In this section you can create magic squares with a variety of different algorithms, where some intermediate steps are highlighted. The exact description of all methods and algorithms can be found in my PDF document.
Detailed description of algorithms to create magic squares
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:
ungerade | die Ordnung ist eine ungerade Zahl |
( n = 3,5,7,9,11, … ) | |
einfach-gerade | die Ordnung durch 2, aber nicht durch 4 teilbar |
( n = 6,10,14,18,22, … ) | |
doppelt-gerade | die Ordnung durch 4 teilbar |
( 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.
64 | 51 | 2 | 11 | 61 | 7 | 9 | 55 |
62 | 50 | 16 | 17 | 21 | 46 | 45 | 3 |
8 | 18 | 35 | 32 | 29 | 34 | 47 | 57 |
52 | 23 | 40 | 26 | 27 | 37 | 42 | 13 |
6 | 41 | 25 | 39 | 38 | 28 | 24 | 59 |
53 | 43 | 30 | 33 | 36 | 31 | 22 | 12 |
5 | 20 | 49 | 48 | 44 | 19 | 15 | 60 |
10 | 14 | 63 | 54 | 4 | 58 | 56 | 1 |
42 | 20 | 61 | 7 | 10 | 52 | 29 | 39 |
63 | 5 | 44 | 18 | 31 | 37 | 12 | 50 |
4 | 58 | 23 | 45 | 36 | 26 | 55 | 13 |
21 | 47 | 2 | 60 | 53 | 15 | 34 | 28 |
46 | 24 | 57 | 3 | 14 | 56 | 25 | 35 |
59 | 1 | 48 | 22 | 27 | 33 | 16 | 54 |
8 | 62 | 19 | 41 | 40 | 30 | 51 | 9 |
17 | 43 | 6 | 64 | 49 | 11 | 38 | 32 |