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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access February 2, 2016

Generation of all magic squares of order 5 and interesting patterns finding

  • Ziqi Lin , Sijie Liu , Kai-Tai Fang and Yuhui Deng
From the journal Special Matrices


This paper presents an enumeration algorithm to generate all magic squares of order 5 based on the ideas of basic form (Schroeppel [7]) and generating vector which is extension of Frénicle Quads (Ollerenshaw and Bondi [6]). The results lead us to extend Frénicle-Amela patterns from the case of order 4 to the case of order 5, which we refer to Frénicle-Amela-Like patterns. We show that these interesting Frénicle-Amela-Like patterns appear simultaneously. The number of these patterns is also calculated.


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Received: 2015-10-19
Accepted: 2016-1-12
Published Online: 2016-2-2

©2016 Ziqi Lin et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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