(a) What is the smallest (positive) multiple of 9 that is written only with the digits 0 and 1?

(b) What is the smallest (positive) multiple of 9 that is written only with the digits 1 and 2?
(a) A number is divisible by 9 if the sum of its digits is a multiple of 9. Therefore, the number must have 9 digits equal to 1. Thus, the smallest number is: 111111111.

(b) We should use the largest possible number of digits equal to 2, which should be placed in the rightmost positions. Thus, the smallest number is: 12222.