Published January 12, 2026 | Version v1

Algebraic Pandiagonal Striped and Semi-Striped Magic Squares of Orders 4 to 12

  • 1. Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Description

This work brings algebraic pandiagonal striped and semi-striped magic squares of orders 4 to 12 for the reduced entries. The even orders are striped magic squares and odd orders are semi-striped magic squares. By reduced or less entries, we understand that instead of normal n^2 entries of a magic square order n, we are using less number of entries. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and negative numbers. Sometimes, we call these kind of magic squares as self-made. It means that these are complete in themselves. Just put the values of the entries and choose the magic sum, we get a magic square. In some cases, there may be decimal or fractional values of the entries depending on the types of magic squares. By striped magic square we understand that it is composed of equal width strips of order 2. The change in only in the lengths of the magic rectangles. There are three types of magic squares studied here. For simplicity we call them as cyclic-type, flat-type and corner-type. This type of work is not known before in the literature of magic square. It is brought for the first time here. For the study on sequential entries magic squares i.e., the idea of double-digit bordered magic squares for sequential number entries is studied by the author. This work is for non-sequential entries.  Moreover, in this work the magic rectangles are considered as  cyclic, flat or corner-types. In case of odd orders, except the magic square of orders 3 or 5, all others are magic rectangles of width 2. The change is always in length of magic rectangles. These kind of magic squares we call as semi-striped. For similar kind of work for different orders in different styles and designs, the readers are suggested to see author’s work

The whole work is also available at author's web-site.

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DD-Pan-Striped-4-12.pdf

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