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I want to prepare for the maths olympiad and I was wondering if you can recommend me some books about combinatorics, number theory and geometry at a beginner and intermediate level. I would appreciate your help.

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Problem solving strategy by Engel. Pretty advanced though

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If you're looking for a good Geometry book, you can check out Evan Chen's book, Euclidean Geometry In Mathematical Olympiads. There are no prerequisites to the book; all you need to do is know how to read proofs. A PDF of the book is $28:

http://www.maa.org/press/ebooks/euclidean-geometry-in-mathematical-olympiads

As a sample, here's a free PDF of chapter 2:

http://www.maa.org/sites/default/files/pdf/ebooks/pdf/EGMO_chapter2.pdf

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One of my favorite mathematical olympiad books is this one: https://www.amazon.es/Mathematical-Olympiad-Challenges-Titu-Andreescu/dp/0817645284 by Andreescu and Gelca. It's more on the itermediate level. It is sort of a compilation on useful techniques with sample problems. I suggest you give it a go.

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