Beauty of Magic Squares: Multiple Order Bordered Striped Magic Squares of Orders 24, 40, 60 and 84

During past years author worked with block-wise bordered magic squares multiples of even and odd number blocks. This means, multiples of 3, 4, 5, 6, etc. This work is little different. It is based on striped magic squares. By striped magic squares we understand that magic squares constructed based on magic rectanagle of equal width (width 2). The lengths depends on the necessity of each magic squares. See below fews works done during past years.

Inder J. Taneja, Striped Magic Squares of Even Orders 4, 6, 8 and 10, Zenodo, November 10, 2023, pp. 1-34, https://doi.org/10.5281/zenodo.15228903.
Inder J. Taneja, Striped Magic Squares of 12 – Revised, Zenodo, September 07, 2024, pp. 1-30, https://zenodo.org/records/13725031.
- Site Link: Striped Magic Squares of Order 12 – Revised (new site)
Inder J. Taneja, 5600+ Striped Magic Squares of Order 16, Zenodo, February 05, 2025, pp. 1-52, https://doi.org/10.5281/zenodo.14807639
- Site Link: 5600+ Striped Magic Squares of Order 16 (new site)
Inder J. Taneja, Striped Magic Squares of 18, Zenodo, June 13, 2024, pp. 1-34, https://doi.org/10.5281/zenodo.11629567.
- Site Link: Striped Magic Squares of Order 18 (new site).
Inder J. Taneja, 8000+ Striped Magic Squares of 20, Zenodo, March 15, 2025, pp. 1-37, https://doi.org/10.5281/zenodo.15032524
- Site Link: Striped Magic Squares of Order 20 (new site).
Inder J. Taneja, Striped and Semi-Striped Double Digits Bordered Magic Squares: Orders 7 to 50, Zenodo, March 13, 2025, pp. 1-30, https://doi.org/10.5281/zenodo.15021581.

This is directly connected to multipled bordered striped magic squares. In case of odd order magic squares we are unable to bring striped magic squares. We shall consider only even-order striped magic squares. Starting with order 4, we went further with borders of orders 6, 8, 10, etc. Some work with non-striped, I mean general magic squares in this direction is given in reference list at the end of this work. Below is link of complete work.

Inder J. Taneja– Multiple Orders Bordered Magic Squares, Zenodo, Jun 9, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.8019330.

Striped Magic Square of Order 12

Below is a striped magic square of order 12.

Let’s consider first the following striped magic square of order 4:

It is magic square of order 4 consisting to two equal sums magic rectangles of order 2×4. Based on this magic square, below is a striped magic square of order 12.

Striped Magic Squares of Order 24

We observe that the above magic square of order 12 is divisible by 6. Based this idea we shall bring magic square of order 24 considering the futher border of order 6. It is based on the following two variations of striped magic squares of order 6.

These are two striped magic squares of order 6, written in different forms. As we have seen that the magic square of order 12 is constructed based on 9 equal sums striped magic squares of order 4. But in this case, the situation is different. In this the striped magic squares of order 24 are constructed with external border of differendt sums striped magic squares of order 6. See below:

Striped Magic Squares of Order 24.

By considering a little different way of writing striped magic square of order 12, we have the same striped magic squares of order 24 given as below:

For further work, we shall consider only the first two striped magic squares of order 24. In future also, we can construct striped magic square of order 24 using 9 equal sums striped magic squares of order 8.

Striped Magic Squares of Order 40

We observe that the above magic squares of order 24 are divisible by 8. Based this idea we shall bring magic square of order 40 considering the futher border of order 8. It is based on the following four variations of striped magic squares of order 8.

These are four striped magic squares of order 8, written in different forms. There are much more striped magic squares of order 8 given in the reference list above, but we have considered only four just to have an idea. Let’s see below the 8 striped magic squares of order 40 based on an external border of order 8 over the two striped magic squares of order 24. In this case, not all the magic squares for border 8 are of equal sums.

Magic Squares of Order 60

We observe that the above magic squares of order 40 are divisible by 5, 8 and 10. Based this idea we shall bring magic square of order 60 considering the futher border of order 10. It is based on the following 6 striped magic squares of order 10.

These are six striped magic squares of order 10, written in different forms. There are much more striped magic squares of order 10 given in the reference list above, but we have considered only six just to have an idea. Let’s see below the 48 striped magic squares of order 60 based on external borders of order 10 over the 8 striped magic squares of order 40. Since the order 60 is a big, don’t fit properly in the screen, we shall represent these only with figure:

In Figures or Designs:

First-Type

Second-Type

Third-Type

Forth-Type

Fifth-Type

Sixth-Type

Above there are only few examples. More examples with excel file can be seen in a work given above in a link

Magic Squares of Order 84

We observe that the above magic squares of order 60 are divisible by 5, 6, 10 and 12. Based this idea we shall bring magic square of order 84 considering the futher borders of order 12. It is based on the following 5 striped magic squares of order 12.

These are five striped magic squares of order 12, written in different forms. There are much more striped magic squares of order 12 given above in the reference list, but we have considered only five just to have an idea. Let’s see below the striped magic squares of order 84 based on external borders of order 12 over the striped magic squares of order 60. Since the order 84 is a big in size, don’t fit properly in the screen, we shall represent these only with figure: