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Optimal Packings of 13 and 46 Unit Squares in a Square

Bentz, Wolfram

Electronic Journal of Combinatorics , 17 (2) (2010), #R126

Let $s(n)$ be the side length of the smallest square into which $n$ non-overlapping unit squares can be packed. We show that $s(m^2?3)=m$ for $m=4,7$, implying that the most efficient packings of 13 and 46 squares are the trivial ones.