Erdős Problem #217
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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For which \(n\) do there exist \(n\) points in \(\mathbb{R}^2\), no three on a line and no four on a circle, that determine \(n-1\) distinct distances whose multiplicities are \(1,2,\ldots,n-1\)? The condition \(n>0\) excludes the empty configuration, since the requested number \(n-1\) of distances is nonnegative.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/217.Attempts
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