Problem 1. One digit of 970405 can be changed to make the result divisible by 225. What is the six-digit number after the modification?

Problem 2. For each positive integer n, let S(n) denote the sum of the digits of n. How many three-digit n's are there such that n+S(n)+S(S(n)) is conguent to 0 (mod 9)?

Nikhil Oct 7, 2020