Bordered and Pandiagonal Magic Squares Multiples of 12
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 108. Based on these two big magic squares, the inner order magic squares multiples of 12 are studied. By inner orders we understand as the magic squares of orders 96, 84, 72, etc. The construction of the bordered magic squares multiples of 12 is based on equal sum blocks of magic squares of order 12. It is done in 16 different ways. Two blocks of order 12 composed with small blocks of order 3 and 4 are pandiagonal. This lead us to write all orders multiples of 12 as pandiagonal magic squares. The only difference is that the pandiagonal magic squares multiples of 12 are no more bordered magic squares. The bordered magic squares also have the same property. For multiples of orders 4, 6, 8 and 10, see author's recent works (multiples-4, multiples-6, multiples-8 and multiples-10). The further multiples, such as multiples, for order 14, shall be done in another works. This work brings examples only up to order 48. Higher order examples are given in Excel files attached with the work.