What is the answer to a riddle?

Julian Sanchez writes:

“In a riddle whose answer is chess, what is the one word you must under no circumstances use?” The question comes from Borges’ short story “The Garden of Forking Paths,” in which the narrator’s ancestor (we’re told) aspired to create an infinite labyrinth. He ultimately constructed his labyrinth not in space but through time and narrative, writing a great sprawling novel in which many possible—and contradictory—futures coexist, converge, and splay off into variegated chaos again. The forbidden word, of course, is “chess”—making that opening question a riddle in violation of its own rule.

I was thinking that the use/mention distinction would save the riddle from self-violation. We should regard the word "chess" as being mentioned and not used by Borges in stating the riddle. (For the time being, let's set aside the issue of whether the question actually counts as a riddle.)

Might we instead say that the locution "A riddle whose answer is X" involves the use of X, rather than the mere mention of X? Well, I would've thought that answers were linguistic entities, so when you talk about the answer to any riddle you're talking about a linguistic entity, and thus mentioning the term rather than using it.

Also, it would be a surprise if questions and answers had different ontological status. While there's a theoretical option of considering answers to be nonlinguistic entities, since they refer to things, I don't see a similar option with questions. A question has to be a series of words, or some abstract entity expressible in words. Unlike an answer, there's no object it can be taken to refer to. If there's good reason to regard answers as the same things as questions, we should regard both as linguistic entities.