Golf you a quine for great good!
People have proposed short quines in various languages.
Puzzle: Find the shortest non-trivial quine in a language of your choice, and prove that it is the shortest. ("Trivial" quines are such things as the empty program, and text that will be echoed directly.)
I expect the solution will involve exhaustive search of all possible programs of length up to the length of the shortest known quine. Some cleverness is probably needed to reduce the search space to a tractable size, and filter out programs that are quines for trivial reasons.