We know that we can always write block-wise magic squares of any order except for the orders of type p and 2p, where p is a prime number. On the other hand we can always write bordered magic squares of any order. The aims of this work is to combine the both, i.e., bordered and block-wise magic squares. Whenever possible, we shall write block-wise magic squares, otherwise block-bordered magic squares. This work is combination of authors previous work in both the direction. The work brings magic squares of orders 10 to 47, either block-wise or block-bordered. Below is a link of a paper for download:
- Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47. Zenodo, January 14, 2021, pp. 1-185, http://doi.org/10.5281/zenodo.4437783
This work is a combination of following works done before divided in two groups. One is Block-Wise Magic Squares and another is Block-Bordered Magic Squares given below:
Block-Wise Magic Squares
- Inder J. Taneja, Block-Wise Constructions of Magic and Bimagic Squares of Orders 8 to 108, May 15, 2019, pp. 1-43, Zenodo, http://doi.org/10.5281/zenodo.2843326.
- Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo, January 31, 2019, pp. 1-17, http://doi.org/10.5281/zenodo.2554288.
- Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo, January 31, 2019, pp. 1-49, http://doi.org/10.5281/zenodo.2554520
- Inder J. Taneja, Block-Wise Equal Sums Magic Squares of Orders 3k and 6k, Zenodo, February 1, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.2554895.
- Inder J. Taneja, Block-Wise Unequal Sums Magic Squares, Zenodo, February 1, 2019, pp. 1-52, http://doi.org/10.5281/zenodo.2555260.
- Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, February 1, 2019, pp. 1-53, http://doi.org/10.5281/zenodo.2555343.
- Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 39 to 45, Zenodo, February 2, 2019, pp. 1-73, http://doi.org/10.5281/zenodo.2555889.
These works can be seen in the following links:
- Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pan Magic Squares, https://inderjtaneja.com/2017/12/07/magic-rectangles-in-construction-of-block-wise-pan-magic-squares/
- Inder J. Taneja, Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24, https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-i/
- Inder J. Taneja,Block-Wise Construction of Magic and Bimagic Squares of Orders 25 to 36, https://inderjtaneja.com/2018/01/10/block-wise-magic-and-bimagic-squares-part-ii/
- Inder J. Taneja, Block-Wise Construction of Magic and Bimagic Squares of Orders 39 to 45, https://inderjtaneja.com/2018/03/02/block-wise-construction-of-magic-and-bimagic-squares-of-orders-39-to-45/
Block-Bordered Magic Squares
- Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I, Zenodo, August 18, 2020, http://doi.org/10.5281/zenodo.3990291, pp. 1-81
- Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – II, Zenodo, August 18, 2020, http://doi.org/10.5281/zenodo.3990293, pp. 1-90
- Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – III, Zenodo, September 01, 2020, http://doi.org/10.5281/zenodo.4011213, pp. 1-93
These works can be seen at the following link:
- Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Orders: I, II and III, https://inderjtaneja.com/2020/10/08/block-bordered-magic-squares-of-prime-and-double-prime-orders-i-ii-and-iii/
Block-Wise and Block-Bordered Magic Squares
- Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares With Magic Sums 21, 21^2 and 2021. Zenodo, December 16, 2020, http://doi.org/10.5281/zenodo.4380343. pp. 1-118.
Below are results given as slides appearing the the above paper:
One thought on “Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47”