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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Beauty of Magic Squares: 3888-Multiple Order Bordered Magic Squares of Order 144 - Part 2

Authors: Inder J. Taneja;

Beauty of Magic Squares: 3888-Multiple Order Bordered Magic Squares of Order 144 - Part 2

Abstract

This paper presents a systematic construction of multiple order bordered magic squares at orders 12, 20, 30, 42, 56, 72, 108 and 144. for a full structural summary. Unlike classical block-wise bordered magic squares, which are built as multiples of a single block size, the structures explored here incorporate successive borders drawn from magic squares of different orders --- specifically orders 3 through 9 --- each contributing a distinct structural layer.To bring order 144, order 9 is used twice, and finally the order 18 is applied. The magic squares orders are considered as 3, 4, 5, 6, 7, 8, 18 and 18. In some cases, even-order borders consist of equal-sum, while odd-order borders consist of different-sum magic squares. In some cases, the even orders are also considered with different magic sums. The combinatorial multiplicity of border types at each level yields a hierarchy of distinct configurations.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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