
Re: Hex Win Proof?
Posted:
Mar 19, 2004 12:50 PM


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

