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Idiot-proof tiles

Published online by Cambridge University Press:  16 November 2021

Branko Grünbaum  and
G. C. Shephard
Branko Grünbaum
Affiliation:
University of Washington, Seattle, U.S.A.
G. C. Shephard
Affiliation:
University of East Anglia, Norwich, England
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Extract

MacKinnon introduced the interesting concept of an idiot-proof tile. This is a polyomino-shaped tile P which has the property that wherever two copies are placed (“by an idiot”) on the square grid, then—so long as the copies do not overlap or enclose a region (“even an idiot would not do that”)—it is possible to adjoin further copies of P so as to complete a tiling of the whole plane. MacKinnon proved that the L-triomino is an idiot-proof tile, and indicated how one could prove that the W-pentomino has the same property. The purpose of this note is to extend MacKinnon’s results, and to formulate some open problems.

Type
Research Article
Information
The Mathematical Gazette , Volume 75 , Issue 472 , June 1991 , pp. 143 - 147
Copyright
Copyright © The Mathematical Association 1991

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Footnotes

*

Research supported in part by NSF grant DMS-9008813.

References

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