Find the smallest positive multiple of 9 that can be written using only the digits: (a) 0 and 1 ; $\quad$ (b) 1 and 2 .
A number is a multiple of 9 if the sum of its digits is a multiple of 9.

(a) The number must have 9 digits all equal to 1, that is, 111111111.

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