Each unit square of the 4x4 grid below is to be filled in with the number 1, 2, 3 or 4, so that:
Each row contains the numbers 1, 2, 3, and 4 in some order,
Each column contains the numbers 1, 2, 3, and 4 in some order, and
Each square (outlined in bold) contains the numbers 1, 2, 3, and 4.
Some of the squares have already been filled in. Find the number of ways of filling in the rest of the grid.
