1. bookVolume 5 (2018): Issue 9 (September 2018)
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
access type Open Access

Optimal Rectangle Packing for the 70 Square

Published Online: 25 Sep 2018
Volume & Issue: Volume 5 (2018) - Issue 9 (September 2018)
Page range: 5 - 47
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
Abstract

Gardner asked whether it was possible to tile/pack the squares 1×1,…, 24×24 in a 70×70 square. Arguments that it is impossible have been given by Bitner–Reingold and more recently by Korf–Mofitt–Pollack. Here we outline a simpler algorithm, which we hope could be used to give an alternative and more direct proof in the future. We also derive results of independent interest concerning such packings.

Keywords

[1] Bitner, J., Reingold, E. “Backtrack Programming Techniques”, Communications of the A.C.M., 18(11), 651–656, 1975.10.1145/361219.361224Search in Google Scholar

[2] Gardner, M. “Mathematical Games: The problem of Mrs. Perkin’s quilt and answers to last month’s puzzles”, Scientific American, 215(3), 264–272, 1966.10.1038/scientificamerican0966-264Search in Google Scholar

[3] Gardner, M. “The problem of Mrs. Perkin’s quilt and other square-packing problems”, Mathematical Carnival, New York: Alfred A. Knopf, 139–149, 1975.Search in Google Scholar

[4] Korf, R., Moffitt, M., Pollack, M. “Optimal rectangle packing”, Ann Oper Res, 179, 261–295, 2010.10.1007/s10479-008-0463-6Search in Google Scholar

[5] Watson, G. “The problem of the square pyramid”, Messenger of Mathematics, New Series, 48, 1–22, 1918.10.1086/479922Search in Google Scholar

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