Foreword 1. Jugs and Stamps: How To Solve Problems 1.1.Introduction 1.2.A Drinking Problem 1.3.About Solving Problems 1.4.Rethinking Drinking 1.5.Summing It Up 1.6.Licking a Stamp Problem 1.7.A Little Explanation 1.8.Tidying Up 1.9.Generalise 1.10.In Conclusion 1.11.Epilogue 1.12.Solutions 2.Combinatorics I 2.1.Introduction 2.2.What is Combinatorics? 2.3.The Pigeonhole Principle 2.4.Counting without Counting 2.5.A Sigma Aside 2.6.Solutions 3.Graph Theory 3.1.Introduction 3.2.K?nigsberg 3.3.So What is a Graph? 3.4.Ramsey 3.5.Euler Tours (Revisited) 3.6.Knight's Tours 3.7.Hamilton 3.8.Trees 3.9.Planarity 3.10.The Four Colour Theorem 3.11.Some Additional Problems 3.12. Solutions 4.Number Theory 1 4.1.What is It? 4.2.Divisibility by Small Numbers 4.3.Common Factors 4.4.Fermat's Little Theorem 4.5.A.P.'s 4.6.Some More Problems 4.7.Solutions 5.Geometry 1 5.1.Introduction 5.2.Squares 5.3.Rectangles and Parallelograms 5.4.Triangles 5.5.Circles 5.6.Solutions 6.Proof
6.1.Introduction 6.2.Why Proof? 6.3.Proof by Contradiction 6.4.Mathematical Induction 6.5.Conclusion 6.6.Solutions 7.Geometry 2 7.1.Cartesian Geometry 7.2.Lines 7.3.Modulus 7.4.Loci: One Fixed Point 7.5.The Cosine Rule 7.6.Loci: Two Points 7.7.Conics 7.8.Solutions 8.Some IMO Problems 8.1.Introduction 8.2.What is the IMO? 8.3.PHIL 1 8.4.MON 1 8.5.MON 6 8.6.UNK 2 8.7.Hints - PHIL 1 8.8.Hints - MON 1 8.9.Hints - MON 6 8.10.Hints - UNK 2 8.11.Solutions Index
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