Block-Wise Bordered Magic Squares Multiples of Orders 4, 6, 8, 10, 12 and 14 – Summary

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. This page brings summary of results obtained by author as multiples of magic squares of orders 4, 6, 8, 10, 12 and 14.

The mais property of this work is that in case bordered magic squares removing external borders, we still left with magic squares. In this work when we remove the external blocks of magic squares, still we left with magic squares.

See below the links and details in each case:

Multiples of Order 4

In this case the work is up to order 108, i.e., orders 4, 8, ….. 104, 108. Below are the links for download the work with excel file:

• 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.
• Excel file for download: 108×108-104×104-4 DOWNLOAD

Full details with examples can be seen at the following link:

• Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4;

Multiples of Order 6

In this case the work is up to order 108, i.e., orders 6, 12, …. ,102, 108. Below are the links for download the work with excel file:

• Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6. Zenodo, https://doi.org/10.5281/zenodo.5500134
• Excel file for download: DOWNLOAD

The work is done in two different ways. One as multiples of magic squares of order 6 and second as multiples of bordered magic squares of order 6.

Full details with examples can be seen at the following link:

• Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6.

Multiples of Order 8

In this case the work is up to order 120, i.e., orders 8, 16, ….. ,112, 120. Below are the links for download the work with excel file:

• Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of 8. Zenodo, September 17, 1-80, https://doi.org/10.5281/zenodo.5514396 
• Excel file for download: 120-112-8×8-onlineDownload

The work is done in a single way, i.e., multiples of bordered magic squares of order 8.

Full details with examples can be seen at the following link:

• Block-Wise Bordered Magic Squares Multiples of 8;

Multiples of Order 10

In this case the work is up to order 120, i.e., orders 10, 20, ….. ,110, 120. Below are the links for download the work with excel file:

• Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of 10, Zenodo, September 17, pp. 1-170, https://doi.org/10.5281/zenodo.5514398
• Excel file for download: 120×120-110×110-10×10-onlineDownload

The work is done in a three different ways:

1. Multiples of magic squares of order 10;
2. Muliples of bordered magic squres of order 10;
3. Multiples of block-boardered magic squares of order 10.

Full details with examples can be seen at the following link:

• Block-Wise Bordered Magic Squares Multiples of 10

Multiples of Order 12

In this case the work is up to order 120, i.e., orders 12, 24, ….. ,108, 120. Below are the links for download the work with excel file:

• Inder J. Taneja, Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12, Zenodo, September 23, pp. 1-170, https://doi.org/10.5281/zenodo.5523608
• Excel file for download: 120-108-12×12-onlineDownload

The work is done in a six different ways:

1. Blocks of Magic squares of order 12 with blocks of order 3;
2. Blocks of Magic squares of order 12 with blocks of order 4;
3. Blocks of Magic squares of order 12 with blocks of order 6;
4. Blocks of Bordered Magic squares of order 12;
5. Blocks of Pandiagonal Magic squares of order 12 with blocks of order 3;
6. Blocks of Pandiagonal Magic squares of order 12 with blocks of order 4.

Full details with examples can be seen at the following link:

• Block-Wise Bordered Magic Squares Multiples of 12

Multiples of Order 14

In this case the work is up to order 140, i.e., orders 14, 28, ….. ,126, 140. Below are the links for download the work with excel file:

• Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of 14 (Version 2). Zenodo, February 16, 2022, pp. 1-233, https://doi.org/10.5281/zenodo.6107943.
• Excel file for download: 140-126-14×14-revisedDownload

The work is done in a six different ways:

1. Magic Squares of Order 14;
2. Block-Bordered Magic square order 14 with inner magic square of order 12 having blocks of order 3;
3. Block-Bordered Magic square order 14 with inner magic square of order 12 having blocks of order 4;
4. Block-Bordered Magic square order 14 with inner magic square of order 12 having blocks of order 6;
5. Bordered Magic square order 14;
6. Block-Bordered Magic square order 14 with inner magic square of order 12 having bordered magic squares of order 6.

Full details with examples can be seen at the following link:

• Block-Wise Bordered Magic Squares Multiples of 14

Author’s work on Magic Squares

For summary work on magic squares see the link below:

• Publications – Magic Squares

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