MathDB
Operation on lattice points

Source: 2018 RMM Shortlist C1

February 21, 2019
combinatoricsRMM Shortlistlattice points

Problem Statement

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