Counting Magic Squares

A magic square is a matrix, where the sum of the entries in all rows, columns and both main diagonals is the same. This constant will be called the magic sum. Moreover, a natural magic square of order n is a magic square such that the entries of the square are the naturalnumbers from 1 to n^2 and that all entries are distinct. In this case the magic sum is equal to n(n^2+1)/2. For example, the magic constant of natural magic squares of order 6 is 111.

The goal of this application is to generate all natural magic squares of order 6 with predefined restrictions, like having the four corner property or being semi pandiagonal magic squares. This will reduce the needed time for computations. This kind of calculation needs a long time. So, the calculation is split into several program runs. Additionally, it uses the symmetries (from mathematical point of view) to reduce the run time. The calculated number will be later multiplied with 16.