Problems versus exercises -- Strategies and tactics -- The problem solver's mind-set -- Searching for patterns -- Closing the deal, proofs and tools -- Pictures, recasting, and points of view -- The great simplifier, parity -- The great unifier, symmetry -- Symmetry wins games -- Contemplate extreme values -- The culture of problem solving -- Recasting integers geometrically.
Recasting integers with counting and series Things in categories, the pigeonhole tactic -- The greatest unifier of all, invariants -- Squarer is better, optimizing 3s and 2s -- Using physical intuition, and imagination -- Geometry and the transformation tactic -- Building from simple to complex with induction -- Induction on a grand scale -- Recasting numbers as polynomials, weird dice -- A relentless tactic solves a very hard problem -- Genius and Conway's infinite checkers frontier -- How versus why, the final frontier.
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