Date: Mar 19, 2004 12:50 PM
Author: Richard Henry
Subject: Re: Hex Win Proof?



"Bill Taylor" <w.taylor@math.canterbury.ac.nz> 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?
>


Looks like an opportunity for an inductive proof. Show that there is always
a winner for a small board, where the number of cases is small and all can
be drawn quickly. Then show that adding a row and column to a finished
board will always yield a winning path for one player or the other.


> --------------------------------------------------------------------------
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> Bill Taylor W.Taylor@math.canterbury.ac.nz
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> The empty board waits.
> Stones cascade down onto it!
> The game is over.
> --------------------------------------------------------------------------

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