Via Mark Dominus:
There are two boxes on a table, one red and one green. One contains a treasure. The red box is labelled “exactly one of the labels is true”. The green box is labelled “the treasure is in this box.”
Can you figure out which box contains the treasure?
As Mark notes, Raymond Smullyan did it first; but I really enjoy Mark’s fleshing-out of the solution, including an explanation of what people usually get wrong about it.
You can (and should!) read the full answer here.