13th Asian Pacific Mathematics Olympiad 2001 Problems

13th Asian Pacific Mathematics Olympiad 2001 Problems A1.  If n is a positive integer, let d be the number of digits in n (in base 10) and s be the sum of the digits. Let n(k) be the number formed by deleting the last k digits of n. Prove that n = s + 9 n(1) + 9 n(2) + ... + 9 n(d).