Affiliation:
1. West Virginia University, California State University Fullerton
Abstract
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.
Subject
General Chemical Engineering
Reference5 articles.
1. [1] Bitner, J., Reingold, E. “Backtrack Programming Techniques”, Communications of the A.C.M., 18(11), 651–656, 1975.10.1145/361219.361224
2. [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/scientificamerican0966-264
3. [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.
4. [4] Korf, R., Moffitt, M., Pollack, M. “Optimal rectangle packing”, Ann Oper Res, 179, 261–295, 2010.10.1007/s10479-008-0463-6
5. [5] Watson, G. “The problem of the square pyramid”, Messenger of Mathematics, New Series, 48, 1–22, 1918.10.1086/479922