{"id":9493,"date":"2023-06-20T16:59:12","date_gmt":"2023-06-20T19:59:12","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9493"},"modified":"2023-08-06T12:57:59","modified_gmt":"2023-08-06T15:57:59","slug":"magic-squares-of-order-31","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9493","title":{"rendered":"Magic Squares of Order 31"},"content":{"rendered":"\n

Recently, author worked with cornered Magic Squares based on two-by-two divisions. These works can be accessed at the following links:
1. Inder Jeet Taneja, Cornered Magic Squares of Orders 5 to 10<\/a>.
2. Inder Jeet Taneja, Cornered Magic Squares of Orders 11 to 13<\/a>.
3. Inder Jeet Taneja, Cornered Magic Squares of Orders 14 to 24<\/a>.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Also, the author worked on even order<\/strong> double digits bordered magic squares<\/strong>. This works starts from order 8 and goes up to order 40. See below the links:

The work for order of type 4k, k=1, 2, 3, … i.e., for orders 8, 12, 16, 20, 24, 28, 32, 36 and 40:
1. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/a>.
2. Two Digits Bordered Magic Squares of Orders 28 and 32<\/a>.
3. Two digits Bordered Magic Squares of Order 36.<\/a>
4. Two digits Bordered Magic Squares of Order 40<\/a>.

The work is for the order of type 4k+2, k=1, 2, 3, …, i.e., for the orders 10, 14, 18, 22, 26, 30, 34 and 38:
1. Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/a>.
2. Two digits Bordered Magic Squares of Orders 26 and 30<\/a>.
3. Two digits Bordered Magic Squares of Order 34<\/a>.
4. Two digits Bordered Magic Squares of Order 38<\/a>. <\/a><\/p>\n\n\n\n

<\/p>\n\n\n\n

This work is for magic square of order 31. It includes five type of magic squares:
1. Traditional centered magic squares.
2. Magic Squares with blocks of order 9
3. Bordered with magic squares of order 9.
4. Bordered with magic squares of order 3.
5. Double digits bordered magic squares.<\/strong>
5.1 Embedded Lower Order Magic Squares.<\/strong>
5.2. Embedded Cornered Magic Squares.<\/strong>

Double digits magic squares can also be constructed using software, the reader can follow H. White’s site: Magic Squares<\/a>.
This work can also be accessed online at:
Inder J. Taneja, Magic Squares of Order 31, Zenodo, August 06, 2023, pp. 1-35, https:\/\/doi.org\/10.5281\/zenodo.8219053<\/a>.

For the previous work on odd orders from 3 to 29<\/strong> see the following links:. <\/p>\n\n\n\n

For the previous work on odd orders from 3 to 31<\/strong> see the following links:<\/p>\n\n\n\n