Crossed Bordered Magic Rectangles and Magic Squares
For the first time we are introducing the idea of magic squares by figures. This work brings magic squares of order 40. In some cases, the idea of construction is explained. It is based on external borders made by magic squares or bordered magic rectangles. Then inner blocks are previously known magic squares of smaller orders. The lack of numbers in figures is due to the fact that the readers can also try to complete them in their own way. Otherwise, the readers can see the results in the author’s other works. Up to order 20 the results can be seen here. A list of work of even order magic squares from orders 6 to 40 can be seen and download at the link. This work brings single- and double-crossed bordered magic rectangles to bring magic squares of order 40. This we have done in two parts:
1. Single Crossed Bordered Magic Rectangles.
2. Double Crossed Bordered Magic Rectangles.
Both these works can be seen at the following links:
- Inder J. Taneja, Single Crossed Bordered Magic Rectangles and Magic Squares of Order 40, Zenodo, January 24, 2023, pp. 1-76, https://doi.org/10.5281/zenodo.7565946
- Inder J. Taneja, Double Crossed Bordered Magic Rectangles and Magic Squares of Order 40, Zenodo, January 30, 2023, pp. 1-102, https://doi.org/10.5281/zenodo.7585787
Below are few examples of single crossed bordered magic rectangles forming magic squares of order 40. These are of different types. The complete work is given at the end as pdf file to download.