A riddle in which a fanciful question is answered by a pun.
A paradoxical, insoluble, or difficult problem; a dilemma: "the conundrum, thus far unanswered, of achieving full employment without inflation"(Arthur M. Schlesinger, Jr.)
1596, Oxford University slang for "pedant," also "whim," etc., later (1790) "riddle, puzzle," also spelled quonundrum; the sort of ponderous pseudo-Latin word that was once the height of humor in learned circles.