For every natural number x, let S(x) be the sum and P(x) the product of

the (decimal) digits of x. Show that for each natural number n there exist infinitely

many values of x such that. $\displaystyle S(S(x)) + P(S(x)) + S(P(x)) + P(P(x)) = n$

The problem is from final round of Austrian MO '83 and I really can't find any solution on the internet. So I am asking for help, maybe you know it, thanks in advance.