數學天才, 一定要看這些題

１．how many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two?

2.    the polynomial f(x) = x^4 + ax^3 + bx^2 + cx + d has real coefficients, and f(2i) = f(2+i) =0, what is a+b+c+d?

3.  for each positive integer n; let S(n) denote the sum of the digits of n. for how many value of n is n+S(n)+S(S(n))=2007?

ha, ha, you should try to do these Qs, they are very diffidult but interesting!