From New Scientist #663, 28th August 1969 [link]
You may have seen those neat calendars where the date is given by two cubes laid side by side in a box, so that only the top face of each is visible. Each face of each cube bears a number and by suitable numbering and the necessary twiddling you can make the exposed faces show any number up to at least 31. (Numbers below 10 are shown as 01, 02 etc).
31 is enough for a calendar. But, in fact, that gives you a bit in reserve. What is the highest number the cubes can be persuaded to count up to without missing any out?
And, while we are at it, suppose you have three cubes and show numbers below 100 as 001, 002… 010, 011 etc., now what is the highest number you can count up to continuously?
[tantalizer114]