"Of twelve coins, one is counterfeit and weighs either more or less than all the others. The others weigh the same. With a balance scale, on which one side may be weighed against the other, you are to use only three weighings to determine the counterfeit."
About a year ago I found this cool puzzle in the collection of short stories
"The Palace Thief Stories" by Ethan Canin.
It's in the story "Batorsag and Szerelem" about a math prodigy. I had a fun time solving it (took me a while) and now I have the solution on loose papers lying around on a shelf. So I thought it would be good to transfer it over to a LaTex document. Stay tuned...
This one's not too bad. A hint: (stop reading here if you don't want a hint) you can narrow the counterfeit to one of three coins with only two weighings.
Sorry, I was a bit stupid there for a second. Uwe, I remember solving this one in the office, but the solution I remembered wasn't one after all. I gotta think about this a bit more before I read your write-up.