Saturday, September 16, 2017

geometry - Tiling rectangles with a Heptomino plus 2x2 square


Inspired by Polyomino T hexomino and rectangle packing into rectangle


See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1


Previous puzzle in this series Tiling rectangles with Heptomino plus rectangle #7


The goal is to tile rectangles as small as possible with each of the given heptominoes (see diagram in example below) plus 2x2 squares.



Example Using the snake heptomino 'e' plus 2x2 squares you can tile a $3\times 5$ as follows: 2_86_3x5


Use each of these heptominoes. Solutions may exist for other heptominoes, I only found solutions for these ones. Note that I omitted labels 'W', 'j', 'l': Heptomino2x2KnownTilersLabelled2


All of these could all be tiled by hand, of course the bigger ones will be challenging. I'm making this one a 'hand tiling only' puzzle. In other words, use a computer to do anything except look up or compute the arrangements.




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