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When I've attended math competition discussions, I've often heard people remark "oh, this is a famous problem" or say that it's similar to one. Most of them I've actually never heard of before. Competition books tend to have a vast list of past problems, and I haven't been able to sift through and tell which ones are supposedly well known and which ones aren't. Contest math isn't especially a priority for me, but it would be nice to at least know of certain problems I should be familiar with.

Could someone give a list of some problems and technique that are part of the "folklore", so to speak? I'm interested in any competition topic, but to narrow the discussion, let's try to emphasize competition problems in calculus/analysis (sequences, series, integrals, etc.)

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closed as too broad by Pete L. Clark, vonbrand, Claude Leibovici, froggie, Sami Ben Romdhane Feb 13 at 7:04

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

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Take several books or collections on problem solving and form the intersection. –  Your Ad Here Feb 12 at 23:27
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Just a suggestion: You may want to be stricter about your restriction to analysis problems. The question is perhaps too broad otherwise. –  Potato Feb 12 at 23:28
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Exactly. Who cares about algebra anyways :-). –  Your Ad Here Feb 12 at 23:29
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See IMO Math. :-) –  Lucian Feb 12 at 23:32