The Collaborative International Dictionary of English v.0.48:

Conundrum \Co*nun"drum\, n. [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.
      [1913 Webster]

            Or pun ambiguous, or conundrum quaint. --J. Philips.
      [1913 Webster]

   2. A question to which only a conjectural answer can be made.
      [1913 Webster]

            Do you think life is long enough to let me speculate
            on conundrums like that?              --W. Black.
      [1913 Webster]

WordNet (r) 3.0 (2006):

conundrum
    n 1: a difficult problem [syn: riddle, conundrum, enigma,
         brain-teaser]