In this paper we introduce and study special types of magic squares of order six. We list some enumerations of these squares. We present a parallelizable code. This code is based on the principles of genetic algorithms. A magic square is a square matrix, where the sum of all entries in each row or column and both main diagonals yields the same number. This number is called the magic constant. A natural magic square of order n is a matrix of size n×n such that its entries consist of all integers from one to square of n. We define a new class of magic squares and present some listing of the counting carried out over two years.


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