Published January 21, 2025 | Version v2
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Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 25

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

Description

There are many ways of representing magic squares with palindromic type entries. Also, we can write magic squares in the composite forms based on pair of Latin squares.  Based on palindromic and composite magic squares we have written  upside-down and/or mirror looking magic squares. By upside-down, we understand that making  180 degrees rotation still we get a magic square. By mirror looking, we understand that putting magic square in front of mirror, still we get another magic square. When the magic square is of both type, upside-down and mirror looking, we call it as universal magic square.  It is a revised and enlarged version of author's previous works on digital-type fonts magic squares.  In case of upside-down situation, the number 6 becomes 9 and 9 as 6.  In case of mirror looking, the numbers 2 becomes 5 and 5 as 2 (writing as digital fonts). Total work of magic squares of orders 3 to 16 and order 20. It is divided in parts. First is for orders 3 to 6, and second part for orders 7 to 10, and third part is for the 11 to 13. The forth part is for the orders 14 to 16. The fifth part is for the orders 17 to 20. The sixth part is for the orders 21 to 25. The seventh part is for the order 24. The work is eight part of the complete project and is for the order 25. It is bimagic with pandiagonal magic squares of blocks of order 5.   For more details,  follow the online links of author's web-site (3to6,  7to1011to15, 1620, 2124 and 25).

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