"Tim Smith" <email@example.com> wrote in message news://htP6c.575$HP.firstname.lastname@example.org... > In article <email@example.com>, Jonathan > 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.