Mathematical olympiad in china

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in China
Problems and Solutions


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Mathematical Olympiad
in China
Problems and Solutions


East China Normal University, China

Xiong Bin

Nanyang Technological University, Singapore

Lee Peng Yee

East China Normal University Press

World Scientific

Published by East China Normal University Press 3663North Zhongshan Road Shanghai 200062 China and World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

MATHEMATICAL OLYMPIADIN CHINA Problems and Solutions Copyright © 2007 by East China Normal University Press and World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permissionfrom the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978-981-270-789-5 (pbk) ISBN-10 981-270-789-1 (pbk)

Printed in Singapore.

XIONG Bin East China ~ o r m a lUniversity,China LEE Peng Yee Nanpng Technological University, Singapore

Original Authors MO Chinese National Coaches Team of 2003 - 2006 English Translators XIONG Bin East China N O ~ T T UUniversity, China Z~
FENG Zhigang shanghai High School, China MA Guoxuan h s t China Normal University, China LIN Lei East China ~ormalUniversity, China WANG Shanping East China Normal university, China Z m N G ZhongyiHigh School Affiliated to Fudan University, China HA0 Lili Shanghai @baa Senior High School, China WEE Khangping Nanpng Technological University, singupore

Copy Editors

NI Ming

m t China N



Universitypress, China Z

Z M G Ji World Scientific Publishing GI. Singapore , xu Jin h s t China Normal Universitypress, China


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PrefaceThe first time China sent a team to IMO was in 1985. A that time, two t students were sent to take part in the 26th IMO. Since 1986, China has always sent a team of 6 students to IMO except in 1998 when it was held in %wan. So far (up to 2006) , China has achieved the number one ranking in team effort for 13 times. A great majority of students have received gold medals. The fact that Chinaachieved such encouraging result is due to, on one hand, Chinese students’ hard working and perseverance, and on the other hand, the effort of teachers in schools and the training offered by national coaches. As we believe, it is also a result of the educational system in China, in particular, the emphasis on training of basic skills in science education. The materials of this book come from a series offour books (in Chinese) on Forurzrd to IMO: a collection of mathematical Olympiad problems (2003 - 2006). It is a collection of problems and solutions of the major mathematical competitions in China, which provides a glimpse on how the China national team is selected and formed. First, it is the China Mathematical Competition, a national event, which is held on the second Sunday of October everyyear. Through the competition, about 120 students are selected to join the China Mathematical Olympiad (commonly known as the Winter Camp) , or in short CMO, in January of the second year. CMO lasts for five days. Both the type and the difficulty of the problems match those of IMO. Similarly, they solve three problems every day in four and half hours. From CMO, about 20 to 30 students are...
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