The 3x3 grid below contains only the numbers 1, 2 and 3. Notice that the sum of the numbers in every column, row and diagonal is a multiple of 3.
a) How many different 3x3 grids are there that contain only the numbers 1, 2 and 3, and in which the sum of the numbers in every column, row and diagonal is a multiple of 3?
b) How many different 3x3 grids are there that contain only the numbers 1, 2, 3 and 4, and in which the sum of the numbers in every column, row and diagonal is a multiple of 4?
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