Erdős Problem #210
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The sharp ordinary-line guarantee for noncollinear sets of \(n\) points. For \(n<3\), there are no such configurations, and the infimum is \(0\).
Let \(f(n)\) be the sharp guarantee such that, for any \(n\) points in \(\mathbb R^2\), not all on a line, there are at least \(f(n)\) lines which contain exactly two points (called ordinary lines). Does \(f(n)\to\infty\)? That \(f(n)\to\infty\) was proved by Motzkin [Mo51].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 9 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/210.Prizenone
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA003034
Original pageerdosproblems.com/210
Attempts
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