Puzzles can be used to discover mathematics, and to illuminate, motivate, and teach it. Paradoxes perplex and sometimes force foundational philosophical changes. In those contexts we'll consider Zeno's paradoxes of motion, the Tower of Hanoi (its "legend" is fraud); SET, Sudoku, the Bridges of Konigsburg, the Banach-Tarski paradox, Arrow's Theorem, Godel's Theorem, and puzzles created by Zeno, Archimedes, Fibonacci, Lewis Carroll, Sam Loyd, E. Rubik, Martin Gardner, Raymond Smullyan, Stewart Coffin, and John H. Conway.