# Bordered and Pandiagonal Magic Squares Multiples of 12 – Revised

Revised on July 12, 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 120 and 108. Based on these two big magic squares, the inner order magic squares multiples of 12 are studied. By inner orders we understand that magic squares of orders 96, 84, 72, etc. The construction of the block-wise bordered magic squares multiples of 12 is based on equal sum blocks of magic squares of order 12. We have taken 16-types of magic squares of order 12. 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 12. For multiples of orders 4, 6, 8 and 10 see the links below:
1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4.
2. Block-Wise Bordered Magic Squares Multiples of Magic and Bordered 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.

This work is up to order 120. 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 12

Below are 16 examples of magic squares of order 12. It includes bordered, double digits, cornered magic squares, etc.

### Magic Squares of Order 24

Below are only 2 examples of magic squares of order 24. The other are given in embedded pdf file. Also, in excel file given at the end.

### Pdf file of 16 Magic Squares of Order 48

The excel files below for download contains bordered magic square with blocks of magic squares of order 12. There are 16 examples in each case. Total work is from orders 12 to 120. There are two files. One is with magic squares of orders 120, 108, 96 and 84. The second file is with magic squares of orders 72, 60, 48, 36, 24 and 12.

### Pandiagonal Magic Squares Multiples of Order 12

Below are pandiagonal magic squares from orders from 12 to 120 multiples of 12. These are of two types. One is formed by magic squares of order 3 and 4. The magic squares of order 3 are with different sums. The magic squares of order 4 are pandiagonal and are with equal sums. 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 12 from order 12 to 120.