What numbers are on the faces of the cubes to allow this?

Question

A corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month.

What numbers are on the faces of the cubes to allow this?

Note: You can’t represent the day “7” with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be “07”.

Answer 1

1st cube has { 0, 1, 2, 3, 4, 5 }
2nd cube has { 0, 1, 2, 6, 7, 8 }
Using these numbers on the 2 cubes any date can be made even without using the number 9. This is because 6 can be inverted to get 9.