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Published September 17, 2021 | Version v1
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Block-Wise Bordered Magic Squares Multiples of 10

Authors/Creators

  • 1. Formarly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Description

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 110. Based on these two big magic inner order magic squares multiples of 10 are studied. By inner orders we understand that magic squares of orders 100, 90, 80, etc. Instead of working in decreasing order, we worked with  increasing orders, such as, orders 10, 20, 30, etc. The construction of the block-wise bordered magic squares multiples of 10. It is done in three different ways. One as normal magic squares of order 10, second as block-bordered magic squares of order 10, where the inner magic square of order 8 is pandiagonal formed by 4 equal sum pandiagonal magic squares of order 4. The third way is with bordered magic square of order 10. In this case, the inner blocks are magic squares of orders 8, 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 10.  For multiples of orders 4, 6 and 8  see author's recent works. The further multiples, such as multiples of 12, 14, etc. shall be done in another works. 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 orders 120.

Notes

The Excel file is attache to see all Examples: Orders 10 to 120.

Files

Block-Bordered-120-110-10.pdf

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