Cube Calendar

[Tiberius]

Yet another mathematical problem for you.

You have two cubes and you need to construct a calendar out of them by adding the numbers 0-9 onto the faces. Your calendar must be able to show the dates of the month 01 through 31, such that both cubes are used to display one of the two digits (so no clever tricks with only one).

You are only allowed to put one number on each face, and leading zeros must not be dropped (so the calendar must display 01, 02, 03, 04, etc rather than just 1, 2, 3, 4.

What numbers go on each cube?

Warning!!! Solution:

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It should become clear that each cube needs a 1 and a 2 (since 11 and 22 are both valid dates). It should also be relatively obvious that to represent all numbers between 01 and 09, you need a 0 on both cubes too. This leaves you with 6 faces left, but 7 digits (3 - 9) to put on them. However, the laterally thinking of you will know that 6 and 9 are rotationally symmetrical, and so can be represented with a single number (either 6 or 9). Thus any solution where the numbers 0, 1, and 2 appear on both cubes and the numbers 3, 4, 5, 6 (or 9), 7, and 8 are dispersed between them is a valid solution.

For instance:

Cube A: 0, 1, 2, 3, 4, 5
Cube B: 0, 1, 2, 6, 7, 8

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