This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Build a calendar from two sets of cubes. On the first set, spell the
months with a letter on each face of three cubes. Use lowercase
three-letter English abbreviations for the names of all twelve months
(e.g., "jan", "feb", "mar"). On the second set, number the days with a
digit on each face of two cubes (e.g., "01", "02", etc.).
First note that there are *nineteen* different letters in the
month abbreviations (abcdef gjlmno prstuv y) so to get them all on the
eighteen faces of 3 cubes, you know right away you're going to have to
resort to trickery.
So I wrote them all down and looked at which ones could be
reversed to make another letter in the set. The only pair that jumped
out at me was the d/p pair. Now I knew that it was at least feasible,
as long as it wasn't necessary to duplicate any letters.
Then I scanned the abbreviations to find ones that had a lot of
common letters. The jan-jun-jul series looked like a good place to
j a n u l
I don't put tails on my u's so it didn't strike me the first time through that n and u could be combined. Cube 1 Cube 2 Cube 3 j a n/u n/u l would let me get away with putting the g on the first cube to get aug, so I did. j a n/u g n/u l (1) Now came the fun part. The a was placed so I had to work around it for the other months that had an a in them (mar, apr, may). m a r d/p y (2) Now the d/p was placed so I had to work around that for sep and dec. This one was easy since they shared an e as well. d/p e s c (3) Now the e was placed so feb had to be worked in. f e b (4) The two months left (oct, nov) were far more complex. Not only did they have two "set" letters (c, n/u), there were two possible n/u's to be set with. That's why I left them for last. o t c n/u v (5) So now I had five pieces to fit together, so that no set would have more than six letters in it. Trial and error provided: j a n/u a b e g n/u l or, c d/p g r s m alphabetically: f l j y c d/p n/u m o e v t s n/u r o f b v t y