake Forest University

email is:
news (dot) post (at) tbrauch (dot) com

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