Pages Without a 1 or a 2

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Word Problems

The pages of a book are numbered with consecutive numbers from 1 to n. In this book

- A is the set of the pages whose number contains the digit 1, - B is the set of the pages whose number contains the digit 2.

If n(A'cap B')=8, what is the sum of the digits of the smallest value of n?