Magic Squares

Bordered and Block-Wise Bordered Magic Squares: Odd Order Multiples

In the previous work we did block-wise bordered and block-wise block-bordered magic squares mutiples of even orders. See the link below:

The even order multiples considered are of orders 6, 8, 10, 12, 14, 16, 18 and 22. In this case, we have blocks or block-wise bordered magic squares of equal sums. There is only two cases where we don’t have equal sums, i.e., of orders 3 and 5.

In case of odd order multiples, still, we don’t have equal sums blocks. In this situation, this work is with unequal sub-block sums of magic squares. For examples, multiple of order 5, lead us to block-wise bordered magic squares of order 15, 20, 25, etc. with unequal sub-block sums. The same is with the multiples of orders 7, 9, 11, 13 and 15. Finally, we wrote block-wise bordered and block-wise block-bordered magic squares of orders 15, 20, 21, 25, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44 and 45. Below is a link for download of complete work:

Below are examples of magic squares studied in this work. In all the cases blocks considered are of unequal sums:

Examples:

Block-Wise Bordered Magic Square of Order 15

Block-Wise Bordered Magic Squares of Order 20

Bordered and Block-Wise Bordered Magic Squares of Order 21

Block-Wise Bordered Magic Squares of Order 25

Block-Bordered and Block-Wise Bordered Magic Squares of Order 27

Block-Bordered and Block-Wise Bordered Magic Squares of Order 28

Block-Wise Bordered Magic Square of Order 30

Block-Bordered and Block-Wise Bordered Magic Squares of Order 33

Block-Bordered and Block-Wise Bordered Magic Squares of Order 35

Block-Bordered and Block-Wise Bordered Magic Squares of Order 36

Block-Bordered and Block-Wise Bordered Magic Squares of Order 39

Block-Bordered and Block-Wise Bordered Magic Square of Order 40

Block-Bordered and Block-Wise Bordered Magic Squares of Order 42

Block-Bordered and Block-Wise Bordered Magic Squares of Order 44

Block-Bordered and Block-Wise Bordered Magic Squares of Order 45

Categories: Magic Squares

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