Mathematics is primarily concerned with problem solving, and there is no better way of gaining an understanding of mathematics than by developing the independent thinking and ability to solve problems (and to set them). The mathematics syllabuses in today's secondary schools contain a wide range of notions and basic facts from various mathematical disciplines. Pupils interested in mathematics should be encouraged to explore the connections between the different topics they encounter, and this book attempts to help in pointing out these connections. By focusing attention on the links between patterns of numbers and shapes, and on between algebraic relations and geometric and combinatorial configurations, the book aims to * motivate deeper study of the concepts related to elementary mathematics * emphasize the importance of the interrelations between mathematical phenomena * foster the interplay of ideas involved in problem solving The material is presented in the form of problems and will prove invaluable and enjoyable for pupils, their teachers, and those studying mathematics or its teaching at university.