SMO Junior · 12. Logic, games and the pigeonhole principle
Case analysis for logic puzzles, the pigeonhole principle with sharp examples, extremal arrangements, and invariants for processes and games.
Solve truth-teller/liar and matching puzzles by complete case analysis.
Apply the pigeonhole principle with well-chosen boxes and show sharpness.
Find maximal arrangements by combining an upper bound with a construction.
Use invariants and colourings to analyse processes and games.
Write a complete 'impossibility' proof.