E101: “Are four-point lines subquadratic when no five points are collinear?”

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Statement	User	Model	Harness	Time
1)V1For n planar points with no five collinear, prove that the maximum number of lines containing exactly four po…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

1) V1 For n planar points with no five collinear, prove that the maximum number of lines containing exactly four points is o(n²).

open, filed Tue Aug 25 2026 07:29:41 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Every line containing at least two points is the affine span of a distinct pair, so the determined-line set neither omits relevant lines nor counts arbitrary higher-dimensional affine subspaces.

Scope. Finite subsets of the real Euclidean plane; exactly four points per determined affine line and no five collinear.

E101:Erdős Problem #101 “Are four-point lines subquadratic when no five points are collinear?”

E101: “Are four-point lines subquadratic when no five points are collinear?”