Packing unit squares in squares: A survey and new results (Q1382966)

For an integer \(n\), let \(s(n)\) denote the side length of the smallest square which admits a packing by \(n\) unit squares (with no restrictions on their positions). The author surveys the best known packings for \(n\leq 100\). He also improves the best known upper bounds for specific values of \(n\) \((\leq 100)\), and presents a relatively simple proof for the exact value of \(s(n)\) for a number of small integers \(n\).