Yesterday I saw a pair of calendar dice that can be rotated and swapped to show all days of a month between 01 and 31.
The dice have a digit painted on each face.
- First die: [0, 1, 2, 3, 4, 5]
- Second die: [0, 1, 2, 6, 7, 8].
The trick is that one of the faces can be rotated to show a 6 or a 9 as required.
With those dice one can also display the number 32. This is the last number that can be reached if we start counting from 01. Even though larger numbers like 42 are possible, there are gaps between 32 and 42 that cannot be represented with those two dice, so we can only count up to 32.
If we were given three dice to count numbers in zero-padded three-digit format starting from 001 and counting up by 1, what would be the largest countable number? How would the dice have to look like?