Beauty of Magic Squares: 3888-Multiple Order Bordered Magic Squares of Order 144 - Part 3

This paper presents a systematic construction of  multiple order bordered magic squares at orders 12, 20, 30, 42, 56, 72, 90, 120 and 144. 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 through 9 --- each contributing a distinct structural layer. To bring order 144, order 12, and order 15 is used over 90 to bring order 120. The magic squares orders are considered as 3, 4, 5, 6, 7, 8, 9, 15 and 12. In some cases, even-order borders consist of equal-sums, while odd-order borders consist of different-sum magic squares.  In some cases, the even orders are also considered with different magic sums. The combinatorial multiplicity of border types at each level yields a hierarchy of distinct configurations.