Course

Book 1. Foundations of Olympiad Combinatorics

Book 1. Foundations of Olympiad Combinatorics

  • 1. Counting Principles
  • 2. Permutations and Arrangements
  • 3. Combinations
  • 4. Counting in Two Ways
  • 5. Pigeonhole Principle I
  • 6. Invariants I
  • 7. Coloring and Board Problems
  • 8. Games and Strategies I
  • 9. Graphs I
  • 10. Recursion and Sequences
  • 11. Mixed Problems I
  • 12. Mock Olympiads I
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Theory Examples Practice Ladders

Chapters

Chapters

Chapter

Counting Principles

The module introduces olympiad counting through order of choice, the sum rule, the product rule, casework, complement counting, and first overcounting traps.
24 Problems
Theory Examples Practice

Chapter

Permutations and Arrangements

The module develops permutations, arrangements, repeated objects, circular seating, blocks, adjacency restrictions, and first inclusion-exclusion problems.
24 Problems
Theory Examples Practice

Chapter

Combinations

The module teaches unordered selection, complement counting, position choices, basic identity proofs, and first nonconsecutive-selection problems.
24 Problems
Theory Examples Practice

Chapter

Counting in Two Ways

The module introduces double counting as a method: pairs, incidences, degree sums, average arguments, subset identities, and first bounds.
24 Problems
Theory Examples Practice

Chapter

Pigeonhole Principle I

The module develops the simple and strengthened pigeonhole principle: residues, pairs, intervals, geometric partitions, partial sums, subset sums, and first Ramsey/Erdos-Szekeres ideas.
24 Problems
Theory Examples Practice

Chapter

Invariants I

The module introduces invariants through parity, sums, residues, coloring, sign products, coordinate invariants, and inversion parity.
24 Problems
Theory Examples Practice

Chapter

Coloring and Board Problems

The module teaches board colorings for impossibility proofs, necessary cell positions, and analysis of piece moves.
24 Problems
Theory Examples Practice

Chapter

Games and Strategies I

The module introduces winning and losing positions, residue strategies, symmetry, pairing, fixed game length, and first nim ideas.
24 Problems
Theory Examples Practice

Chapter

Graphs I

The module introduces vertices, edges, degrees, the handshaking formula, connectedness, trees, cycles, bipartite graphs, and first extremal arguments.
24 Problems
Theory Examples Practice

Chapter

Recursion and Sequences

The module teaches recurrences by last step, last tile, last symbol, and last point of a path, and introduces extra states.
24 Problems
Theory Examples Practice

Chapter

Mixed Problems I

The module trains method selection without topic hints: counting, pigeonhole, invariants, colorings, games, graphs, paths, and recurrences.
24 Problems
Theory Examples Practice

Chapter

Mock Olympiads I

The module contains six mini-sets of four problems for training method choice and solution writing.
24 Problems
Theory Examples Practice