The Moscow Puzzles: 359 Mathematical Recreations

Translated by ALBERT PARR Y, Professor Emeritus of Russian Civilization and Language Colgate University The Moscow Puzzles 359 Mathematical Recreations BORIS A. KORDEMSKY Edited and with an introduction by MARTIN GARDNER, Editor of the Mathematical Games Department, SCIENTIFIC AMERICAN CHARLES SCRIBNER'S SONS/ NEW YORK Copyright © 1972 Charles Scribner's Sons Some of the puzzles appeared IlIst in Horizon. Copyright © 1971 Charles Scribner's Sons. This book published simultaneously in the United States of America and in Canada Copyright under the Berne Convention AU rights reserved. No part of this book may be reproduced in any form without the permission of Charles Scribner's Sons. 35791113151719 VIP 2018161412108642 Printed in the United States of America Library of Congress Catalog Card Number 74-16277 0 ISBN 0-684-14870-6 Contents I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. Introduction vii Amusing Problems 1 Difficult Problems 31 Geometry with Matches 50 Measure Seven Times Before You Cut 59 Skill Will Find Its Application Everywhere 69 Dominoes and Dice 82 Properties of Nine 91 With Algebra and without It 95 Mathematics with Almost No Calculations 109 Mathematical Games and Tricks 120 Divisibility 135 143 Cross Sums and Magic Squares 157 Numbers Curious and Serious 173 Numbers Ancient but Eternally Young Answers 185 Index 303 Introduction The book now in the reader's hands is the first English translation of Mathematical Know-how, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions, as well as translations from the original Russian into Ukranian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold. Outside the U.S.S.R. the book has been published in Bulgaria, Rumania, Hungary, Czechoslovakia, Poland, Germany, France, China, Japan, and Korea. The author, Boris A. Kordemsky, who was born in 1907, is a talented high school mathematics teacher in Moscow. His first book on recreational mathematics, The Wonderful Square, a delightful discussion of curious properties of the ordinary geometric square, was published in Russian in 1952. In 1958 his Essays on Challenging Mathematical Problems appeared. In collaboration with an engineer he produced a picture book for children, Geometry Aids Arithmetic (I 960), which by lavish use of color overlays, shows how simple diagrams and graphs can be used in solving arithmetic problems. His Foundations of the Theory of Probabilities appeared in 1964, and in 1967 he collaborated on a textbook about vector algebra and analytic geometry. But it is for his mammoth puzzle collection that Kordemsky is best known in the Soviet Union, and rightly so, for it is a marvelously varied assortment of brain teasers. Admittedly many of the book's puzzles will be familiar in one form or another to puzzle buffs who know the Western literature, especially the books of England's Henry Ernest Dudeney and America's Sam Loyd. However, Kordemsky has given the old puzzles new angles and has presented them in such amusing and charming story forms that it is a pleasure to come upon them again, and the story backgrounds incidentally convey a valuable impression of contemporary Russian life and customs. Moreover, mixed with the known puzzles are many that will be new to Western readers,