Mazes. & Coprime Grids

[Leroy Quet]

By the way...

Regarding my maze question:

According to
http://www.astrolog.org/labyrnth/glossary.htm

the type of maze I am wondering about, where there is exactly one path 
from any square in the maze to any other square, is called a "perfect 
maze".

If we did not require the mazes to not in any way be perfect, or even to 
have a solution, then the maze counting is easy.
For m-by-n grid, we have 2^(m+n-2) mazes, each one of the patterns 
created by turning inner wall segments either on or off.
(So even the following would be a legal maze under this scheme.)
:)

!    -------+
!           !
+---+   +   +       
!           !
!   +   +---+
!       !   !
+-------+   !

==

Regarding coprime-grid question.

We could also ask about grids with toroidal topology.
(Elements at top row must be coprime to respective elements in bottom 
row; elements in left column must also be coprime to respective elements 
in right column.)

thanks,
Leroy Quet