ONE POSSIBLE SOLUTION:
One of the cubes had the digits: 0, 1, 2, 3, 4, and 5.
The other cube had the digits 0, 1, 2, 6, 7, and 8.
By using some combination of the two cubes — and placing the ’6′ cube upside down for the ’9′ when necessary — you could use these two cubes to indicate any date from 01 to 31.
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