Consider a \(3 \times 3\) square, where each \(1 \times 1\) square is filled with one of the integers from 1 to 13. A square is called mystical if each row sums to a multiple of 13, each column sums to a multiple of 13 and each of the two main diagonals sums to a multiple of 13. How many mystical squares are there?
Details and assumptions
Numbers in the square are not necessarily distinct.
2 mystical squares are considered different if they differ in any entry. In particular, rotations are (generally) considered distinct.