## Eyal Ackerman, Kevin Buchin, Christian Knauer, Rom Pinchasi, and
Günter
Rote:

# There are not too many magic configurations

*In: Proceedings of the 23rd Annual Symposium on Computational
Geometry, Gyeongju, South Korea, June 6-8, 2007. Association
for Computing Machinery, 2007, pp. 142-149. *doi:10.1145/1247069.1247098
*Discrete and Computational Geometry 39 (2008), pp. 3-16.
*doi:10.1007/s00454-007-9023-0

### 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 a magic configuration
consists
either of points in general position, or all points are collinear, with
the
possible exception of one point, or they form a special configuration
of 7
points.
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Last update: August 14, 2017.