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Optimal Packings of 13 and 46 Unit Squares in a Square

Wolfram Bentz

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Source: Crossref

Published: Sep 13, 2010

DOI: 10.37236/398

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Source abstract

Let s(n)s(n) be the side length of the smallest square into which nn non-overlapping unit squares can be packed. We show that s(m2−3)=ms(m^2-3)=m for m=4,7m=4,7, implying that the most efficient packings of 13 and 46 squares are the trivial ones.

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Optimal Packings of 13 and 46 Unit Squares in a Square — Mathematical Frontier Network