# Bordered Magic Squares Multiples of 10 – Revised

#### ByInder J. Taneja

Feb 13, 2022

Revised on July 12, 2023

During past years author worked with block-wisebordered 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 110. Based on these two big magic inner order magic squares multiples of 10 are studied. By inner orders we understand that magic squares of orders 90, 80, 70, etc. The construction of the block-wise bordered magic squares multiples of 10 is based on equal sum blocks of magic squares of order 10. We have taken 14-types of magic squares of order 10. 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. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 10. For multiples of orders 4, 6 and 8 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

The further multiples, such as multiples of 12, 14, 16 etc. shall be written soon. This work is up to order 120. Examples below are only up to order 40. The higher order examples can be seen in Excel file attached at the end of this work. This work also can be seen as online:

Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of 10, Zenodo, September 17, pp. 1-170, https://doi.org/10.5281/zenodo.5514398.

Below are few examples up to order 40 studied in this work. The work is up to order 120.
The complete excel file with 14 examples in each case is given at the end for download.

#### Magic Squares of Order 10

Below are 14 examples of magic squares of order 10. It includes bordered, double digits, cornered magic squares, etc.

#### Magic Squares of Order 20

Below are only 2 examples of magic squares of order 20. The other are given in embedded pdf file. Also, in excel file given at the end.

### Pdf file of 14 Magic Squares of Order 30

#### Magic Squares of Order 40

Below are only 2 examples of magic squares of order 40. The other are given in embedded pdf file. Also, in excel file given at the end.

### Pdf file of 14 Magic Squares of Order 40

The excel file below for download contains magic squares multiples of order 10 from orders 10 to 120. There are 14 examples in each case.