Erdős Problem #101
OPENdatabase updated 2025-08-31
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 maximum number of lines containing exactly \(4\) points among all sets \(S\) of \(n\) points in \(\mathbb{R}^2\) satisfying the condition that no five points are collinear.
Given \(n\) points in \(\mathbb{R}^2\), no five of which are on a line, the number of lines containing four points is \(o(n^2)\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/101.Prize$100
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA006065
Original pageerdosproblems.com/101
Attempts
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Live page status is “OPEN - $100”, with 0 claimed proofs, but “Currently working on this problem” lists rubicon (accessed 2026-07-28); the mandatory collision rule therefore forbids an attempt.
SKIPPED