Erdős Problem #132
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Prize$100
Topicsdistances
Statement in Leannot yet
Solution in Leanno
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Clemen, Dumitrescu, and Liu proved that every convexly positioned planar n-point set, n>=5, has a non-diameter distance occurring at most n times. Their proof combines the Altman-Fishburn equality classification with a short pair count. This is a published partial; the arbitrary-set and growth questions remain open.
PARTIAL