co·nun·drum

[kuh-nuhn-druhm]
noun
1.
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.
2.
anything that puzzles.

Origin:
1590–1600; pseudo-L word of obscure origin

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Based on the Random House Dictionary, © Random House, Inc. 2013.
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Collins
World English Dictionary
conundrum (kəˈnʌndrəm) [Click for IPA pronunciation guide]
 
n
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
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00:10
Conundrum is an SAT word you need to know.
So is germane. Does it mean:
closely or significantly related; relevant; pertinent:
tremulous fear, alarm, or agitation
Etymonline
Word Origin & History

conundrum
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 fact, the fact that they are changeable and mutable is what brought me into
  this conundrum in the first place.
Few movies have worked out that conundrum so powerfully, or so effectively
  dramatized the folly of judging by partial evidence.
For the moment, the broadly unanticipated behavior of world bond markets
  remains a conundrum.
The solution to this conundrum, in the eyes of many governments, is nuclear
  power.
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