Reddit reviews Mathematical Olympiad Challenges

Hi, here I will post some great books, some free (by Santos), some not (others).

Junior problem seminar: Santos

Number Theory for Mathematical contests: Santos

The Art and Craft of Problem solving: Zeitz

Problem-Solving Strategies: Engel

Mathematical Olympiad Treasures: Andreescu, Enescu

Mathematical Olympiad challenges: Andreescu, Gelca

Problems from the book: Andreescu

Those are more or less the "general" books, they always contain the main topics of mathematical olympiads, they usually aren't focused on just one topic, for one-topic books see here: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=319&t=405377

Oh wait the red book. I was looking for mathematical olympiad challenges. But here's the source for that answer

A nice pair of books you might like is the two volume set Challenging Mathematical Problems with Elementary Solutions, by Yaglom and Yaglom. Here's the table of contents from volume 1 and the table of contents from volume 2, so you can see what areas the problems are drawn from.

I haven't looked at this book, but noticed it on the site while looking up the details on the above two books: The USSR Olympiad Problem Book. It's from the height of the cold war, when Russia was generally kicking ass in math, so I'd expect it to be pretty good.

Actually, there's about a bazillion books of problems at Dover, most quite affordable, so I'd recommend browsing around that site a bit.

Plenty of problem books have been put together from the International Mathematical Olympiad problems, such as this one. I think you can find most of these problems online if you prefer.

A book less of the "here are problems you can solve!" variety and more of the "here are some neat problems and their solutions!" is 100 Great Problems of Elementary Mathematics: Their History and Solution by Heinrich Dorrie. It covers everything from the Hermite-Lindemann theorem to calculating how to tack into a north wind as quickly as possible. It's just all over the place, which might be something you'd like given your desire for variety. Here's the table of contents.