2 problems

Let $S(n)$ denote the largest edge length of a square that can be covered by $n$ unit squares, and let $\Pi(2)$ denote the minimum number of unit squares needed to cover a square o…

Let $k$ be a positive integer, and let $k^{2}+1$ non-overlapping squares lie inside a unit square. The circumference of a square is its perimeter, and the total circumference is th…