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The source of the material contained in this book is the column ‘Student Problems’ which began in 1992 in the Mathematical Gazette. The book contains the 57 problems that have been used, all with full solutions and many with alternatives. It also includes the names of the many students who successfully tackled any of the problems. The editor of the book is extremely grateful to Tim Cross who saw the need for such an enterprise and has operated it since it started. This gratitude related to his work over the ten years as well as for his assistance with the book itself. Credit and thanks must also be given to Dr Geoff Smith of the University of Bath and to Professor Adam McBride of the University of Strathclyde. Both are heavily involved in the UK Olympiad preparation and without their valuable assistance the book would not have achieved such a high standard.