Current Day of the Month

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.

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Amazing Facts

Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.