Prove that any two counters can be made to coincide
Source: All-Russian Olympiad 1996, Grade 10, First Day, Problem 2
April 18, 2013
analytic geometryvectoralgorithmnumber theoryEuclidean algorithmcombinatorics proposedcombinatorics
Problem Statement
On a coordinate plane are placed four counters, each of whose centers has integer coordinates. One can displace any counter by the vector joining the centers of two of the other counters. Prove that any two preselected counters can be made to coincide by a finite sequence of moves.Р. Sadykov