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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 .

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  • $\begingroup$ Perhaps standard textbooks on Discrete Mathematics might meet your requirements. They tend to include basics of mathematical proof, combinatorics, graph theory, logic, etc. $\endgroup$ – Manan Aug 6 '20 at 10:22
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    $\begingroup$ Maybe this helps,Principles and Techniques in Combinatorics $\endgroup$ – Baba Yaga Aug 6 '20 at 16:03
  • $\begingroup$ Thank You @arjun .I will start this book. Thank you so much . $\endgroup$ – Sunaina Pati Aug 6 '20 at 16:55
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    $\begingroup$ 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 $\endgroup$ – Baba Yaga Aug 6 '20 at 17:02
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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.

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  • $\begingroup$ Thanks , I will go through this book ! $\endgroup$ – Sunaina Pati Aug 6 '20 at 16:54
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Here is a list of books for perfect olympiad combinatorics preparation.

For general study:

(1) A Path to Combinatorics for Undergraduates

(2) Principles and Techniques in Combinatorics

(3) Problem-Solving Methods in Combinatorics: An Approach to Olympiad Problems

For practising problem-solving:

(1) 102 Combinatorial Problems

(2) Combinatorics: A Problem-Based Approach

(3) The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition

For Olympiad Graph theory:

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

(1) Graph Theory: In Mathematical Olympiad And Competitions

(2) IMO Training 2008: Graph Theory

For probabilistic methods in olympiad combinatorics:

(1) Expected uses of probability

(2) Unexpected uses of probability

For generating functions and recurrence relations:

Generatingfunctionology

For combinatorial inequality type problems:

Combinatorial Extremization

For various advanced techniques:

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!

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    $\begingroup$ OMG!! thank you so much.. this will really help me. $\endgroup$ – Sunaina Pati Aug 7 '20 at 10:00
  • $\begingroup$ @Shubhangi you're most welcome 😊 $\endgroup$ – Shubhrajit Bhattacharya Aug 7 '20 at 10:01
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    $\begingroup$ @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. $\endgroup$ – Shubhrajit Bhattacharya Aug 8 '20 at 16:25
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I think Olympiad combinatorics book, by Pranav A. Sriram will help you much

https://artofproblemsolving.com/community/c6h601134

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    $\begingroup$ that is really hard !! I tried reading the first chapter , and realised that is was very hard . Not that it is not beautiful but just very above my level . Perhaps, I will make my basics strong and use this for further training . Thanks. $\endgroup$ – Sunaina Pati Aug 6 '20 at 16:54
  • $\begingroup$ But it will make you wining EGMO and... Did India participated on EGMO this year? $\endgroup$ – Aqua Aug 6 '20 at 18:28
  • $\begingroup$ thank you so much !! I will surely read ! Yes , India participated in EGMO . However, India never got a gold medal in EGMO. $\endgroup$ – Sunaina Pati Aug 7 '20 at 1:52

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