Zamyatin $B$.

Vladimir wants to make a set of cubes of the same size and write one digit on each face of each cube so that he can use these cubes to form any 30-digit number. What is the smallest number of cubes he will need? (The digits 6 and 9 do not turn into each other when flipped.)

#
No less than 30 units, twos, ..., nines, and no less than 29 zeros. In total, no less than 50 cubes. It is not difficult to arrange no less than 30 instances of each digit on 50 cubes so that the digits on each cube do not repeat.

## Answer

50 cubes.