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In short — you can try, but there is no great way to do it.

The most useful approach is to just give the problem to friends who are very experienced — see if someone has seen it before. Another thing is stripping any story and trying to formulate the problem in a few words — then attempting to look for it online, but that'll rarely work.

The truth is that as time goes by and the amount of competitions just keeps increasing, it's inevitable to repeat problems. It's unpleasant but there's little you can do about it.

Testers and a coordinator will sometimes tell you that this is well known, and also you can google a concise statement or some related terms. If something looks simple (in terms of statement), I usually don't use it (the con is that I can throw away a nice short problem), or first ask several experienced people if they saw something like that.

The point to realize is that it is okay to repeat problems. We are not doing research here, and it is not a competition on how you can solve novel problems. Rather it is a sport about how fast one can construct ideas, associate it to well defined algorithms and code cleanly and efficiently to avoid bugs. So its okay to repeat problems, just dont make it that obvious that its easily googleale. For that you can break down your problem into formal statements and try to google if its already easily search.