KöMaL 2006 K105

A book contains 700 psalms, numbered from 1 to 700. The congregation sings one of them every Sunday. The number of the chosen psalm is displayed as a 3-digit number on a special counter, fabricated from three small wooden cubes. (One or two-digit numbers are displayed with leading zeros, e.g. 3 appears as 003 and 28 as 028.) The is one digit on faces of the cubes, respectively, and 6 can also be interpreted as a 9. $a$) How many cubes are needed to display every possible number? How the digits are arranged on the faces? $b$) How many more psalms can be included in the book without adding further cubes?