ABSTRACT
Many mathematical problems require nothing more sophisticated than searching for a solution. But unless the search is done systematically, the would-be solver is likely to miss the answer or give up trying. In this chapter, thirteen puzzles and a theorem are put to work showing the benefits of systematic search. The reader is asked to find: the best full house in poker; the first odd number in the dictionary; a way to measure 45 seconds with two minute-long fuses; a way to get a big salary without having the right to vote; and all configurations of four points in the plane that determine only two different distances. In one puzzle, together with the theorem, the reader finds the unique way to arrange “seven cities of gold” in such a way that among any three, two are exactly 100 furlongs apart.
