Show that a path on an m by n square grid which
starts at the north-west corner, goes through each point
exactly once and ends at the south-east corner divides the grid
into two equal halves:
(a) those regions opening north or east;
and
(b) those regions opening south or west.
Proposed by David Ficher, Karen Collins & Lucia Krompart
in "The American Mathematical Monthly", Volume
101, Number 8/October 1994