世界数学奥林匹克经典：组合问题

　　This book consists of three parts： fundamental knowledge， basic methods and typical problems. These three parts introduce the fundamental knowledge of solving combinatorial problems， the important solutions to combinatorial problems and some typical problems with often-used solutions in the high school mathematical competition respectively.In each chapter there are necessary examples and exercises with solutions. These examples and exercises are of the same level of difficulty as the China Mathematical League Competitions which are selected from mathematical competitions at home and abroad in recent years. Some test questions are created by the author himself and a few easy questions in China Mathematical Olympiad （CMO） and IMO are also included. In this book， the author pay attention to leading readers to explore， analyze and summarize the ideas and methods of solving combinatorial problems. The readers' mathematical concepts and abilities will be improved remarkably after acquiring knowledge from this book.

　　作者简介张垚，1938年生，湖南师范大学数学与计算机科学学院教授，中国数学奥林匹克教练，湖南省数学奥林匹克主教练，从1992年起享受国务院政府特殊津贴，曾荣获湖南省优秀教师，全国优秀教师，曾宪梓教育高等师范院校教师奖，湖南省教育委员会科步奖等多项表彰和奖励。1987～1999年任湖南省数学会副理事长兼普及工作委员会主任，负责全省数学竞赛的组织及培训工作，并任长沙市各中学理科班数学竞赛的主教练，还主持了全国1989年初中及1997年高中数学联赛的命题工作。张教授所培训的学生有100余人入全国中学生数学冬令营，其中有40余人入国家集训队，14人入国家队，在国际数学奥林匹克竞赛（IMO）中，共获得10枚金牌和3枚银牌

Introduction
Preface
PART ONE Fundamental Knowledge
Chapter 1 Principles and Formulas of Counting
Exercise 1
Chapter 2 Pigeonhole Principle and Mean Value Principle
Exercise 2
Chapter 3 The Generating Functions
Exercise 3
Chapter 4 Recurrence Sequence of Numbers
Exercise 4
PART TWO Basic Method
Chapter 5 Classification and Method of Fractional Steps
Exercise 5
Chapter 6 Correspondent Method
Exercise 6
Chapter 7 Counting in Two Ways
Exercise 7
Chapter 8 Recurrence Method
Exercise 8
Chapter 9 Coloring Method and Evaluation Method
Exercise 9
Chapter 10 Reduction to Absurdity and the Extreme Principle
Exercise 10
Chapter 11 Local Adjustment Method
Exercise 11
Chapter 12 Construction Method
Exercise 12
PART THREE Typical Problems
Chapter 13 Combinatorial Counting Problems
Exercise 13
Chapter 14 Existence Problems and the Proofs of Inequalities in Combinatorial Problems
Exercise 14
Chapter 15 Combinatorial Extremum Problems
Exercise 15
Solutions to Exercises