MathDB

Let

m,\ n

be integers such that

2\leq m\leq n

and let

a,\ a'

be integers which are less than or equal to

m

and let

b,\ b'

be integers which are less than or equal to

n

such that

(a,b)\neq (a'\ b').

Given a town of the rectangular shaped chessboard which is made up of

m's

road running north and south which is called Line and

n's

road running west and east which is called Street. Denote the intersection point of the

a

th Line from the west and

b

th Street from the north by

A

, and

a'

th Line from the west and

b'

th Street from the north by

B,

including the edge for both cases.Find all pair of

(m,n,a,b,a', b')

such that by passing through each crossroads of the town exactly one time, you can reach the point

B

from the point

A

including in the start point and goal one.

Problem Statement