Erdős Problem #1085
OPENdatabase updated 2025-10-17
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The maximal number of pairs of points which are distance 1 apart that a set of `n` points in `ℝ^d` make.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · 7 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1085.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA186705
Original pageerdosproblems.com/1085
Attempts
submit one →Read our working report →
Proved the exact near-simplex band \(f_d(n)\) for \(n\le2d\) (including \(f_d(d+3)=\binom{d+3}{2}-3\) in every dimension), proved \(f_3(7)=15\), and corrected the live page's three-dimensional upper b
PARTIAL