Figured Magic Squares of Order 18: A Systematic Procedure

ByInder J. Taneja

Nov 29, 2022

For the first time we are introducing the idea of magic squares by figures. This work brings magic squares of order 18. 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 inicial work is up to order30. Further orders shall be written in futures. The lack of numbers in figures is due to the fact that the readers can also try to complete them in their own ways. Otherwise, the readers can see the results in the author’s other works. Up to order 20 the results can be seen here. Below is a list of work of even order magic squares from orders 6 to 30. The readers can download from the links

1. Inder J. Taneja, Figured Magic Squares of Orders 6, 10, 12, 14 and 16 Using Bordered Magic Rectangles, Zenodo, November 29, 2022, pp. 1-31, https://doi.org/10.5281/zenodo.7377674.
2. Inder J. Taneja, Figured Magic Squares of Orders 18 and 20 Using Bordered Magic Rectangles, Zenodo, November 29, 2022, pp. 1-87, https://doi.org/10.5281/zenodo.7377689.
3. Inder J. Taneja, Figured Magic Squares of Order 22 Using Bordered Magic Rectangles, Zenodo, November 29, 2022, pp. 1-61, https://doi.org/10.5281/zenodo.7377706.
4. Inder J. Taneja, Figured Magic Squares of Order 24 Using Bordered Magic Rectangles, Zenodo, November 29, 2022, pp. 1-104, https://doi.org/10.5281/zenodo.7377779.
5. Inder J. Taneja, Figured Magic Squares of Order 26 Using Bordered Magic Rectangles, Zenodo, November 29, 2022, pp. 1-88, https://doi.org/10.5281/zenodo.7377794.
6. Inder J. Taneja, Figured Magic Squares of Order 28 Using Bordered Magic Rectangles, Zenodo, December 02, 2022, pp. 1-179, https://doi.org/10.5281/zenodo.7390666.
7. Inder J. Taneja, Figured Magic Squares of Order 30 Using Bordered Magic Rectangles, Zenodo, December 02, 2022, pp. 1-179, https://doi.org/10.5281/zenodo.7390705.

Magic Squares of Order 18

Below are a few examples of magic squares of order 18. In some cases, the idea of construction is explained. At the end there is a Pdf file for download. The examples are divided in following parts:

• Part 1: Bordered and Block-Wise Magic Squares of Order 18
• Part 2: Cornered Magic Squares of Order 4
• Part 3: Closed Border of Order 4
• Part 4: Closed Border of Order 6
• Part 5: Blocks of Orders 8 and 10 and Two BMRs of Order 8×10
• Part 6: Extra Examples