### 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.

Original language | English |
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Pages (from-to) | 3-16 |

Journal | Discrete and Computational Geometry |

Volume | 39 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2008 |

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## Cite this

Ackerman, E., Buchin, K., Knauer, C., Pinchasi, R., & Rote, G. (2008). There are not too many magic configurations.

*Discrete and Computational Geometry*,*39*(1-3), 3-16. https://doi.org/10.1007/s00454-007-9023-0