trilemma

noun3

1. •
   A circumstance in which a choice must be made between three options that seem equally undesirable.

   • With all these dilemmas and trilemmas crowding the mind, if one did not know better, one might be tempted to doubt whether any such versions were ever made at all. — 1853
2. •
   A situation in which a choice must be made among three desirable options, only two of which are possible at the same time.
3. •
   An argument containing three alternatives, jointly exhaustive either under any condition(s) or under all condition(s) consistent with the universe of discourse of that argument, that each imply the same conclusion.