Part 1. Disc 1. Lecture 1. Problems versus exercises -- Lecture 2. Strategies and tactics -- Lecture 3. Problem solver's mind-set -- Lecture 4. Searching for patterns -- Lecture 5. Closing the deal, proofs and tools -- Lecture 6. Pictures, recasting, and points of view -- Disc 2. Lecture 7. Great simplifier, parity -- Lecture 8. Great unifier, symmetry -- Lecture 9. Symmetry wins games -- Lecture 10. Contemplate extreme values -- Lecture 11. Culture of problem solving -- Lecture 12. Recasting integers geometrically.

Part 2. Disc 3. Lecture 13. Recasting integers with counting and series Lecture 14. Things in categories, the pigeonhole tactic -- Lecture 15. Greatest unifier of all, invariants -- Lecture 16. Squarer is better, optimizing 3s and 2s -- Lecture 17. Using physical intuition, and imagination -- Lecture 18. Geometry and the transformation tactic -- Disc 4. Lecture 19. Building from simple to complex with induction -- Lecture 20. Induction on a grand scale -- Lecture 21. Recasting numbers as polynomials, weird dice -- Lecture 22. A relentless tactic solves a very hard problem -- Lecture 23. Genius and Conway's infinite checkers frontier -- Lecture 24. How versus why, the final frontier.