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

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

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

Algebraic Pandiagonal Striped Magic Squares of Even Orders

Below are algebraic pandiagonal striped magic squares of even orders, i.e., of orders 4, 6, 8, 10 and 12. These are followed by examples for each orders.

Striped Pandiagonal Magic Square of Order 4

Result 1. Striped Magic Square of Order 4

Example 1.

See below an example of a striped pandiagonal magic square of order 4 based on above result

Below are sums of strips:

Striped Pandiagonal Magic Squares of Order 6

Result 2. Striped Pandiagonal Magic Square of Order 6

Example 2.

See below an example of a striped pandiagonal magic square of order 6 based on the Result 1.

Below are sums of strips:

Result 3. Striped Pandiagonal Magic Square of Order 6

Example 3.

See below an example of a striped pandiagonal magic square of order 6 based on the Result 2

Below are sums of strips:

Result 4. Striped Pandiagonal Magic Square of Order 6

Example 4.

See below an example of a striped pandiagonal magic square of order 6 based on the Result 4

Below is pandiagonal magic square of order 4 appearing in upper-left corner.

Striped Pandiagonal Magic Squares of Order 10

Result 5. Striped Pandiagonal Magic Square of Order 10

Example 5.

See below an example of a striped pandiagonal magic square of order 8 based on the Result 5.

Below is a pandiagonal magic square of order 4 appearing in the middle.

Result 6. Striped Pandiagonal Magic Square of Order 8

Example 6.

See below an example of a striped pandiagonal magic square of order 8 based on the Result 6

Below is a pandiagonal magic square of order 4 appearing in the middle.

Result 7. Striped Pandiagonal Magic Square of Order 8

Example 7.

See below an example of a striped pandiagonal magic square of order 8 based on the Result 7

Below are pandiagonal magic squares of orders 6 and 4 appearing in the upper-left corner.

Striped Pandiagonal Magic Squares of Order 10

Result 8. Striped Pandiagonal Magic Square of Order 10

Example 8.

See below an example of a striped pandiagonal magic square of order 10 based on the Result 8.

Below is a pandiagonal magic square of order 6 appearing in the middle. The sum of strips is also given

Result 9. Striped Pandiagonal Magic Square of Order 10

Example 9.

See below an example of a striped pandiagonal magic square of order 10 based on the Result 9

Below is a pandiagonal magic square of order 6 appearing in the middle. The sum of strips is also given

Result 10. Striped Pandiagonal Magic Square of Order 10

Example 10.

See below an example of a striped pandiagonal magic square of order 10 based on the Result 10

Below are pandiagonal magic squares of orders 8, 6 and 4 appearing in the upper-left corner.

Striped Pandiagonal Magic Squares of Order 12

Result 11. Striped Pandiagonal Magic Square of Order 12

Example 11.

See below an example of a striped pandiagonal magic square of order 12 based on the Result 11.

Below are pandiagonal magic squares of orders 8 and 4 appearing in the middle.

Result 12. Striped Pandiagonal Magic Square of Order 12

Example 12.

See below an example of a striped pandiagonal magic square of order 12 based on the Result 12

Below are pandiagonal magic square of order 8 and 4 appearing in the middle.

Result 13. Striped Pandiagonal Magic Square of Order 12

Example 13.

See below an example of a striped pandiagonal magic square of order 11 based on the Result 13

Below are pandiagonal magic squares of orders 10, 8, 6 and 4 appearing in the upper-left corner.

Algebraic Pandiagonal Semi-Striped Magic Squares of Odd Orders

Below are algebraic pandiagonal semi-striped 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.