Conundrum, n.
Etymology: [Origin unknown.]
1. A kind of riddle based upon some fanciful or fantastic resemblance between things quite unlike; a puzzling question, of which the answer is or involves a pun. Or pun ambiguous, or conundrum quaint. J. Philips.
2. A question to which only a conjectural answer can be made. Do you think life is long enough to let me speculate on conundrums like that W. Black.
Shades of meaning
Fernald has no entry of its own for conundrum; he lists it under riddle.
Where he writes about it:
Conundrum, a word of unknown origin, signifies some question or statement in which some hidden and fanciful resemblance is involved, the answer often depending upon a pun; an enigma is a dark saying; a paradox is a true statement that at first appears absurd or contradictory; a problem is something thrown out for solution; puzzle (from oppose) referred originally to the intricate arguments by which disputants opposed each other in the old philosophic schools. — from riddle
The riddle is an ambiguous or paradoxical statement with a hidden meaning to be guessed by the mental acuteness of the one to whom it is proposed; the riddle is not so petty as the conundrum, and may require much acuteness for its answer; a problem may require simply study and scholarship, as a problem in mathematics; a puzzle may be in something other than verbal statement, as a dissected map or any perplexing mechanical contrivance. — from riddle