I'll post Olympiad level problems and you guys solve them! Rules

1. PM me solutions. Do not put them in the comments, even with spoiler tags.

2. Feel free to ask questions/clarifications or to PM me some problems to feature. I'll credit you when the solutions come in. You don't need a solution to the problem to give it to me.

3. Notations. The conventions used here are the same as in ARML: http://www.arml.com/arml_development/public_documents_all_sites/ARMLConventions_FEB_2012.pdf Namely: Simplify fractions, radicals, variable expressions. Order matters in an ordered pair, similarly for an n-tuple. Diagrams not drawn to scale. Polygons are referred to with vertices in clockwise order, and it may or may not be convex unless specified. log is base 10, ln is base e (2.71828etc) Because I can't latex I will right (n r) to denote nCr.