11

Part of 1992 Romania Team Selection Test

Problems(1)

lattice polygon P with sides parallel to coordinate axes

Source: Romania IMO TST 1992 p11

In the Cartesian plane is given a polygon

P

whose vertices have integer coordinates and with sides parallel to the coordinate axes. Show that if the length of each edge of

P

is an odd integer, then the surface of P cannot be partitioned into

2\times 1

combinatoricslattice