For the first time we are introducing the idea of magic squares by figures. This work brings magic squares of order 32. 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. Below is a list of work of even order magic squares from orders 6 to 32. 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.
  8. Inder J. Taneja, Figured Magic Squares of Order 32 Using Bordered Magic Rectangles, Zenodo, December 22, 2022, pp. 1-310, https://doi.org/10.5281/zenodo.7472891.

Magic Squares of Order 32

Below are a few Examples of Figured Magic Squares of Order 32 using bordered magic rectangles. Below are only 282 magic squares of order 32, but there are many more possibilities. This shall be presented later on. In some cases, the idea of construction is explained. In the end there are two PDF files of work embedded for download. One is with figures, and another is with numbers. The examples are divided in following parts:

  • Part 1: Block-Wise Magic Square of Order 32
  • Part 2: Cornered Magic Squares of Order 4
    • BMRs of Orders 4×10 and 4×14
    • BMRs of Orders 4×10
  • Part 3: Closed Border of Order 4
  • Part 4: Cornered Magic Squares of Order 6
    • BMRs of Order 6×20
    • BMRs of Order 6×8 and Magic Squares of Order 6
  • Part 5: Cornered Magic Squares of Order 8
    • BMRs of Order 6×8 and 6×10
    • Equal Sums Magic Squares of Order 8
  • Part 6: Closed Border of Order 8
  • Part 7: Cornered Magic Squares of Order 10
  • Part 8: Closed Border of Order 10
  • Part 9: Cornered Magic Squares of Order 12
  • Part 10: Closed Border of Order 12
  • Part 11: Cornered Magic Squares of Order 14
  • Part 12: Closed Border of Order 14
  • Part 13: Magic Squares of Order 16
  • Part 14: Consecutive BMRs of Orders 14×16 and 16×18
  • Part 15: PDF File for Download
    • Figures
    • Numbers

Part 1: Block-Wise Magic Square of Order 32

Part 2: Cornered Magic Squares of Order 4: BMRs of Orders 4×10 and 4×14

Part 2: Cornered Magic Squares of Order 4: BMRs of Orders 4×10

Part 3: Closed Border of Order 4

Part 4: Cornered Magic Squares of Order 6: BMRs of Order 6×20

Part 4: Cornered Magic Squares of Order 6: BMRs of Order 6×8 and Magic Squares of Order 6

Part 5: Cornered Magic Squares of Order 8: BMRs of Order 6×8 and 6×10

Part 5: Cornered Magic Squares of Order 8: Equal Sums Magic Squares of Order 8

Part 6: Closed Border of Order 8

Part 7: Cornered Magic Squares of Order 10

Part 8: Closed Border of Order 10

Part 9: Cornered Magic Squares of Order 12

Part 10: Closed Border of Order 12

Part 11: Cornered Magic Squares of Order 14

Part 12: Closed Border of Order 14

Part 13: Magic Squares of Order 16

Part 14: Consecutive BMRs of Orders 14×16 and 16×18

Part 15: PDF File for Download (Figures)

Part 15: PDF File for Download (Numbers)

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