It is not surprising that magic squares are not very easy to construct. In particular there is no method that creates a magic square for any order. So we have to distinguish between three categories:

odd order

the order is an odd number

( n = 3,5,7,9,11, … )

single-even

the order can be divided by 2, but not by 4

( n = 6,10,14,18,22, … )

double-even

the order can be divided by 4

( n = 4,8,12,16,20, … )

The differentiation between single-even and double-even magic squares is quite astonishing. But the consequences to which these orders lead, are very different, so that there are only a few construction-methods that apply for all maqic squares of even order.

In particular the single-even magic squares are very obstinate and hard to create. This becomes clear by intuition, because in such a symmetrical formation we have to work with only one half of the square - and in this case the half is of an odd number. So the problems overlap.

Choose the kind of a special square, the construction method and the desired order. The algorithms can create magic squares of any order. However, the maximum order has been arbitrarily set to a maximum of n=20. Methods by which a variety of different magic squares can be constructed are each provided with a special icon.