During past years author worked with block-wise, bordered and block-bordered magic squares. This work make connection between block-wise and bordered magic squares. We started with block-wise bordered magic squares of orders 108 and 102. Based on these two big magic squares inner order magic squares multiples of 6 are studied. By inner order we understand that magic squares of orders 96, 90, 84, etc. Instead of working in decreasing order, we worked with increasing orders, such as, orders 6, 12, 18, etc. The construction is based on equal sum blocks of magic squares of order 6. It is done in two ways. One as normal magic squares of order 6 and another as bordered magic squares of order 6, where the inner magic square of order 4 is pandiagonal. The advantage in studying block-wise bordered magic squares is that when we remove external border, still we left with magic squares with sequential entries. This is the same property of bordered magic squares. The difference is that instead of numbers here we have blocks of equal sum magic squares. This work is for multiples of order 6.

The further multiples, such as multiples, 8, 10, 12, etc. shall be done in another works. For multiples of order 4 see author’s recent work.

This work brings examples only up to order 48. Higher orders examples can be seen in Excel file attached with the work. The total work is up to order 108.

Below are the links of the work for download including Excel file:

Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6. Zenodo, https://doi.org/10.5281/zenodo.5500134

Below are some examples studied in the work. The work is upto order 108. The example below are from order 66 in decreasing orders. The block-wise magic squares multiples of order 6:

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 66: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 60: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 54: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 48: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 42: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 36: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 30: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 24: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

BLOCK-WISE BORDERED MAGIC SQUARE OF ORDER 18: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

MAGIC SQUARES OF ORDER 12: BLOCKS OF MAGIC AND BORDERED MAGIC SQUARES OF ORDER 6

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