dilemma vs problem

dilemma

noun
  • A difficult circumstance or problem. 

  • A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true". 

  • A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable. 

  • Offering to an opponent a choice between two (equally unfavorable) alternatives. 

problem

noun
  • A difficulty that has to be resolved or dealt with. 

  • A puzzling circumstance. 

  • A set of moves required to complete a climb. 

  • A question to be answered, schoolwork exercise. 

  • Objection. 

  • Difficulty in accepting or understanding or refusal to accept or understand. 

adj
  • Causing a problem; problematic; troublesome. 

  • Difficult to train or guide; unruly. 

How often have the words dilemma and problem occurred in a corpus of books? (source: Google Ngram Viewer )