Erdős problem 105 · problems.science

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 $B$ ?

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

105.lean

Retained formal statement4 of 4

It remains possible that this holds with $n-4$ (or in general with $n-O(1)$ or $(1-o(1))n$ ).

FormalConjectures/ErdosProblems/105.leanErdos105.erdos_105.variants.sub_four3 linesExact file

1True ↔2  ∀ (A B : Finset (EuclideanSpace ℝ (Fin 2))),3    Disjoint A B → A.card = B.card + 4 → ¬Collinear ℝ ↑A → ∃ p ∈ A, ∃ q ∈ A, p ≠ q ∧ ∀ b ∈ B, b ∉ affineSpan ℝ {p, q}

OpenStatement only, no proof

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