<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Optimal Rectangle Packing for the 70 Square

West Virginia University, California State University Fullerton

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Optimal Rectangle Packing for the 70 Square"}

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...

Optimal Rectangle Packing for the 70 Square

Published Online: Sep 25, 2018

Page range: 5 - 47

DOI: https://doi.org/10.2478/rmm-2018-0001

Keywords
packing problems, 70 × 70 square

© 2018 Brian Laverty et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Optimal Rectangle Packing for the 70 Square

Published Online: Sep 25, 2018

Page range: 5 - 47

DOI: https://doi.org/10.2478/rmm-2018-0001

Keywordspacking problems, 70 × 70 square

© 2018 Brian Laverty et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
packing problems, 70 × 70 square