...which leaves algebra. With the constraint that according to my preference a problem-oriented textbook should contain solutions, would people say that the relevant chapters in Engel's Problem Solving Strategies and in Andreescu's Maths Olympiad Challenges are sufficient (plus loads of actual problems of course, but they're easy to find) for the IMO?
I know there are many books and other sources from various countries which cover areas treated in IMO-y algebra (inequalities, functional equations, etc.) well in places. But I like to keep my number of textbooks down to a small number of outstanding ones, and they must have solutions. (So where algebra is concerned, this rules out the text by Naoki Sato for example!)
owlie