Mystical squares

Probability Level 5

Consider a 3×33 \times 3 square, where each 1×11 \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.


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