USSR Problem Book, #19 hint

#19. (a) Find the smallest integer whose first digit is 1 and which has the property that if this digit is transferred to the end of the number the number is tripled.

(b) With what digits is it possible to begin a (nonzero) integer such that the integer will be tripled upon the transfer of the initial digit to the end? Find all such integers.

Hint. Look for two-digit solutions, three-digit solution, and so on. Once finding a solution for 1, look for a recurring pattern to find more solutions for 1. Handle the other digits similarly.