conundrum

Conundrum is a situation where there is no clear right answer or no good solution. (noun)

An example of a conundrum is a challenging riddle to which you can't figure out the answer.

See conundrum in Webster's New World College Dictionary

noun

a riddle whose answer contains a pun (Ex.: “What's the difference between a jeweler and a jailer?”“One sells watches and the other watches cells.”)
any puzzling question or problem

See conundrum in American Heritage Dictionary 4

(kə-nŭnˈdrəm)

noun

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.)

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