Erdős Problem #99
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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A set has minimum distance \(1\) if all pairwise distances are at least \(1\), and the minimum is achieved.
Three points form an equilateral triangle of side length 1.
For sufficiently large n, is it the case that any set of n points with minimum distance \(1\) that minimizes diameter must contain an equilateral triangle of side length 1?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/99.Attempts
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