Let us denote f(n) = 12...12 (repeated n times) and g(n) = 3...3 (repeated n times). For example: f(3) = 121212 and, g(3) = 333.
(i) Determine the distinct digits in the base ten expansion of f(n)*g(n) whenever n ≥ 3
(ii) Express s.o.d (f(n)*g(n)) in terms of n
*** s.o.d (x) denotes the sum of digits in the base ten expansion of x