TITLE: covering a square with unit squares
QUESTION [15 upvotes]: Can some square of side length greater than $n$ be covered by $n^2+1$ unit squares?  (The unit squares may be rotated. The large square and its interior must be covered.)

REPLY [7 votes]: $\Pi(3)>10$ according to "A note on covering a square with equal squares", Januszweski, The American Mathematical Monthly Vol. 116, No. 2 (Feb., 2009), pp. 174-178.