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

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Brian Chandler

Posts: 1,899
Registered: 12/6/04
Re: Hex Win Proof?
Posted: Mar 19, 2004 2:09 AM
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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?


Imagine the board tipped up, so player A goes from top to bottom,
player B from left to right. Suppose the board is actually two sheets
of clear plastic, and two players have "stones" of white sugar (A) and
red granite (B), and moreover these stones "plug" the hexagon cells
(in the obvious way).

Now pour water in at the top. Either it dissolves through the sugar
and reaches the bottom, in which case A has a path, or it doesn't, in
which case there must be a continuous boundary of impervious granite,
and B has a path.

(Does this help? I think it does (slightly) use some facts about the
behaviour of liquids to help the imagination along.)

Brian Chandler
http://imaginatorium.org



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

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