```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 messagenews://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 alwaysa  winner for a small board, where the number of cases is small and all canbe drawn quickly.  Then show that adding a row and column to a finishedboard will always yield a winning path for one player or the other.> ------------------------------------------------------------------------------->                Bill Taylor        W.Taylor@math.canterbury.ac.nz> ------------------------------------------------------------------------------->                     The empty board waits.>                     Stones cascade down onto it!>                     The game is over.> -------------------------------------------------------------------------------
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