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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, user63181 Feb 13 '14 at 7:04

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Take several books or collections on problem solving and form the intersection. $\endgroup$ – J.R. Feb 12 '14 at 23:27
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    $\begingroup$ Just a suggestion: You may want to be stricter about your restriction to analysis problems. The question is perhaps too broad otherwise. $\endgroup$ – Potato Feb 12 '14 at 23:28
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    $\begingroup$ Exactly. Who cares about algebra anyways :-). $\endgroup$ – J.R. Feb 12 '14 at 23:29
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    $\begingroup$ See IMO Math. :-) $\endgroup$ – Lucian Feb 12 '14 at 23:32