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Bin Xiong - Mathematical Olympiad in China (2009-2010)

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Bin Xiong Mathematical Olympiad in China (2009-2010)
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The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002 2008 appear in an earlier volume, Mathematical Olympiad in China.

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Mathematical Olympiad Series

ISSN: 1793-8570

Series Editors: Lee Peng Yee (Nanyang Technological University, Singapore) Xiong Bin (East China Normal University, China)


Published

Vol.

A First Step to Mathematical Olympiad Problems
by Derek Holton (University of Otago, New Zealand)

Vol.

Problems of Number Theory in Mathematical Competitions
by Yu Hong-Bing (Suzhou University, China)
translated by Lin Lei (East China Normal University, China)

Vol.

Graph Theory
by Xiong Bin (East China Normal University, China) &
Zheng Zhongyi (High School Attached to Fudan University, China)
translated by Liu Ruifang, Zhai Mingqing & Lin Yuanqing
(East China Normal University, China)

Vol.

Combinatorial Problems in Mathematical Competitions
by Yao Zhang (Hunan Normal University, P. R. China)

Vol.

Selected Problems of the Vietnamese Olympiad (19622009)
by Le Hai Chau (Ministry of Education and Training, Vietnam)
& Le Hai Khoi (Nanyang Technology University, Singapore)

Vol.

Lecture Notes on Mathematical Olympiad Courses:
For Junior Section (In 2 Volumes)
by Xu Jiagu

Vol.

A Second Step to Mathematical Olympiad Problems
by Derek Holton (University of Otago, New Zealand &
University of Melbourne, Australia)

Vol.

Lecture Notes on Mathematical Olympiad Courses:
For Senior Section (In 2 Volumes)
by Xu Jiagu

Vol.

Mathemaitcal Olympiad in China (20092010)
edited by Bin Xiong (East China Normal University, China) &
Peng Yee Lee (Nanyang Technological University, Singapore)

Published by World Scientific Publishing Co Pte Ltd 5 Toh Tuck Link - photo 1

Published by

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 Olympiad SeriesVol.
MATHEMATICAL OLYMPIAD IN CHINA (20092010)
Problems and Solutions

Copyright 2013 by 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 permission from 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 978-981-4390-21-7 (pbk)

Printed in Singapore by World Scientific Printers.

Editors

XIONG Bin East China Normal University, China

Lee Peng Yee Nanyang Technological University

Original Authors

MO Chinese National Coaches of

2009 2010

English Translators

XIONG Bin East China Normal University, China

FENG Zhigang Shanghai High School, China

WANG Shanping East China Normal University, China

Yao Yijun Fudan University, China

Qu Zhenhua East China Normal University, China

Copy Editors

NI Ming East China Normal University press, China

ZHANG Ji World Scientific Publishing Co., Singapore

WONG Fook Sung Temasek Polytechnic , Singapore

KONG Lingzhi East China Normal University press, China

Preface

The first time China participate in IMO was in 1985, two students were sent to the 26th IMO. Since 1986, China has a team of 6 students at every IMO except in 1998 when it was held in Taiwan. So far, up to 2011, China has achieved the number one ranking in team effort 17 times. A great majority of students received gold medals. The fact that China obtained 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 education system in China, in particular, the emphasis on training of basic skills in science education.

The materials of this book come from a series of two books (in Chinese) on Forward to IMO: a collection of mathematical Olympiad problems (2009 2010). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed. First, there is the China Mathematical Competition, a national event. It is held on the second Sunday of October every year. Through the competition, about 200 students are selected to join the China Mathematical Olympiad (commonly known as the winter camp), or in short CMO, in the next January. CMO lasts for five days. Both the type and the difficulty of the problems match those of IMO. Similarly, students are given three problems to solve in 4. 5 hours each day. From CMO, about 50 to 60 students are selected to form a national training team. The training takes place for two weeks in the month of March. After four to six tests, plus two qualifying examinations, six students are finally selected to form the national team, taking part in IMO in July of that year.

In view of the differences in education, culture and economy of western part of China in comparison with the coast part in east China, mathematical competitions in West China did not develop as fast as in the rest of the country. In order to promote the activity of mathematical competition, and to enhence the level of mathematical competition, starting from 2001, China Mathematical Olympiad Committee organizes the China Western Mathematical Olympiad. The top two winners will be admitted to the national training team. Through the CWMO, there have been two students entering the national team and receiving gold medals for their performance at IMO.

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