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All four problems are based on the operation of subtraction, the computation of differences. A practical scenario is the measurement of length. Suppose we align a marked ruler against a line segment. If the left endpoint corresponds to the marking of 3 cm
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Kseniya Garaschuk Andy Liu
Grade Five Competition from the Leningrad Mathematical Olympiad 1979–1992
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA
More information about this series at http://www.springer.com/series/714
Kseniya Garaschuk • Andy Liu
Grade Five Competition from the Leningrad Mathematical Olympiad 1979–1992
Kseniya Garaschuk Department of Mathematics and Statistics University of the Fraser Valley Abbotsford, BC, Canada
Andy Liu Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, Canada
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-030-52945-1 ISBN 978-3-030-52946-8 (eBook) https://doi.org/10.1007/978-3-030-52946-8 Mathematics Subject Classification (2020): 00A07, 00A09, 97-XX © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface The Leningrad Mathematical Olympiad was the oldest mathematics competition in the former Soviet Union. It began in the spring of 1934, predating the Tbilisi Mathematical Olympiad by a few months and the Moscow Mathematical Olympiad by one year. It was organized as a three-stage contest. The first (School level) round was quite informal and often the teachers skipped the selection, simply telling the willing students they should go and take part in the second round. However, the teachers were supplied with the lists of training and selection problems distributed by the local district instructors. The second (District level) round was a regular formal writt
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