Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4

During past years author worked with block-wise, bordered and block-bordered magic squares. This work make connection between block-wise and bordered magic squares. We started with block-wise bordered magic squares of orders 108 and 104. Based on these two big magic squares inner order magic squares multiples of 4 are studied. By inner order we understand that magic squares of orders 100, 96, 92, etc. Instead of working in decreasing order, we worked with increasing orders, such as, orders 4, 8, 12, etc. The construction of the block-wise bordered magic squares multiples of 4 is based on equal sum blocks of pandiagonal magic squares of order 4. The block-wise bordered magic squares studied are not pandiagonal. Redistributing the same blocks in each case, we get pandiagonal magic squares of order 4, 8, 12, etc. This work is only for the multiples of order 4. The further multiples, such as multiples, 6, 8, 10, etc. can be seen at the following link:

• Inder J. Taneja, Multiple Orders Bordered Magic Squares

The above link give bordered magic squares up to order 20.

Examples given below are only up to order 48. Higher orders examples can be seen in Excel file attached with the work. The total work is up to order 108.

Below are the links of the work:

Bordered Magic Squares Multiples of 4

• Inder J. Taneja, Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4. Zenodo, August 31, 2021, pp. 1-148, https://doi.org/10.5281/zenodo.5347897.

Pandiagonal Magic Squares Multiples of 4

• Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo, January 31, 2019, pp. 1-17, https://doi.org/10.5281/zenodo.2554288.
• Inder J. Taneja, A Simplified Procedure to Construct Pandiagonal Magic Squares Multiples of 4 (Revised), Zenodo, August 10, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8236754.

Excel files for download are given at the end of each part.

Below are some examples studied in the work. The total work is up to order 108. The example below are only up to order 48. The examples are given in two blocks:

1. First Block: Block-wise bordered magic squares from order 12 to 48;
2. Second Block: Pandiagonal Magic Squares from orders 4 to 48.
3. Higher orders are already in attached excel files.

Block-Bordered Magic Squares

Magic Squares of Orders 4 and 8

Block-Wise Bordered Magic Square of Order 12

Block-Wise Bordered Magic Square of Order 16

Block-Wise Bordered Magic Square of Order 20

Block-Wise Bordered Magic Square of Order 24

Block-Wise Bordered Magic Square of Order 28

Block-Wise Bordered Magic Square of Order 32

Block-Wise Bordered Magic Square of Order 36

Block-Wise Bordered Magic Square of Order 40

Block-Wise Bordered Magic Square of Order 44

Block-Wise Bordered Magic Square of Order 48

Pdf file for Download

Pandiagonal Magic Squares Multiples of 4

Pandiagonal Magic Squares of Orders 4 and 8

Pandiagonal Magic Squares of Order 12

Pandiagonal Magic Squares of Order 16

Pandiagonal Magic Squares of Order 20

Pandiagonal Magic Squares of Order 24

Pandiagonal Magic Squares of Order 28

Pandiagonal Magic Squares of Order 32

Pandiagonal Magic Squares of Order 36

Pandiagonal Magic Squares of Order 40

Pandiagonal Magic Squares of Order 44

Pandiagonal Magic Squares of Order 48

Pdf file of Pandiagonal Magic Squares Multiples of 4: Orders 4 to 108