Erdős problem 214

Let $S\subset \mathbb{R}^2$ be such that no two points in $S$ are distance $1$ apart. Must the complement of $S$ contain four points which form a unit square?

Sources

The source's own material, retained exactly.

6 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

214.lean

Retained formal statement2 of 6

The best known bounds currently are $4\leq k\leq 7.$

FormalConjectures/ErdosProblems/214.leanErdos214.erdos_214.variants.bounds1 lineExact file

14 ≤ Erdos214.k ∧ Erdos214.k ≤ 7

SolvedStatement only, no proof