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

 Messages: [ Previous | Next ]
 Dvd Avins Posts: 1 Registered: 12/13/04
Re: Hex Win Proof?
Posted: Mar 19, 2004 11:57 PM

"Tim Smith" <reply_in_group@mouse-potato.com> wrote in message
> Welton wrote:

> > 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

>
> The key fact I need is that if a red path is blocked from going around

blue
> hex A by blue hex B, then A and B are adjacent. That property does not
hold
> on a checkerboard. Is this what you mean by using the hex nature of the
> board?

I'm sure that's what he means. In simple terms, there's no corner where
spaces touch diagonally. Spaces have an edge in common, or they don't touch
at all.

If you want to get a little more detailed, you can prove that there can't be
any corner-touching if there's no place where more than three spaces come
together. And with hexes, they don't.

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