Published March 3, 2023 | Version v1
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Double-cross Bordered Magic Rectangles and Magic Squares of Order 42

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

Description

Recently, author constructed even order magic squares from orders 6 to 20 with different styles and models, for examples the order 20 is with 1616 magic squares, order 18 with 810 magic squares, etc. For details see the link.  A systematic procedure to construct these magic squares is given. It is based on the magic squares and bordered magic rectangles (BMR) of orders 4, 6, 8 etc. forming external borders. The inner blocks  are filled with previous known magic squares. For the orders multiples of 4, we can always write magic squares with equal sums blocks of magic squares of order 4. This procedure is very helpful for the orders of type 2p, where p is a prime number, for examples, 14, 22, 26, 34, 38, etc. For the orders like 18, 30, etc., we can make good external blocks with order 4, and for orders like 16, 20, 28, 32, etc. we can make good external borders of order 6, and so on. In this work we have considered crossed bordered magic rectangles for the magic squares of order 40. It is done with double-cross bordered magic rectangles. The work is with few examples. The pdf files of full work can be downloaded at author's site

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