Problem 831

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Statement. Let $h(n)$ be maximal such that in any $n$ points in $\mathbb{R}^2$ (with no three on a line and no four on a circle) there are at least $h(n)$ many circles of different radii passing through three points. Estimate $h(n)$.

Status. Open.

Source. erdosproblems.com/831, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #831, https://www.erdosproblems.com/831.

Formalization. None recorded.

Progress

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