This section introduces a very limited selection of simple methods for constructing magic squares. You can find a detailed description of many other methods in my PDF book.
Detailed description of algorithms to create magic squares.
For the methods presented here, only the basic algorithms are explained. Further variants of these algorithms can be found in my PDF book and also in the menuentry Construction, where you can choose between different parameters for these algorithms.
15 | 18 | 10 | 4 | 35 | 29 |
24 | 21 | 1 | 7 | 26 | 32 |
34 | 28 | 14 | 17 | 12 | 6 |
25 | 31 | 23 | 20 | 3 | 9 |
2 | 5 | 36 | 30 | 22 | 16 |
11 | 8 | 27 | 33 | 13 | 19 |
32 | 38 | 44 | 1 | 14 | 20 | 26 |
40 | 46 | 3 | 9 | 15 | 28 | 34 |
48 | 5 | 11 | 17 | 23 | 29 | 42 |
7 | 13 | 19 | 25 | 31 | 37 | 43 |
8 | 21 | 27 | 33 | 39 | 45 | 2 |
16 | 22 | 35 | 41 | 47 | 4 | 10 |
24 | 30 | 36 | 49 | 6 | 12 | 18 |
10 | 2 | 53 | 61 | 51 | 59 | 16 | 8 |
9 | 1 | 54 | 62 | 52 | 60 | 15 | 7 |
39 | 47 | 28 | 20 | 30 | 22 | 33 | 41 |
40 | 48 | 27 | 19 | 29 | 21 | 34 | 42 |
23 | 31 | 44 | 36 | 46 | 38 | 17 | 25 |
24 | 32 | 43 | 35 | 45 | 37 | 18 | 26 |
58 | 50 | 5 | 13 | 3 | 11 | 64 | 56 |
57 | 49 | 6 | 14 | 4 | 12 | 63 | 55 |
As usual, a distinction must be made between squares of different orders, since all construction methods depend on the order of the square, for example to use symmetries. A basic distinction is made between three different kind of orders, where no method is known that can create squares for several of these basic orders.
odd | the order is an odd number |
( n = 3,5,7,9,11, … ) | |
single-even | the order is divisible by 2, but not by 4 |
( n = 6,10,14,18,22, … ) | |
double-even | double-even the order is divisible by 4 |
( n = 4,8,12,16,20, … ) |