An ordinary line is one that passes through exactly two points.
Scaling weights of a magic configuration so that the weights on each line
sum to 1,
the weight of the points on ordinary lines must be
in any magic configuration other than the third example above.
It is known that, for n≥3 noncollinear points,
n lines must be ordinary [CS93].
Settled in [ABK+08], the journal version
of a paper that originally appeared in the Proceedings of
the 2007 Symposium
on Computational Geometry.