- Ch. 1CountingSteps multiply, cases add; divide out repeats, subtract overlaps.
- Ch. 2The Pigeonhole PrincipleMore objects than boxes: some box gets two. The hard part is building the boxes.
- Ch. 3ColoringTrying can't prove “impossible”. Color the squares, count, and one sentence can.
- Ch. 4Operations and GamesLook for what never changes or only goes down; solve games from the end.
- Ch. 5Extremal Problems in CombinatoricsA max needs two answers: a construction that reaches it, a proof of no more.