MathDB

In a

m\times n

square grid, with top-left corner is

A

, there is route along the edges of the grid starting from

A

and visits all lattice points (called "nodes") exactly once and ending also at

A

.
a. Prove that this route exists if and only if at least one of

m,\ n

is odd. b. If such a route exists, then what is the least possible of turning points?
*A turning point is a node that is different from

A

and if two edges on the route intersect at the node are perpendicular.

Problem Statement