There are not too many magic configurations

Eyal Ackerman, Kevin Buchin, Christian Knauer, Rom Pinchasi, Günter Rote

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3-16
Number of pages14
JournalDiscrete and Computational Geometry
Issue number1-3
StatePublished - Mar 2008
Externally publishedYes

Bibliographical note

Funding Information:
The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.


  • Discharging method
  • Euclidean plane
  • Euler's formula
  • Lines
  • Magic configuration
  • Murty's conjecture
  • Points

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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