
Re: Hex Win Proof?
Posted:
Mar 18, 2004 11:03 PM


w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote in 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? >
Here's what I'm thinking...
Suppose you have red going topbottom and blue going leftright. If red does not win, then there must be a path that divides the board into to pieces, a top and a bottom piece. Red cannot be in any position in that path, so it must be blue. Thus blue wins. Rotate pi/2 and switch colors. QED
 Tim
 Timothy M. Brauch Graduate Student Department of Mathematics Wake Forest University
email is: news (dot) post (at) tbrauch (dot) com

