Published June 9, 2023 | Version v1
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Multiple Order Bordered Magic Squares

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

Description

During past years author worked with block-wise bordered magic squares of even and odd number blocks. In case of even number orders, these are with equal sums magic squares of orders 4, 6, 8, 10, 12 and 14.  It is an extension of classical bordered magic squares. Recently, the author also worked with odd orders bordered magic squares. This work is for the blocks of orders 3, 5, 7, 9 and 11. This work is little different. It brings multiple types borders for magic squares. Initially, we start with magic square of order 12 formed by blocks of magic squares of order 3. Then external border is made with blocks of pandiagonal magic squares of order 4 resulting in magic squares of order 20. Proceeding in the same way we get magic squares of orders 30, 42, 56, 72, 90, 110 and 132 based on borders of magic squares of orders 5, 6, 7, 8, 9, 10 and 11 respectively. The same procedure can be applied for further orders. The whole work can be seen in excel files attached with the work.

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Multiple Order.pdf

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