The International Mathematical Olympiad (IMO), the oldest of the International Science Olympiads, is an annual contest for pre-college students. China has taken first place most of the last ten years. The author is one of the “senior coaches of China's IMO National Team” and this text is nominally a training tool. The reader does not require an IMO future to find this book useful. It is an introductory probability text that can serve as an adjunct to a more detailed text, or a collection of classroom capsules also touching on algebra, number theory, combinatorics, graph theory, and geometry.
Sixty-five short chapters make up the main content. At least to Western readers, this collection of probability problems, nicely arranged in increasing difficulty, has an exotic flavor. Inspiration and sources often come from Chinese culture: oral history and opera, legend and literature. Even Chinese dice play leads to problem setups not seen in a typical Western text. Typical card choosing setups are augmented with problems from bridge. These and more mainstream topics in introductory probability are given concise, even elegant, development, often exploring multiple approaches.
This being aimed at advanced — or at least ambitious — pre-college students, the content enters into the college level. The Bayesian coverage is as complete and effective an introduction as I have seen in any first-year college text. The biggest obstacle appears to have arisen from translation into English without sufficient follow-up editing. By my reckoning, about ten percent of the pages have grammatically difficult sentences, such as “Who is more possible to gamble away?” That same cause I am sure explains why instead of the notation \(C_k^n\) there is the form \(C_n^k\), standard in Chinese texts.
Among the numerous problems explored are single elimination competition, binomial distribution, the birthday problem, induction, derangements, balls into drawers considering distinguishable and indistinguishable scenarios (“called the pot problem”), Buffon's needle, expected value, de Méré's Problem, and more. Often, particular solutions are building blocks to general solutions for one, then two variables. 107 exercises and their answers augment and conclude this varied gallery of probability problems.
Tom Schulte is a software architect at SaaS ERP provider Plex Systems in Troy, Michigan.