No Tiling of the 70 × 70 Square with Consecutive Squares

Sgall, Jiří; Balogh, János; Békési, József; Dósa, György; Hvattum, Lars Magnus; Tuza, Zsolt

doi:10.4230/LIPIcs.FUN.2024.28

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Document Identifiers

DOI: 10.4230/LIPIcs.FUN.2024.28
URN: urn:nbn:de:0030-drops-199362

Author Details

Jiří Sgall

Computer Science Institute of Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

János Balogh

University of Szeged, Hungary

József Békési

University of Szeged, Hungary

György Dósa

University of Pannonia, Veszprém, Hungary

Lars Magnus Hvattum

Molde University College, Norway

Zsolt Tuza

University of Pannonia, Veszprém, Hungary
HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary

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Jiří Sgall, János Balogh, József Békési, György Dósa, Lars Magnus Hvattum, and Zsolt Tuza. No Tiling of the 70 × 70 Square with Consecutive Squares. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FUN.2024.28

Abstract

The total area of the 24 squares of sizes 1,2,…,24 is equal to the area of the 70× 70 square. Can this equation be demonstrated by a tiling of the 70× 70 square with the 24 squares of sizes 1,2,…,24? The answer is "NO", no such tiling exists. This has been demonstrated by computer search. However, until now, no proof without use of computer was given. We fill this gap and give a complete combinatorial proof.

Subject Classification

ACM Subject Classification

Mathematics of computing → Combinatorics

Keywords

square packing
Gardner’s problem
combinatorial proof

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References

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