dilemma

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A situation that requires a choice between options that are or seem equally unfavorable or unsatisfactory.
• noun Usage Problem A problem that seems to defy a satisfactory solution.
• noun Logic An argument that presents two alternatives, each of which has the same consequence.

from The Century Dictionary.

• noun A form of argument in which it is shown that whoever maintains a certain proposition must accept one or other of two alternative conclusions, and that each of these involves the denial of the proposition in question.
• noun A difficult or doubtful choice; a state of things in which the alternatives appear to be equally bad or undesirable.

from the GNU version of the Collaborative International Dictionary of English.

• noun (Logic) An argument which presents an antagonist with two or more alternatives, but is equally conclusive against him, whichever alternative he chooses.
• noun 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.
• noun alternatives, each of which is equally difficult of encountering.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable.
• noun this sense) (disputed) A difficult circumstance or problem.
• noun logic 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".
• noun rhetoric Offering to an opponent a choice between two (equally unfavorable) alternatives.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun state of uncertainty or perplexity especially as requiring a choice between equally unfavorable options