Call a point in the Cartesian plane with integer coordinates a lattice point. Given a finite set S of lattice points we repeatedly perform the following operation: given two distinct lattice points A,B in S and two distinct lattice points C,D not in S such that ACBD is a parallelogram with AB>CD, we replace A,B by C,D. Show that only finitely many such operations can be performed.[I]Proposed by Joe Benton, United Kingdom. combinatoricsRMM Shortlistlattice points