文档介绍：Math Problem Book I
compiled by
Kin Y. Li
Hong Kong Mathematical Society
International Mathematical Olympiad
Hong mittee
(Supported by the Quality Education Fund)
Math Problem Bo ok I
c ompile dby
Kin Y. Li
Dep artment of Mathematics
Hong Kong University of Scienc e and T e chnolo gy
c
Cop yrigh t
2001 Hong Kong Mathematical So ciet y IMO(HK) Committee.
Prin ted in Hong Kong
Preface
There are o v er ft y coun tries in the w orld no w ada ys that hold math-
ematical olympiads at the secondary sc ho ol lev el ann ually . In Hungary ,
Russia and Romania, p etitions ha v e a long history , dat-
ing bac k to the late 1800's in Hungary's case. Man y professional or ama-
teur mathematici ans dev elop ed their in terest in math b yw orking on these
olympiad problems in their y ouths and some in their adultho o ds as w ell.
The problems in this b o ok came from man y sources. F or those in v olv ed
in in ternational p etitions, they no doubt will recognize man yof
these problems. W e tried to iden tify the sources whenev er p ossible, but
there are still some that escap e us at the momen t. Hop efully , in future
editions of the b o ok w e can ll in these missing sources with the help of the
kno wledgeable readers.
This b o ok is for studen ts who ha v e creativ e minds and are in terested in
mathematics . Through problem solving, they will learn a great deal more
than sc ho ol curricula can o er and will sharp en their analytical skills. W e
hop e the problems collected in this b o ok will stim ulate them and seduce
them to deep er understanding of what mathematic s is all ab out. W e hop e
the in ternational m unities supp ort our e orts for using these bril-
lian t problems and solutions to attract our y oung studen ts to mathematics .
Most of the problems ha v e b een used in practice sessions for studen ts
participated in the Hong Kong IMO training program. W e are esp eciall y