Question

A number A has 2018 digits and is divisible by 9. The sum of all digits of A is a. The sum of all digits of a is b. The sum of all digits of b is c. Find the value of c.

Answer 1

If a number is divisible by 9, the sum of its digits will also be divisible by 9.

The largest a can be, then, is 18162 (that's 2018 '9s'). b is then 18 in this case.
The largest b can be is 36 (one possibility of that is when a is 9999). So, b can only ever be 36, 18, or 9. The sum of all these digits is 9, so...

c must be 9.