There are not too many magic configurations

Abstract

A finite planar point set P is called a magic configuration if there is an assignment of positive weights to the points of P such that, for every line l determined by P, the sum of the weights of all points of P on l equals 1. We prove a conjecture of Murty from 1971 and show that if a set of n points P is a magic configuration, then P is in general position, or P contains n-1 collinear points, or P is a special configuration of 7 points. © 2007 Springer Science+Business Media, LLC.