# Book recommendation : Olympiad Combinatorics book

Can anyone recommend me an olympiad style combinatorics book which is suitable for a high schooler ? I know only some basics like Pigeon hole principle and stars and bars . I hope to find a book which contains problems which purely test our originality ( the problems with beautiful constructions like USAMO 2017 -TSTST P2: Which words can Ana pick?, Nim problems, games,tillings, etc ) . More specifically problems which doesn't require theory but requires out of the box thinking .

I don't know much about recurrence relations, generating functions or graph theory, so I would also love to see a book which introduces these topics .

• Perhaps standard textbooks on Discrete Mathematics might meet your requirements. They tend to include basics of mathematical proof, combinatorics, graph theory, logic, etc. Aug 6, 2020 at 10:22
• Maybe this helps,Principles and Techniques in Combinatorics Aug 6, 2020 at 16:03
• Thank You @arjun .I will start this book. Thank you so much . Aug 6, 2020 at 16:55
• I knew it will be a good idea to share this one, the books in the answers are among the best but out of league for High school students. Good luck with it Aug 6, 2020 at 17:02

Here is a list of books for perfect olympiad combinatorics preparation.

For general study:

For practising problem-solving:

Olympiad uses of graph theory is a bit different from formal graph theory taught in university courses. The best book for this is

For probabilistic methods in olympiad combinatorics:

For generating functions and recurrence relations:

Generatingfunctionology

For combinatorial inequality type problems:

Combinatorial Extremization

Extremal Combinatorics

For elementary combinatorial problems with geometric flavour:

Elementary Combinatorial Geometry

For ultimate problem solving (hard):

Problems from the Book

Pranav A. Sriram's book contains more than enough higher combinatorics contents which are only needed to tackle notoriously difficult (but not so elegant) Chinese TST problems. But what I have listed is enough for achieving success in EGMO or even in IMO!

Happy Problem Solving!

• OMG!! thank you so much.. this will really help me. Aug 7, 2020 at 10:00
• @Shubhangi I have added two books. In one of them, named Elementary Combinatorial Geometry, you can find problems involving tilings, colourings and more combinatorial olympiad problems with a geometric flavour. Also, there is a section where you can find techniques to apply the pigeonhole principle to solve combinatorial problems with a geometric flavour. Aug 8, 2020 at 16:25

One possibility is Problem-Solving Methods in Combinatorics: An Approach to Olympiad Problems by Pablo Soberon. As the title says, it's intended to prepare the student for Olympiad problems, and the author won a gold medal in the International Mathematical Olympiad. Some of the exercises in the book are drawn from recent Olympiads.

Coverage includes the pigeonhole principle, graph theory, generating functions, and partitions.

• Thanks , I will go through this book ! Aug 6, 2020 at 16:54