Dickens uses the word "conundrum". It occurred to me that I had no idea of the etymology, but sounds a bit like Latin.
American Heritage® Dictionary of the English Language: Fourth Edition. 2000.

conundrum

SYLLABICATION: co·nun·drum
PRONUNCIATION: k-nndrm
NOUN: 1. A riddle in which a fanciful question is answered by a pun. 2. A paradoxical, insoluble, or difficult problem; a dilemma: “the conundrum, thus far unanswered, of achieving full employment without inflation” (Arthur M. Schlesinger, Jr.).
ETYMOLOGY: Origin unknown.

Offhand, I can't remember any conundrums (conunda?) for which answer is a pun. The only one I remember at the moment is "Why is Nancy Reagan like the Panama Canal?"
Answer: "The Panama Canal is a busy ditch, and she's vice versa." But that answer doesn't seem to be a pun.
Got a better example?