Combinatorics
Combinatorics
Lecture notes on Combinatorics (for Math Olympiad — IOQM, RMO, INMO)
- Warm up
- Coloring proofs
- Auxiliary configuration
- Induction
- Inclusion-exclusion principle
- Invariance principle
- Pigeonhole principle
- Extremal principle
- Arrange in order
- Grouping in pairs
- Counting
- Counting via bijections
- Counting the complement
- Counting in two different ways
- Generating functions
Problem sets by Amit Kumar Mallik from INMOTC 2025, MP region
References/Resources
- Olympiad Training Materials from IMOmath
- Mathematical circles (Russian experience) by Fomin, Genkin, Itenberg.
- Problem-solving methods in combinatorics by Pablo Soberón, who received a Gold medal in IMO 2006.
- Problem-solving strategies by Engel.
- OTIS Excerpts by Evan Chen.
- Olympiad Combinatorics, by Pranav A. Sriram. Its chapters are available in posts #1, #11, #49 of this page. There is a forum for solutions of the problems which are not in the contest collections but from this book.
- A video by Zlatko Salko Lagumdžija.
These notes may be useful
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to the students who would like to have a look at some of the past RMO problems, in order to have an idea of the notions/topics involved, and/or to have a glimpse before getting started, or just curious about it.
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to the students, who would like to prepare and would like to have the relevant questions organized across the topics and sub-topics.