In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.

First cube has the following numbers:

0, 1, 2, 3, 4, 5

Second cube has the following numbers:

0, 1, 2, 6, 7, 8

If you noticed, we have not used number 9 on any cube. This is because, you can always invert the number 6 to make it 9.

Please note that an alternate solution is also available for this problem. If you can find it, do post in the comments section.