Summary: Many readers are familiar with the International Mathematical Olympiad (IMO), a pinnacle in the yearly calendar of mathematics competitions. Here we introduce its cousin in computer science, the International Olympiad in Informatics (IOI). In this paper we take the reader on a brief tour of the IOI, paying particular attention to its relationships with traditional mathematics competitions. We begin in Section 1 with the structure of a typical IOI problem, including an outline of the mathematical ideas that lie behind such problems. For illustration, two problems are worked through in detail in Section 2. In Section 3 we compare the different ways in which mathematics and informatics contests encourage students to think mathematically. Section 4 closes with suggestions for students and teachers who wish to become involved in the IOI.