{"id":17599,"date":"2026-01-12T10:32:20","date_gmt":"2026-01-12T13:32:20","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=17599"},"modified":"2026-01-17T02:14:33","modified_gmt":"2026-01-17T05:14:33","slug":"algebraic-pandiagonal-striped-and-semi-striped-magic-squares-of-orders-4-to-12","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=17599","title":{"rendered":"Algebraic Pandiagonal Striped and Semi-Striped Magic Squares of Orders 4 to 12"},"content":{"rendered":"\n

This work brings algebraic pandiagonal striped<\/strong> and semi-striped<\/strong> magic squares of orders 4 to 12 for the reduced entries<\/strong>. The even orders are striped<\/strong> magic squares and odd orders are semi-striped<\/strong> magic squares. By reduced<\/strong> or less entries<\/strong>, we understand that instead of normal n^2<\/strong> entries of a magic square order n<\/strong>, 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<\/strong>. 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<\/strong> 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<\/strong>, flat-type<\/strong> and corner-type<\/strong>. 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<\/strong> 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<\/strong>, flat<\/strong> or corner-types<\/strong>. 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<\/strong>. For similar kind of work for different orders in different styles and designs, the readers are suggested to see author\u2019s work<\/p>\n\n\n\n

<\/p>\n\n\n\n

This work is online available at the following link:
Inder J. Taneja<\/strong>, Algebraic Pandiagonal Striped and Semi-Striped Magic Squares of Orders 4 to 12, Zenodo<\/strong>, January 12, 2026, pp. 1-52, https:\/\/doi.org\/10.5281\/zenodo.18221904<\/a>.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Algebraic Pandiagonal Striped Magic Squares of Even Orders<\/h3>\n\n\n\n

Below are algebraic pandiagonal striped<\/strong> magic squares of even orders, i.e., of orders 4, 6, 8, 10 and 12. These are followed by examples for each orders.<\/p>\n\n\n\n

Striped Pandiagonal Magic Square of Order 4<\/h3>\n\n\n\n

Result 1. Striped Magic Square of Order 4<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 1. <\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 4 based on above result<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are sums of strips:<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Striped Pandiagonal Magic Squares of Order 6<\/h3>\n\n\n\n

Result 2. Striped Pandiagonal Magic Square of Order 6<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 2.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 6 based on the Result 1.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are sums of strips:<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 3. Striped Pandiagonal Magic Square of Order 6<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 3.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 6 based on the Result 2<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are sums of strips:<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 4. Striped Pandiagonal Magic Square of Order 6<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 4.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal <\/strong>magic square of order 6 based on the Result 4<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is pandiagonal magic square of order 4 appearing in upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

Striped Pandiagonal Magic Squares of Order 10<\/h3>\n\n\n\n

Result 5. Striped Pandiagonal Magic Square of Order 10<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 5.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 8 based on the Result 5.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic square of order 4 appearing in the middle.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 6. Striped Pandiagonal Magic Square of Order 8<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 6.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 8 based on the Result 6<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic square of order 4 appearing in the middle.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 7. Striped Pandiagonal Magic Square of Order 8<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 7.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal <\/strong>magic square of order 8 based on the Result 7<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal magic squares of orders 6 and 4 appearing in the upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Striped Pandiagonal Magic Squares of Order 10<\/h3>\n\n\n\n

Result 8. Striped Pandiagonal Magic Square of Order 10<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 8.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 10 based on the Result 8.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic square of order 6 appearing in the middle. The sum of strips is also given<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Result 9. Striped Pandiagonal Magic Square of Order 10<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 9.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 10 based on the Result 9<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic square of order 6 appearing in the middle. The sum of strips is also given<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Result 10. Striped Pandiagonal Magic Square of Order 10<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 10.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal <\/strong>magic square of order 10 based on the Result 10<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal magic squares of orders 8, 6 and 4 appearing in the upper-left corner.<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Striped Pandiagonal Magic Squares of Order 12<\/h3>\n\n\n\n

Result 11. Striped Pandiagonal Magic Square of Order 12<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 11.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 12 based on the Result 11.<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal<\/strong> magic squares of orders 8 and 4 appearing in the middle. <\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Result 12. Striped Pandiagonal Magic Square of Order 12<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 12.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal<\/strong> magic square of order 12 based on the Result 12<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal<\/strong> magic square of order 8 and 4 appearing in the middle. <\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Result 13. Striped Pandiagonal Magic Square of Order 12<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 13.<\/h4>\n\n\n\n

See below an example of a striped pandiagonal <\/strong>magic square of order 11 based on the Result 13<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal magic squares of orders 10, 8, 6 and 4 appearing in the upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Algebraic Pandiagonal Semi-Striped Magic Squares of Odd Orders<\/h3>\n\n\n\n

Below are algebraic pandiagonal semi-striped<\/strong> magic squares of odd orders, i.e., of orders 5, 7, 9 and 11. These are followed by examples for each orders. We call them as semi-striped because there is either magic square of order 3 or 5, that don’t satisfy the property of strip. Strip we understand as a magic rectangle with width 2. <\/p>\n\n\n\n

Semi-Striped Pandiagonal Magic Square of Order 5<\/h3>\n\n\n\n

Result 14. Semi-Striped Pandiagonal Magic Square of Order 5<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 14.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 5 based on the Result 14<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is a magic squares of order 3 appearing in the upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Semi-Striped Pandiagonal Magic Square of Order 7<\/h3>\n\n\n\n

Result 15. Semi-Striped Pandiagonal Magic Square of Order 7<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 15.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 7 based on the Result 15<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below is a magic squares of order 3 appearing in the middle of above magic square;<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 16. Semi-Striped Pandiagonal Magic Square of Order 7<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 16.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 7 based on the Result 16<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic squares of order 5 appearing in the upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Semi-Striped Pandiagonal Magic Square of Order 9<\/h3>\n\n\n\n

Result 17. Semi-Striped Pandiagonal Magic Square of Order 9<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 17.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 9 based on the Result 17<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below is a pandiagonal magic squares of order 5 appearing in the middle of the above magic square.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 18. Semi-Striped Pandiagonal Magic Square of Order 9<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 18.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 9 based on the Result 18<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below is are pandiagonal magic squares of orders 7 and 5 appearing in the upper-left corner.<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Semi-Striped Pandiagonal Magic Square of Order 11<\/h3>\n\n\n\n

Result 19. Semi-Striped Pandiagonal Magic Square of Order 11<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 19.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 7 based on the Result 15<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

Below is are magic squares of order 7 and 3 appearing in the middle. The magic square of order 7 is pandiagonal<\/strong>.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Result 20. Semi-Striped Pandiagonal Magic Square of Order 11<\/h4>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Example 20.<\/h4>\n\n\n\n

See below an example of a semi-striped pandiagonal <\/strong>magic square of order 11 based on the Result 20<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Below are pandiagonal<\/strong> magic squares of orders 9, 7 and 5 appearing in the upper-left corner.<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

References<\/h3>\n\n\n\n

Part 1: Day and Dates of the Year – 2025 in Terms of Magic Squares<\/mark><\/h4>\n\n\n\n