Conundrum

co·nun·drum

/kəˈnəndrəm/

noun

1. a confusing and difficult problem or question.

   "one of the most difficult conundrums for the experts".

    a problem that is difficult to deal with.

    A conundrum is a problem or puzzle which is difficult or impossible to solve. 

    a question asked for amusement, typically one with a pun in its answer; a riddle.

    The definition of conundrum is a situation where there is no clear right answer or no good solution. 

    A paradoxical, insoluble, or difficult problem; a dilemma.