Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24

This paper summarizes some of the results done by author in previous works on different ways are writing block-wise magic squares. The details can be seen in the links given below. The work is for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35 and 36. In some cases, the magic squares are pan diagonal, bimagic or semi-bimagic. In all the cases, there is at least one representation that is pan diagonal except the orders 18 and 30.

Since there are total 40 examples, the work is divided in two parts. The first part is for the orders 12 to 24 and the second part is for the orders 25 to 36. Below are the links for  dowloading the works:

Link for download (Main Work):  Block-Wise Magic and Bimagic Squares

For details of previous works see the links below:

  1. Block-Wise Equal Sums Pan Magic Squares of Order 4k;
  2. Block-Wise Equal Sums Magic Squares of Orders 3k and 6k
  3. Block-Wise Unequal Sums Magic Squares;
  4. Magic Rectangles in construction of Block-Wise Pan Magic Squares.

The Examples included in this part are given as below:

IN1

Below are corresponding examples:

12A12B12C15A15B16A16B18A18B20A20B20C21A21B24A24B24C24D

Again below are links for download:

(Main Work):  Block-Wise Magic and Bimagic Squares

For details of previous works see the links below:

  1. Block-Wise Equal Sums Pan Magic Squares of Order 4k;
  2. Block-Wise Equal Sums Magic Squares of Order 3k;
  3. Block-Wise Unequal Sums Magic Squares;
  4. Magic Rectangles in construction of Block-Wise Pan Magic Squares;
  5. Block-Wise Equal Sums Magic Squares of Orders 6k.

 

 

 

 

 

32 thoughts on “Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s