Ultramagic squares

A magic square is said to be an ultramagic square, if it has the following properties:

Let us take a look at the following magic square of order n=4. You can easily see that this square is pandiagonal, as all rows, columns and diagonals sum to S=65.

  • 11522189
    23196512
    102132416
    14212073
    17841125
  • arrow
  • 25114817
    37202114
    162413210
    12561923
    91822151

Now we transform this magic square into its complement and we can see that a rotation with an angle of 180° will produce the original square again. So it is selfcomplement and hence ultramagic.