# Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16

#### ByInder J. Taneja

Jul 13, 2023

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 144 and 128. Based on these two big magic squares, the inner order magic squares multiples of 16 are studied. By inner orders we understand that magic squares of orders 112, 96, 80, etc. The construction of the block-wise bordered magic squares multiples of 16 is based on equal sum blocks of magic squares of order 16. We have taken 25 different types of magic squares of order 16. The advantage in studying block-wise bordered magic squares is that when we remove external border, still we are left with magic squares with sequential entries. It is the same property of bordered magic squares with single digits numbers. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 16. For multiples of orders 4, 6, 8, 10, 12 and 14 see the links below:
1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4.
2. Block-Wise Bordered Magic Squares Multiples of Magic Squares of Order 6.
3. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 – Revised
4. Block-Wise Bordered Magic Squares Multiples of 10 – Revised.
5. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12 – Revised.
6. Block-Wise Bordered Magic Squares Multiples of 14 – Revised.

This work is up to order 144. Examples below are only up to order 48. The higher order examples can be seen in Excel file attached at the end of this work.

### Magic Squares of Order 16

Below are only three examples of magic squares of order 16. It includes bordered, double digits, cornered magic squares, etc. Total 25 examples are considered in this work. The other examples are either in excel file and pdf file.

### Magic Squares of Order 32

Below are only 3 examples of magic squares of order 32. The other are given in attached pdf file and in excel file given at the end.

### Pdf file of 25 Magic Squares of Order 48

The excel files below for download contains bordered magic square with blocks of magic squares of order 16. There are 25 examples in each case. Total work is from order 16 to 144. There are three files. One is with magic squares of orders 144 and 128. The second file is with magic squares of orders 112 and 96. The third file is with orders 80, 64, 48, 32 and 16.

### Pandiagonal Magic Squares Multiples of Order 16

Below are pandiagonal magic squares from orders 16 to 144 multiples of 16. These are formed by equal sum pandiagonal magic squares of order 4. In the end there is an excel file of all the pandiagonal magic squares for download.

### Pandiagonal Magic Square of Order 48

The excel file below for download contains pandiagonal magic squares multiples of order 16 from order 16 to 144.