ABSTRACT
Sometimes a problem can be solved only by trying out ideas and modifying them until a solution is reached. In this chapter, twenty-two puzzles of this kind ask the reader to get three couples across a river, lay out sprinklers in a field, make a fair decision with a bent coin, find the number missing from a list, cover boards with dominoes, detect visits to a room, escape from a vicious dog, design a worm-free bedroom, win a dice game, share a pizza, and help prisoners find their names in boxes. The chapter ends with a marvelous tool called “Pick's Theorem” concerning “lattice polygons” whose vertices are points on a plane grid. The theorem says that the area of any such polygon can be computed by adding the number of internal grid points to half the number of grid points on the boundary, and then subtracting one.
