Beauty of Magic Squares: 3888-Multiple Order Bordered Magic Squares of Order 144 - Part 1

This paper presents a systematic construction of multiple order bordered magic squares at orders 12, 20, 30, 42, 56, 72, 90, 108 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 9 is used twice to bring 108, and finally the order 18 is applied over 108 to bring 144. The magic squares orders are considered as 3, 4, 5, 6, 7, 8, 9, 9 and 18. In some cases, even-order borders consist of equal-sum, 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.