We all love solving new problems :) But I have got this question, how do the problem setters make sure that they are creating a novel problem which did not appear on any judge before. Because If a person has solved a kind of problem before then he will likely to recognize that problem and hence there will be no fun in it.
So how do they check that their problem is unique?
I think googling will not help here as this is more of a "semantic thing" than mere "syntax" and hence there should be some other way?
If someone is writing contest, it means s/he also good experience in competitive programming (such as knowing a lot type of problems etc.). So, author thinks the problem is not used in other contests and googling it for being sure. Also, testers and coordinators of contest are viewing problems (they are really experienced coders), same thing for them.
However, there can be repetition :) That doesn't mean you must downvote author and comment "ugh thats not fair", everyone can make mistakes.