MathDB
TOT 008 1981 Spring J2 almost centre of symmetry

Source:

August 17, 2019
symmetrygeometrygeometric transformation

Problem Statement

MM is a finite set of points in a plane. Point OO in the plane is called an “almost centre of symmetry” of set MM if it is possible to remove from MM one point in such a way that among the remaining members OO is the centre of symmetry in the usual sense. How many such “almost centres of symmetry” may a finite point set in a plane have? Indicate all such points.
(V Prasolov, Moscow)