Erdős Problem #105
DISPROVED LEANdatabase updated 2025-11-22
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(A,B\subset \mathbb{R}^2\) be disjoint sets of size \(n\) and \(n-3\) respectively, with not all of \(A\) contained on a single line. Is there a line which contains at least two points from \(A\) and no points from \(B\)? This has been disproved by Xichuan in the comments, who has found three explicit counterexamples.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/105.Prize$50
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/105
Attempts
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