Revised on July 16, 2023
Recently, the author revised and improved the block-wisebordered magic squares multiples of even number blocks. This means, multiples of 4, 6, 8, etc. The work is up to order 20. These works can be accessed at the following links.
1. Bordered and Pandiagonal Magic Squares Multiples of 4.
2. Bordered Magic Squares Multiples of Magic Squares of Order 6.
3. Bordered and Pandiagonal Magic Squares Multiples of 8 – Revised
4. Bordered Magic Squares Multiples of 10 – Revised.
5. Bordered and Pandiagonal Magic Squares Multiples of 12 – Revised.
6. Bordered Magic Squares Multiples of 14 – Revised.
7. Bordered and Pandiagonal Magic Squares Multiples of 16.
8. Bordered Magic Squares Multiples of 18.
9. Bordered and Pandiagonal Magic Squares Multiples of 20.
Author also worked with odd number blocks. The work is for multiples of order 3, 5, 7, 9, 11 and 13. See the links below:
1. Bordered and Pandiagonal Magic Squares Multiples of 3.
2. Bordered and Pandiagonal Magic Squares Multiples of 5.
3. Bordered and Pandiagonal Magic Squares Multiples of 7.
4. Bordered Magic Squares Multiples of 9 – Revised.
5. Bordered Magic Squares Multiples of Order 11- Revised.
6. Bordered Magic Squares Multiples of 13.
7. Bordered Magic Squares Multiples of 15.
8. Bordered Magic Squares Multiples of 17.
The advantage in studying block-wise bordered magic squares is that when we remove external borders, still we left with magic squares with sequential entries.
We observe that the above study of even order blocks starting from 4. Recently, author studied the double digit or two digits borders resulting in interesting magic squares. These studies can be accessed at the following link:
1. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24.
2. Two Digits Bordered Magic Squares of Orders 28 and 32.
3. Two digits Bordered Magic Squares of Order 36.
4. Two digits Bordered Magic Squares of Order 40.
The work is for the order of type 4k+2, where k>1, i.e., for the orders 10, 14, 18, 22, 26 and 30 can be access at the following links:
1. Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22.
2. Two digits Bordered Magic Squares of Orders 26 and 30.
3. Two Digits Bordered Magic Squares of Orders 28 and 32.
Some studies towards cornered magic squares are also made. See the following links:
1. Cornered Magic Squares of Orders 5 to 10.
2. Cornered Magic Squares of Orders 11 to 13.
3. Cornered Magic Squares of Orders 14 to 24.
Below are examples of bordered magic squares multiples of order 11 up to order 55. Total we worked with 20 different types of magic squares of order 11. Up to order 55 pdf files of each order are attached for download. Excel files of whole work are also attached at the end.
This work can also be accessed at the following link:
Inder J. Taneja, Bordered Magic Squares Multiples of 11, Zenodo, July 24, pp. 1-34, 2023, https://doi.org/10.5281/zenodo.8176475.
Magic Squares Multiples of 11
Below are 20 magic square of order 11. We have used these magic squares to bring bordered magic squares up to order 154 as multiples of 11.
Bordered Magic Squares Multiples of 11
Magic Squares of Order 33
Below are only few examples of magic square of order 33. The other examples are given in attached pdf file.
Pdf file of Order 33
Bordered Magic Squares Multiples of 11
Magic Squares of Order 44
Below are only few examples of magic square of order 44. The other examples are given in attached pdf file.
Pdf file of Order 44
Bordered Magic Squares Multiples of 11
Magic Squares of Order 55
Below are only few examples of magic square of order 55. The other examples are given in attached pdf file.
Pdf file of Order 55
Excel files for download
File 1:
File 2:
File 3:
The first file is only with first eight examples, while the other two files are with all the 20 examples of bordered magic squares multiples of order 11.