PPL 067 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 067Erdős Problem #604

Permanent problem IDPPL 067

Verified openErdősconjecture

Geometry

Erdős Problem #604

Given n distinct points A⊂ℝ^2 must there be a point x∈ A such that \#{ d(x,y) : y ∈ A} ≫ n^(1-o(1))? Or even ≫ n/√(log n)?

geometrydistances
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The problem

Given n distinct points A⊂ℝ^2 must there be a point x∈ A such that \#{ d(x,y) : y ∈ A} ≫ n^(1-o(1))? Or even ≫ n/√(log n)?

Open since1957earliest source
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$500Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

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Sources & reading

2 unique reference linksCanonical problem page Claim or award rules
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Related open targets

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