Diabolic square

A diabolic square is the most powerful version of a magic square: here the same sum can be found not only in rows and diagonals, but in a variety of different regular and geometric configurations.

For example, the following square:

<math> \begin{bmatrix}

 15 & 10 & 3 & 6 \\
 4 & 5 & 16 & 9 \\
 14 & 11 & 2 & 7 \\
 1 & 8 & 13 & 12

\end{bmatrix} </math>

is a diabolic square where the sum 34 can be found in 86 different ways: rows, columns, the two diagonals, and 70 different geometric ways. For example, the square can be divided in 4 little squares with sum 34. The four corners have the same sum. The four numbers at the center. The two number in the middle of the top line, plus the two in the middle of the bottom line, and the same way on the sides. And so on.

See also: Magic square, Satanic square