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conundrum
- 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.
- A paradoxical, insoluble, or difficult problem; a dilemma.
- 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.
- A question to which only a conjectural answer can be made.
Source: dictionary.reference.com
http://dictionary.reference.com/browse/conundrum