Introduction to Combinatorics

By Gerry Leversha and Dominic Rowland. The subject of combinatorics provides a rich source of material for mathematics competitions. At one level it can be thought of as a sort of extreme counting—how do we enumerate the number of ways of different ways of doing something? However, the subject is broader than that. It addresses situations which involve organising things so as to satisfy certain criteria—placing tiles on a chessboard, seating people in a circle, chopping up a cube—and then asks whether or not a certain outcome is possible. This accessible text aims to give the enthusiastic student plenty of tips on how to tackle questions of this nature. The structure of this book is, as befits the subject, problem-based. Each chapter proceeds through a series of challenges which introduce the important ideas slowly and carefully.In particular, we have tried to show how to tackle each problem from first principles but building on previously acquired knowledge and technique.