Course

Book 2. Olympiad Combinatorics Methods

Book 2. Olympiad Combinatorics Methods

  • 1. Advanced Double Counting
  • 2. Inclusion-Exclusion
  • 3. Bijections and Encoding Objects
  • 4. Extremal Principle
  • 5. Invariants II and Monovariants
  • 6. Ramsey-Type Ideas
  • 7. Graphs II
  • 8. Matching and Hall's Theorem Intro
  • 9. Generating Functions I
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Theory Examples Practice Ladders

Chapters

Chapters

Chapter

Advanced Double Counting

This module develops double counting into counting pairs, triples, incidences, intersections, and inequalities through averages.
20 Problems
Theory Examples Practice

Chapter

Inclusion-Exclusion

This module develops inclusion-exclusion for forbidden conditions, derangements, surjections, fixed points, and distributions.
20 Problems
Theory Examples Practice

Chapter

Bijections and Encoding Objects

This module teaches bijective correspondences: subsets and strings, paths and words, compositions and bars, partitions and diagrams, and Catalan-style reflections.
20 Problems
Theory Examples Practice

Chapter

Extremal Principle

The module teaches how to choose a maximal or minimal object: a longest path, a minimal counterexample, a maximal configuration, or an extreme interval. The method is used in graphs, tournaments, set problems, and finite processes.
20 Problems
Theory Examples Practice

Chapter

Invariants II and Monovariants

The module develops invariants beyond the basic level: parity, residues, gcd, product of signs, board colourings, weighted sums, and monovariants for proving termination of processes.
20 Problems
Theory Examples Practice

Chapter

Ramsey-Type Ideas

The module introduces forced-structure ideas: edge colourings, monochromatic triangles, friend-stranger problems, the fact \(R(3,3)=6\), Ramsey recursion, and first multicolour bounds.
20 Problems
Theory Examples Practice

Chapter

Graphs II

The module develops graph methods: degrees, trees, forests, connectedness, cycles, bipartiteness, Euler trails, basic matchings, and planar bounds.
20 Problems
Theory Examples Practice

Chapter

Matching and Hall's Theorem Intro

The module introduces matchings, systems of distinct representatives, Hall's condition, regular bipartite graphs, and augmenting paths.
20 Problems
Theory Examples Practice

Chapter

Generating Functions I

The module introduces generating functions as coefficient language for counting sums, bounded compositions, weighted subsets, partitions, and recurrences.
20 Problems
Theory Examples Practice