How many ways is there to color an $n\times n$ square grid with $n$ colors such that each column and each row contains exactly one $1\times 1$ square of each color?
And how many ways if the same is required of the two diagonals?
How many ways is there to color an $n\times n$ square grid with $n$ colors such that each column and each row contains exactly one $1\times 1$ square of each color?
And how many ways if the same is required of the two diagonals?