• No Tiling of the 70 × 70...

Result: No Tiling of the 70 × 70 Square with Consecutive Squares

Title:
No Tiling of the 70 × 70 Square with Consecutive Squares
Authors:
Sgall Jiří, Balogh János, Békési József, Dósa György, Hvattum Lars Magnus, Tuza Zsolt
Contributors:
Jiří Sgall and János Balogh and József Békési and György Dósa and Lars Magnus Hvattum and Zsolt Tuza
Publisher Information:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2024.
Publication Year:
2024
Subject Terms:
01.02. Számítás- és információtudomány, ddc:004, Gardner's problem, square packing, combinatorial proof
Document Type:
Conference Conference object<br />Article<br />Part of book or chapter of book
File Description:
application/pdf; text
Language:
English
DOI:
10.4230/lipics.fun.2024.28
Access URL:
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.28
Rights:
CC BY
Accession Number:
edsair.dedup.wf.002..1807ce5a8363e4d997597cf6eaa4001c
Database:
OpenAIRE

Further Information

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.