LIPIcs.FUN.2024.28.pdf
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No Tiling of the 70 × 70 Square with Consecutive Squares
Authors
Jiří Sgall 
,
János Balogh ,
József Békési ,
György Dósa ,
Lars Magnus Hvattum ,
Zsolt Tuza
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Part of:
Volume:
12th International Conference on Fun with Algorithms (FUN 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Fun with Algorithms (FUN) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-05-29
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Document Identifiers
Author Details
- Computer Science Institute of Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
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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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