Beauty of Magic Squares: 3240-Multiple Order Bordered Magic Squares of Order 108 - Part 2

This paper presents a systematic construction of multiple order bordered magic squares at orders 20, 30, 42, 56, 72 and 108. for a full structural summary.
Unlike classical block-wise bordered magic squares, which are built as multiples of a single block size, the structures explored here incorporate successive borders drawn from magic squares of different orders --- specifically orders 3, 4, 5, 6, 7, 8 and 18 --- each contributing a distinct structural layer. To bring order 108, order 18 is used after order 8. The innermost core is a magic square of order~12 formed by different-sum magic squares of order~3.  Successive borders of orders 4, 5, 6, 7, 8 and 18 are then applied; even-order borders consist of equal-sum, while odd-order borders consist of different-sum magic squares. In case of order 8 and 18, some are with equal sums and some of them are with different magic sums. The combinatorial multiplicity of border types at each level yields a hierarchy of distinct configurations. The further study of multiple order bordered magic squares of orders 110, 120, 132 and 144 are given in details in the reference list.

This work is available online at author's web-site.