Definition

A magic square is a square array of numbers 1, 2, 3, … , n2 arranged in such a way that the sum of each row, each column and both diagonals is constant.

sums

The number n is called the order of the magic square.

As will be seen in later sections, the order of a magic square plays an important role in both the properties and the construction of squares. While it is obvious for reasons of symmetry that a distinction between even and odd orders makes sense, it turns out that, surprisingly, the even orders need to be further subdivided.

When considering properties and construction methods of magic squares, it is useful to categorize magic squares in three classes:

  • 211147
    151036
    181312
    16549
  • 51122819
    23920112
    162132410
    14256173
    71841521
  • 430831335
    365289321
    293433276
    131217222126
    181410272319
    111615202524
odd orderthe order is an odd number
( n = 3,5,7,9,11, … )
single-eventhe order can be divided by 2, but not by 4
( n = 6,10,14,18,22, … )
double-eventhe order can be divided by 4
( n = 4,8,12,16,20, … )