This book is the essential companion to the authors' earlier book Counting (World Scientific, 2002), an introduction to combinatorics for junior college students. It provides supplementary material both for the purpose of adding to the reader's knowledge about counting techniques and, in particular, for use as a textbook for junior college students and teachers in combinatorics at H3 level in the new Singapore mathematics curriculum for junior college. The emphasis in combinatorics within the syllabus is to hone basic skills and techniques in general problem solving and logical thinking. The book also gives solutions to the exercises in Counting. There is often more than one method to solve a particular problem and the authors have included alternative solutions whenever they are of interest.

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This book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.

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