By Andrew Jobbings. This book includes all 500 problems from the twenty Intermediate Mathematical Challenge papers set by the UKMT between 1997 and 2016. The problems—which are not given as multiple-choice questions—have been grouped together in two ways: by difficulty; and by topic. The answer to every problem in the book is included. Also,nearly every problem has a remark of some sort. Each remark is not intended to be a ‘full written solution’, but sketches one method, providing a sequence of pointers so that, hopefully, the reader is then able to go on and solve the problem. The Challenges series is aimed at students at secondary school who are interested in tackling stimulating problems, such as those posed in the Mathematical Challenges administered by the UKMT and similar organisations.