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PROVED This has been solved in the affirmative.
Let $t(n)$ be the minimum number of points in $\{1,\ldots,n\}^2$ such that the $\binom{t}{2}$ lines determined by these points cover all points in $\{1,\ldots,n\}^2$.

Estimate $t(n)$. In particular, is it true that $t(n)=o(n)$?
A problem of Erdős and Purdy, who proved $t(n) \gg n^{2/3}$.

Resolved by Alon [Al91] who proved $t(n) \ll n^{2/3}\log n$.

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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #798, https://www.erdosproblems.com/798, accessed 2026-01-16