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The title is self-explanatory, but what I'm looking for is a collection of good training problems for middle school students. AoPS is not an option, because I want the problem lists to be free!

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    Is AMO the Australian Mathematical Olympiad? (Only matching acronym at http://en.wikipedia.org/wiki/List_of_mathematics_competitions ). If so, that's for high school students, not middle school, so I am a little confused. Please be more specific about what you are looking for. For Olympiad level problems in general, try http://amc.maa.org/a-activities/a7-problems/problemUSAMO-IMOarchive.shtml and http://www.imomath.com/index.php?mod=232012-08-20

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You could try this... http://cage.ugent.be/~hvernaev/olympiad.html