Magic Squares of Order 42 Using Bordered Magic Rectangles: A Systematic Procedure

For the first time we are introducing the idea of magic squares by figures. This work brings magic squares of order 42. 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. 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 40. The readers can download from the links.

Block 1: Even Order Magic Squares from 6 to 30

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.

Block 2: Even Order Magic Squares from 32 to 40

1. 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.
2. Inder J. Taneja, Figured Magic Squares of Order 34 Using Bordered Magic Rectangles, Zenodo, December 27, 2022, pp. 1-193, https://doi.org/10.5281/zenodo.7486540.
3. Inder J. Taneja, Figured Magic Squares of Order 36 Using Bordered Magic Rectangles, Zenodo, December 27, 2022, pp. 1-140, https://doi.org/10.5281/zenodo.7486548.
4. Inder J. Taneja, Figured Magic Squares of Order 38 Using Bordered Magic Rectangles, Zenodo, January 03, 2023, pp. 1-133, https://doi.org/10.5281/zenodo.7500188.
5. Inder J. Taneja, Figured Magic Squares of Order 40 Using Bordered Magic Rectangles, Zenodo, January 03, 2023, pp. 1-157, https://doi.org/10.5281/zenodo.7500192.

Block 3: Even Order Magic Squares from 42 to 50

1. Inder J. Taneja, Magic Squares of Order 42, Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, March 03, 2023, pp. 1-92, https://doi.org/10.5281/zenodo.7695834.
2. Inder J. Taneja, Magic Squares of Order 44 Using Bordered Magic Rectangles: A Systematic Procedure, Under construction.
3. Inder J. Taneja, Magic Squares of Order 46 Using Bordered Magic Rectangles: A Systematic Procedure, Under construction.
4. Inder J. Taneja, Magic Squares of Order 48 Using Bordered Magic Rectangles: A Systematic Procedure, Under construction.
5. Inder J. Taneja, Magic Squares of Order 50 Using Bordered Magic Rectangles: A Systematic Procedure, Under construction.

Magic Squares of Order 42

Below are a few Examples of Magic Squares of Order 42 using bordered magic rectangles. Below are only 80 magic squares of order 42, but there are many more possibilities. These are given in PDF files at the end of this work

• Part 1: Block-Wise and Bordered
• Part 2: Cornered Magic Squares of Order 4
• Part 3: Closed Border of Order 4
• Part 4: Cornered Magic Squares of Order 6
• Part 5: Closed Border of Order 6
• Part 6: Cornered Magic Squares of Order 8
• Part 7: Closed Border of Order 8
• Part 8: Cornered Magic Squares of Order 10
• Part 9: Closed Border of Order 10
• Part 10: Cornered Magic Squares of Order 12
• Part 11: Closed Border of Order 12
• Part 12: Equal Sums Magic Squares of Order 14
• Part 13: Closed Border of Order 14
• Part 14: Cornered Magic Squares of Order 16
• Part 15: Closed Border of Order 16
• Part 16: Cornered Magic Squares of Order 18
• Part 17: Closed Border of Order 18
• Part 18: Two Consecutive BMRs of Orders 20 × 20 and 22 × 22

Part 1: Block-Wise and Bordered

Part 2: Cornered Magic Squares of Order 4

Part 3: Closed Border of Order 4

Part 4: Cornered Magic Squares of Order 6

Part 5: Closed Border of Order 6

Part 6: Cornered Magic Squares of Order 8

Part 7: Closed Border of Order 8

Part 8: Cornered Magic Squares of Order 10

Part 9: Closed Border of Order 10

Part 10: Cornered Magic Squares of Order 12

Part 11: Closed Border of Order 12

Part 12: Equal Sums Magic Squares of Order 14

Part 13: Closed Border of Order 14

Part 14: Cornered Magic Squares of Order 16

Part 15: Closed Border of Order 16

Part 16: Cornered Magic Squares of Order 18

Part 17: Closed Border of Order 18

Part 18: Two Consecutive BMRs of Orders 20 × 20 and 22 × 22

Part 19: Pdf files for download

File 1

File 2