A Square-Covering Problem

Abstract

Erdős and Soifer \([3]\) and later Campbell and Staton \([1]\) considered a problem which was a favorite of Erdős \([2]\): Let \(S\) be a unit square. Inscribe \(n\) squares with no common interior point. Denote by \(\{e_1, e_2, \ldots, e_n\}\) the side lengths of these squares. Put \(f(n) = \max \sum\limits_{i=1}^n e_i\). And they discussed the bounds for \(f(n)\). In this paper, we consider its dual problem – covering a unit square with squares.