a riddle, the answer to which involves a pun or play on words, as What is black and white and read all over? A newspaper.
anything that puzzles.

1590–1600; pseudo-L word of obscure origin Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
conundrum (kəˈnʌndrəm)
1.  a riddle, esp one whose answer makes a play on words
2.  a puzzling question or problem
[C16: of unknown origin]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

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.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
In this case, the conundrum is how to keep your water from freezing in the
  narrow tube between your pack and the mouthpiece.
Few movies have worked out that conundrum so powerfully, or so effectively
  dramatized the folly of judging by partial evidence.
Astronomers have proposed two solutions to this conundrum.
The only way out of this conundrum is to hypothesise some kind of catastrophe
  that brings an end to the universe.
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