Mathematical Puzzles by Peter Winkler

Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Features

A collection of the world's best mathematical puzzles

Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof

Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.