This work consists of a series of "masterclasses", short sessions of mathematics beyond the standard school syllabus, aimed at 10 to 15-year-olds with a flair for mathematics who want to stretch themselves. The book is aimed to provide teachers with a source of novel and interesting topics to supplement their standard material, and as independent reading for pupils themselves. It will be helpful to teachers who require interesting and novel topics, beyond the standard syllabus and normal textbook material, for capable pupils.