Erdős problem 659 · problems.science

Is there a set of $n$ points in $\mathbb{R}^2$ such that every subset of $4$ points determines at least $3$ distances, yet the total number of distinct distances is $\ll \frac{n}{\sqrt{\log n}}$ ?

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AI alongside literature
Erdős AI contributions wiki · 2 Feb, 2026
Machine
Aletheia
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Formalization
Erdős AI contributions wiki · 14 Jan, 2026
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Aristotle
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AI collaborating with humans
Erdős AI contributions wiki · 13 Jan, 2026
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Gemini 3
People
Benjamin Grayzel
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argument
VibeMathed
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Gemini 3, Aletheia
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Benjamin Grayzel
Reported outcome
resolved
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