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 order 30. 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, November 30, 2022,
  7. Inder J. Taneja, Figured Magic Squares of Order 30 Using Bordered Magic Rectangles, Zenodo, November 30, 2022,

Magic Squares of Order 20

Below are a few Examples of Figured Magic Squares of Order 20. Below are only 45 magic squares of order 20, but at the link readers can find 1616 different styles of magic squares of order 20. 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 20
  • Part 2: Magic Squares of Order 20 with BMRs
  • Part 3: Cornered Magic Squares of Order 4
  • Part 4: Closed Border of Order 4
  • Part 5: Cornered Magic Squares of Order 6
  • Part 6: Closed Border of Order 6
  • Part 7: Magic Squares of Order 10
  • Part 8: Two Consecutive BMR
  • Part 9: Pdf File for Download

Part 1: Bordered and Block-Wise Magic Squares of Order 20

Part 2: Magic Squares of Order 20 with BMRs

Part 3: Cornered Magic Squares of Order 4

Part 4: Closed Border of Order 4

Part 5: Cornered Magic Squares of Order 6

Part 6: Closed Border of Order 6

Part 7: Magic Squares of Order 10

Part 8: Two Consecutive BMRs of Orders 8×10 and 10×12

Part 9: Pdf File for Download