Tony Gardiner's text contains the problems from the U. K. Junior Mathematical Olympiads from the years 1989 - 1994 and sixty additional problems that were considered for the competitions. The problems, which are meant to be done without a calculator, are difficult. They draw upon number sense, estimation, algebra, geometry, trigonometry, and combinatorics. Since these are Olympiad problems, you should work through Gardiner's Mathematical Challenge first. Unless you can handle most of those problems with ease, you will find working through this text frustrating. With the exception of the experimental test given in 1989, which consists of 13 open-ended problems, the tests have two sections. Section A contains 10 problems for which a numerical answer is sought. Section B contains six open-ended problems in which the answer must be justified with some sort of proof. Of the sixty additional problems, forty are Section A problems and the remainder are Section B problems. Answers are provided to all the section A problems. In addition, Gardiner includes sections containing hints and outline solutions for the problems that appeared in the actual competitions. There are no answers, outline solutions, or even hints for the additional Section B problems. The hints Gardiner provides suggest how to approach a problem. The outline solutions allow the reader to complete the solution to a problem by filling in the blanks. Since complete solutions are rarely given, it is difficult to fully check your answers to the section B problems. However, Gardiner provides sufficient feedback for you to determine if you are approaching a problem correctly. Working through this text is an excellent way to prepare for middle or high school mathematics contests.
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