Two cubes, ten digits each, and every date of the month
A desk calendar shows any day of the month, 01 through 31, using just the front faces of two cubes side by side. Each cube has only 6 faces, so between them they have 12 faces for 10 digits (0-9) — with two digits appearing twice. How do you arrange the digits on the two cubes so every date from 01 to 31 can always be displayed?
Reveal the answer
One cube gets 0, 1, 2, 3, 4, 5; the other gets 0, 1, 2, 6, 7, 8. The trick is that 6 and 9 are the same digit flipped upside down, so the '6' face doubles as a '9'. Both cubes carry 0, 1 and 2 so dates like 11 and 22 are still possible. The puzzle was popularized by Martin Gardner in Scientific American after he spotted a two-cube calendar in a shop window; it had been patented by John S. Singleton in 1957.
— Martin Gardner, Mathematical Games column — Scientific American