China has participated in the International Mathematical Olympiad (IMO) 21 times since 1985 and has earned the top country ranking 15 times, including 2008 and 2009, 1997 and 1999-2002 (They did not participate in 1998.) They must be doing something right.

The Preface and Introduction of this book sketch the history of mathematical competitions worldwide, especially the IMO, and illuminate team selection and preparation procedures in China. What follows the front matter is a collection of original problems with solutions that China used to train their Olympiad team in the period 2006–2008. These problems range over the usual topics ― number theory, geometry, combinatorics, inequalities, and functional equations ― and include questions from the 2006 and 2007 China Girls’ Mathematical Olympiad.

The level of these problems is high. Consider this example from the 2007 China National Team Selection Test:

There are 63 points on a circle C with radius 10. Let S be the number of triangles whose sides are longer than 9 and whose vertices are chosen from the 63 points. Find the maximum value of S.

The solution (23,121) takes 5 pages to explain! Try this one from the 2007 China Western Mathematical Olympiad:

Let T = {1, 2, 3, 4, 5, 6, 7, 8}. Find the number of all nonempty subsets A of T such that 3 divides S(A) and 5 does not divide S(A), where S(A) is the sum of all elements of A.

(The reviewer will provide the answer on request.)

This book is a sequel to *Mathematical Olympiad in China*, which covers problems from various Chinese competitions from 2002 to 2006 and includes questions from the 2003-2006 IMOs. The introductory material in the two books is identical.

If you like challenging problems or are involved with preparing students for mathematical competitions, this is a good book to have in your personal collection and in your school library. I also recommend Andy Liu’s problem collections, *Chinese Mathematics Competitions and Olympiads 1981–1993 *and the volume for 1993–2001. For a broader look at Chinese mathematical education, see *How Chinese Learn Mathematics*.

Henry Ricardo (henry@mec.cuny.edu) has retired from Medgar Evers College (CUNY), but continues to serve as Governor of the Metropolitan NY Section of the MAA. He is the author of A Modern Introduction to Differential Equations (Second Edition). His linear algebra text was published in October 2009 by CRC Press.