Tilings of (2 × 2 × n)-board with coloured cubes and bricks

• László Németh ^[1]
  1. [1] University of Sopron
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 51, Nº. 5, 2020, págs. 786-798
• Idioma: inglés
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• Resumen

  • Several articles deal with tilings with squares and dominoes on 2- dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with coloured cubes and bricks on a (2 × 2 × n)-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of the tilings of an n-long board considering the (n − 1)-long board. It describes recursively the number of possible breakable and unbreakable tilings. Finally, we give some identities for the recursions using breakability.