ANZIAM J.
48 (2006), 151164

Computer solution to the 17point ErdösSzekeres problem

George Szekeres
(deceased)
School of Mathematics
University of NSW
Sydney NSW 2052
Australia



Lindsay Peters
Pacific Knowledge Systems
Australian Technology Park
Eveleigh NSW 1430
Australia
l.peters@pks.com.au



Abstract

We describe a computer proof of the 17point
version of a conjecture originally made by
KleinSzekeres in 1932 (now commonly known as
the "Happy End Problem") that a planar
configuration of 17 points, no 3 points
collinear, always contains a convex 6subset. The
proof makes use of a combinatorial model of
planar configurations, expressed in terms of
signature functions satisfying certain simple
necessary conditions. The proof is more general
than the original conjecture as the signature
functions examined represent a larger set of
configurations than those which are realisable.
Three independent implementations of the computer
proof have been developed, establishing that the
result is readily reproducible.

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