do contradictions exist???

i was going trough ayan rand philosophy and there i came across a statement that contradictions do not exist and if there are any then check the premise one of them must be wrong...

i was wondering that how it can be???? what about the gray shades of life??? what about the unanswerable questions of the great universe??? is it again a continuum of debate of rationality of "i think therefore i am" and the indian tradition of thinking beyond rationality???

while i wonder and ponder about these question one thing that comes in mind is that ya it is true that contradictions do not exist.. but at the same time there are certain questions where there are no correct answers and then we may get struck...but it is because of the fact that we do not have the answer...where is the contradiction....

i am still pondering....