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:[[de Bruijn's theorem]]: A box can be packed with a [[harmonic brick]] ''a'' × ''a b'' × ''a b c'' if the box has dimensions ''a p'' × ''a b q'' × ''a b c r'' for some [[natural number]]s ''p'', ''q'', ''r'' (i.e., the box is a multiple of the brick.)<ref name="Gems2"/>
The study of polyomino tilings largely concerns two classes of problems: to tile a rectangle with [[congruence (geometry)|congruent]] tiles, and to pack one of each ''n''-omino into a rectangle.
A classic puzzle of the second kind is to arrange all twelve [[pentomino]]es into rectangles sized 3×20, 4×15, 5×12 or 6×10.
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