Simple magic squares satisfy only the minimum conditions, namely that all rows, columns and diagonals sums always give the magic sum. Other special structures, such as are described in the following sections, do not exist.

It may be surprising that these squares are listed separately nevertheless. However, it is sometimes not so easy to create simple magic squares, as some algorithms for constructing may have very specific properties.

On the other hand, it is not sure that such simple magic squares exist. The only magic square of the third order for example is symmetrical.

Furthermore, the characterization as a simple magic square doesn't always mean that the numbers are not arranged in a particular structure. The fourth-order square shown below has a very special situation of mutually complementary numbers.