Some methods to create magic squares

This section introduces a limited selection of simple methods for constructing magic squares. You can find a detailed description of many other methods in my PDF document.

For the methods presented here, only the basic algorithms are explained. Further variants of these algorithms can be found in the PDF document and also in the menuentry Construction, where you can choose between different parameters for these algorithms.

  • 15181043529
    2421172632
    34281417126
    2531232039
    2536302216
    11827331319
  • 3238441142026
    404639152834
    4851117232942
    7131925313743
    821273339452
    1622354147410
    2430364961218
  • 10253615159168
    9154625260157
    3947282030223341
    4048271929213442
    2331443646381725
    2432433545371826
    58505133116456
    57496144126355

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.

oddthe order is an odd number
( n = 3,5,7,9,11, … )
single-eventhe order is divisible by 2, but not by 4
( n = 6,10,14,18,22, … )
double-evendouble-even the order is divisible by 4
( n = 4,8,12,16,20, … )