This puzzle is very simple to state, but not so easy to solve. In fact it might seem impossible, but there is most definitely a solution.
The challenge is to determine the digits on the faces of two cubes that will allow you to display all the numbers from 1 to 31 - the numbers needed to show the date.
Each face of the cubes has a single digit. The numbers from one to nine must be displayed as 01 - 09. The two cubes can be used in either order, so either cube can be used on the left with the other on the right.
What are the six digits on the faces of the two cubes?
Because you have to be able to display 11 and 22 there must be a one and a two on both cubes.
If only one cube has a zero then, at most, only six of the numbers from 01 to 09 can be displayed, so there must be a zero on both cubes.
If both cubes have zero, one and two that is six of the twelve faces occupied, leaving six free faces for the seven digits from three to nine. This would appear to be an insurmountable problem!
Except that a six can be turned upside down to become a nine.
The first cube has the digits zero, one, two, three, four and five. And the second has the digits zero, one, two, six (nine), seven and eight.