The correct answer is 18,816 different ways. The general formula for six
fleurs-de-lys for all squares greater than 2^{2} is simply this: Six
times the square of the number of combinations of _n_ things, taken three
at a time, where _n_ represents the number of fleurs-de-lys in the side
of the square. Of course where _n_ is even the remainders in rows and
columns will be even, and where _n_ is odd the remainders will be odd.