2026-07-24T10:14:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19936 2024-05-29T09:43:30Z ddc:004 open_access

No Tiling of the 70 × 70 Square with Consecutive Squares Sgall, Jiří Balogh, János Békési, József Dósa, György Hvattum, Lars Magnus Tuza, Zsolt square packing Gardner’s problem combinatorial proof 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jiří Sgall and János Balogh and József Békési and György Dósa and Lars Magnus Hvattum and Zsolt Tuza 2024 Is Part Of LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FUN.2024.28 urn:nbn:de:0030-drops-199362 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.28 eng https://creativecommons.org/licenses/by/4.0/legalcode