Saturday, 12 April 2014

Squared square

My interest in the squared square was sparked after reading Chris Shepherd's Squared.  A square is said to be squared if it is completely covered by smaller squares of integer side lengths without overlapping.  A squared square is simple if it does not contain a smaller squared rectangle.  It is perfect if all its constituent squares are of different sizes.  Discovered only as recently as in 1978 by A.J.W. Duijvestijn, the smallest possible simple perfect squared square contains 21 smaller squares and has a side length of 112, with Bouwkamp code [50, 35, 27], [8, 19], [15, 17, 11], [6, 24], [29, 25, 9, 2], [7, 18], [16], [42], [4, 37], [33]:

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