Double-Digit Cyclic-Type Bordered Reduced Entries Algebraic Magic Squares of Orders 7 to 20

This work brings double-digit cyclic-type algebraic magic squares of orders 7 to 20 for \textbf{reduced entries}. By reduced or less entries, we understand that instead of normal n^2 entries of a magic square order n, we are using less number of entries. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and negative numbers. Sometimes, we call these kind of magic squares as self-made. It means that these are complete in themselves. Just put the values of entries and choose the magic sum, we get a magic square. In some cases, there maybe decimal or fractional values of the entries depending on the types of magic squares. The idea of double-digit is applied to bring these of magic squares.  Moreover, we have considered the magic rectangles in a cyclic way, i.e, all the four side in each case are of equal sums in widths and lengths.  For similar kind of work for different orders in different styles and ways, the readers are suggested to see author’s work given in reference lists.

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