Day of the month on 2 cubes

                                                

During a visit to my interior decorator friend, I noticed 2 wooden cubes of size about an inch kept side by side on his showcase. There was one number painted each on the faces facing me, a 0 and an 8.

Noticing my intent look at this he explained: this is the day of the month.

I then remembered it was 8^th December.

It aroused my curiosity. My mathematical mind started working.

I asked: You may need to display 31 different dates (Gregorian Calendar). All will be accommodated?

He: Well, you need only 2 digits at a time.

He did not elaborate. I felt his mysticism was to give my mental ability maximum flexing.

I: On the left-hand side cube you may need 0,1,2 and 3 to represent the ten’s position of the date on the cube. And you may need all the ten digits on the unit’s position. How can all this be accommodated on just 12 faces of 2 cubes?

This time he elaborated a little: The left and right cubes can be exchanged. As you guessed, 0,1 and 2 need to be on both the cubes as we need to show 11,22 also. Luckily there is no date 33. Therefore 3 needs to be only on one of the cubes.

My doubt had not been completed washed off. I argued: 0,1 and 2 on both cubes. This takes up 6 faces, leaving 6 for other digits. Let us keep 3 on the first cube. Now we have 5 faces remaining and 6 digits to display 4,5,6,7,8 and 9. How will you….

Fearing that my analysis may stumble upon the full solution, he cut me short: The remaining you take as homework. Now let us have tea.

Cruel guy! He did not venture to open the showcase and let me examine the actual numbers on the face of the cube.

I do the same to you: Work at home and find out how he accommodated 6 numbers on the remaining 5 faces?