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The problems in this book, over 60 together with suggested solutions, are all accessible to students on A-level or Scottish Higher courses. Many can, however, be solved using mathematics covered lower down the school. They are designed to stimulate interest and, we hope, anyone in danger of being bored mathematics will be fascinated by surprisingly simple and elegant solutions to what looks like involved questions - solutions often so short that they will stick in the memory. All of the problems encourage the development of problem solving skills and should "hook" students into hunting for a solution and help to develop a sense of wonder at the power of mathematics.