Two cubes

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”.

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Solution:

Cube One has the following numbers: 0, 1, 2, 3, 4, 5
Cube two has the following numbers: 0, 1, 2, 6, 7, 8
The 6 doubles as a 9 when turned the other way around.
There is no day 00, but you still need the 0 on both cubes in order to make all the numbers between 01 and 09.
Alternate solutions are also possible e.g.
Cube One: 1, 2, 4, 0, 5, 6
Cube Two: 3, 1, 2, 7, 8, 0

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