Diagonal/Non-diagonal Grid Filling

[Jim Nastos]

> > My code finds no solution for 5 x 5 starting either diagonally or
> > orthogonally; trying 7 x 7 now.

> Odd squares cannot be filled, wherever you start.

> Since only 2 squares can be start/end points, there are never enough
> squares available for the outside edge to connect to.


One can always fill n^2-2n+5 squares of an n-by-n board with a
simple pattern (that starts in a corner,) and my programs have not
been able to beat that bound for any value, so I'm inclined to guess
that it's as far as one can get. (On square, odd grids, with paths 
allowing to diagonally intersect themselves.)

J