In this work, magic squares are written with equal and unequal sums blocks of magic rectangles. The magic squares studied are of orders 12, 15, 20, 21, 24, 27, 28, 30, 33, 35, 39 and 45. The equal sum blocks magic rectangles are for the magic squares of orders 12, 20, 24, 28 and 30. This lead us to semi-magic squares. After making necessary changes in the entries the semi-magic squares are written as magic squares. The unequal sum blocks magic rectangles are for the magic squares of orders 15, 21, 27, 33, 39 and 45. Order 45 is written two different ways. One as different sum blocks of order 5×9 and second as different sum blocks of order 3×15.
Link for download the work:
- Inder J. Taneja, Construction of Magic Squares With Magic Rectangles Blocks, May 30, 2022, pp. 1-32, Zenodo, https://doi.org/10.5281/zenodo.6592027.
Below are examples of magic squares.
Odd Order Magic Squares
Magic Square of Order 15 With Blocks of Order 3×5
Magic Square of Order 21 With Blocks of Order 3×7
Magic Square of Order 27 With Blocks of Order 3×9
Magic Square of Order 33 With Blocks of Order 3×11
Magic Square of Order 35 With Blocks of Order 5×7
Magic Square of Order 39 With Blocks of Order 3×13
Magic Square of Order 45 With Blocks of Order 5×9
Magic Square of Order 45 With Blocks of Order 3×15
Even Order Magic Squares
Magic Square of Order 12 With Equal Sum Blocks of Order 4×6
Magic Square of Order 20 With Equal Sum Blocks of Order 4×10
Magic Square of Order 24 With Equal Sum Blocks of Order 4×6
Magic Square of Order 28 With Equal Sum Blocks of Order 4×14
Magic Square of Order 30 With Equal Sum Blocks of Order 6×10
Numbers Magic 