1. What is the most romantic song you know that doesn't use the word "love"?
No instrumentals, please--the song should have lyrics. And there shouldn't be any inflected forms (loved, loving, lover, etc.).
2. What's the rockingest song you know that doesn't use drums?
I think some good solutions to #1 are here.
My answer to #2 is pretty strong I think.
(For #2, a song with a very different feel also came to mind - not usually thought of as a rock song, though it did make #12 on the "Mainstream Rock" charts.)
These are subjective, so I suppose they're more like discussion questions. But they do have something in common with puzzles, in that they ask for an optimum subject to given constraints.