Dilemma

n.
  1. (Logic) An argument which presents an antagonist with two or more alternatives, but is equally conclusive against him, whichever alternative he chooses.
  2. A state of things in which evils or obstacles present themselves on every side, and it is difficult to determine what course to pursue; a vexatious alternative or predicament; a difficult choice or position.
    3. Horns of a dilemma ,
    alternatives, each of which is equally difficult of encountering.