Math Problem Book I

There are over fty countries in the world nowadays that hold math
ematical olympiads at the secondary school level annually. In Hungary,
Russia and Romania, mathematical competitions have a long history, dat
ing back to the late 1800’s in Hungary’s case. Many professional or ama
teur mathematicians developed their interest in math byworking on these
olympiad problems in their youths and some in their adulthoods as well.
The problems in this book camefrom many sources. For those involved
in international math competitions, they no doubt will recognize manyof
these problems. We tried to identify the sources whenever possible, but
there are still some that escape us at the moment. Hopefully, in future
editions of the book we can ll in these missing sources with the help of the
knowledgeable readers.
This book is for students who have creative minds and are interested in
mathematics. Through problem solving, they will learn a great deal more
than school curricula can o er and will sharpen their analytical skills. We
hope the problems collected in this book will stimulate them and seduce
them to deeper understanding of what mathematics is all about. We hope
the international math communities support our e orts for using these bril
liant problems and solutions to attract our young students to mathematics.
Most of the problems have been used in practice sessions for students
participated in the Hong Kong IMO training program. We are especially
pleased with the e orts of these students. In fact, the original motivation
for writing the book was to reward them in someways, especiallythose who
worked so hard to become reserve or team members. It is only tting to
list their names along with their solutions. Again there are unsung heros
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who contributed solutions, but whose names we can only hope to identify
in future editions.
As the title of the book suggest, this is a problem book. So very little
introduction materials can be found. We do promise to write another book
presenting the materials covered in the Hong Kong IMO training program.
This, for certain, will involve the dedication of more than one person. Also,
this is the rst of a series of problem books we hope. From the results of
the Hong Kong IMO preliminary contests, we can see waves of new creative
minds appear in the training program continuously and they are younger
and younger. Maybe the next problem book in the series will be written by
our students.
Finally,wewould like to express deep gratitude to the Hong Kong
Quality Education Fund, which provided the support that made this book
possible.