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Some thoughts on polyomino tiles

Published online by Cambridge University Press:  01 August 2016

Nick Mackinnon
Nick Mackinnon*
Affiliation:
Winchester College
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Suppose you are trying to tile an infinite grid of unit squares with 2 x 1 rectangles so that each rectangle covers two squares. You place two of the rectangles without thinking. Can the tiling now be accomplished? As the answer is “yes” I call the rectangle an “idiot-proof tile”. In general a polyomino will be called idiot proof if the infinite grid can be tiled irrespective of the positions of two of the tiles (the idiotic tiles), except that the idiotic tiles shall not be overlapping and shall not completely surround an area that is less than that of the tile (not even an idiot would do that!). The first interesting idiot-proof tile (IPT) is the L-tromino.

Type
Research Article
Information
The Mathematical Gazette , Volume 74 , Issue 467 , March 1990 , pp. 31 - 33
Copyright
Copyright © The Mathematical Association 1990

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