Published February 2, 2019 | Version v1
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Palindromic, Patterned Magic Sums, Composite, and Colored Patterns in Magic Squares

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

Description

There are many ways of representing magic squares with palindromic type entries. This paper works with magic squares of order 3 to 10. In each case, the magic squares written for the entries from the digits 3 to 8 with all palindromic numbers. These entries are arranged in such a way that their magic sum turns number patterns.  In some cases, using digital type letters, these palindromic magic squares are made in such a way that they becomes upside down and mirror looking. The study is extended to composite magic squares and double colored patterns. Some particular case resulting in upside down and mirror looking magic squares are also considered. In case of magic square of order 9, we have considered two different situations. One with bimagic and another with pandiagonal magic squares. In case of magic square of order 10, to make it palindromic-type, we considered some numbers as 010, 020, etc. In some other examples, we also used the idea of symmetry as 010, 020, etc. This is reorganized version of author's previous works 15, 16, 30] done in 2015 and 2018.

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