I remember when I got my first "desk" job... My desk had a funky calendar that was really nothing but two cubes and a little stand to place the two cubes side-by-side for the date. I also used a manual typewriter, but that's just showing my age.

Anyway, this two-cube calendar didn't indicate the month or the day of the week; just the date. Each of the six sides on the two cubes depicted a single digit. By placing some combination of the two cubes in the slots on the stand, you could indicate any date from 01 to 31. (You had to keep a cube in each slot... you wouldn't want to hide one of them and lose it.)

Today's question (and it's probably a bit trickier than it seems at first glance):

What were the digits on the sides
of the two 'date' cubes that allowed
every possible date to appear
using both cubes?

Here's one SOLUTION.

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.