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 120 and 112. Based on these two big magic inner order magic squares multiples of 8 are studied. By inner orders we understand that magic squares of orders 96, 88, 80, etc. Instead of working in decreasing order, we worked with increasing orders, such as, orders 8, 16, 24, etc. The construction of the block-wise bordered magic squares multiples of 8 is based on equal sum blocks of bordered magic squares of order 8. In this case, the inner blocks are magic squares of orders 6 and 4. The magic squares of order 4 are 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. It is the same property of bordered magic squares. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 8. For multiples of orders 4 and 6 see the links below:
- Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4
- Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6
The further multiples, such as multiples of 20, 12, 14, etc. shall be written soon. This work brings examples only up to order 72. Higher orders examples can be seen in Excel file attached with the work. The total work is up to orders 120.
Below are the links of the work for download including Excel file:
- Inder J. Taneja, Block-Wise Bordered Magic Squares Multiples of 8. Zenodo, September 17, 1-80, https://doi.org/10.5281/zenodo.5514396
- Excel file for download:
Below are some examples studied in the work. The work is up to order 120. The examples below are till order 78. The block-wise magic squares multiples of order 8: