Download the full e-books 50+ sex guide ebooks 100+ ebooks about IQ, EQ, … teen21.tk ivankatrump.tk ebook999.wordpress.com Read Preview the book 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 ISBN 0-684-14870-6 Contents I II III IV V VI VII VIII IX X XI XII XIII XIV Introduction vii Amusing Problems 31 Difficult Problems Geometry with Matches 50 Measure Seven Times Before You Cut 59 69 Skill Will Find Its Application Everywhere 82 Dominoes and Dice 91 Properties of Nine 95 With Algebra and without It 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 185 303 Index 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, some of them no doubt invented by Kordemsky himself The only other Russian writer on recreational mathematics and science who can be compared with Kordemsky is Yakov I Perelman (1882-1942), who in addition to books on recreational arithmetic, algebra, and geometry, wrote similar books on mechanics, physics, and astronomy Paperback editions of Perelman's works are still The Moscow Puzzles widely sold throughout the U.S.S.R., but Kordemsky's book is now regarded as the outstanding puzzle collection in the history of Russian mathematics The translation of Kordemsky's book was made by Dr Albert Parry, former chairman of Russian Studies at Colgate University, and more recently at Case Western Reserve University Dr Parry is a distinguished American scholar of Russian origin whose many books range from the early Ga"ets and Pretenders (a colorful history of American bohemianism) and a biography entitled Whistler's Father (the father of the painter was a pioneer railroad builder in prerevolutionary Russia) to The New Class Divided, a comprehensive, authoritative account of the growing conflict in the Soviet Union between its scientific-technical elite and its ruling bureaucracy As editor of this translation I have taken certain necessary liberties with the text Problems involving Russian currency, for example, have been changed to problems about dollars and cents wherever this could be done without damaging the puzzle Measurements in the metric system have been altered to miles, yards, feet, pounds, and other units more familiar to readers in a nation where, unfortunately, the metric system is still used only by scientists Throughout, wherever Kordemsky's original text could be clarified and sometimes simplified, I have not hesitated to rephrase, cut, or add new sentences Occasionally a passage or footnote referring to a Russian book or article not available in English has been omitted Toward the end of his volume Kordemsky included some problems in number theory that have been omitted because they seemed so difficult and technical, at least for American readers, as to be out of keeping with the rest of the collection In a few instances where puzzles were inexplicable without a knowledge of Russian words, I substi· tuted puzzles of a similar nature using English words The original illustrations by Yevgeni Konstantinovich Argutinsky have been retained, retouched where necessary and with Russian letters in the diagrams replaced by English letters In brief, the book has been edited to make it as easy as possible for an English-reading public to understand and enjoy More than 90 percent of the original material has been retained, and every effort has been made to convey faithfully its warmth and humor I hope that the result will provide many weeks or even months of entertainment for all who enjoy such problems Martin Gardner The Moscow Puzzles The Moscow Puzzles Here are some similar problems Try to make your solutions symmetrical (A) Place 12 light bulbs in rows with bulbs in each row (There is more than one solution.) (B) Plant 13 bushes in 12 rows with bushes per row (C) On the triangular terrace shown, a gardener raises 16 roses in 12 straight-line rows with roses in each row Then he prepares a flower bed and transplants to it the 16 roses in 15 rows with roses in each How? (D) Now arrange 25 trees in 12 rows with trees in each row lOS PLANTING OAKS A pretty sight, these 27 oaks in a six-pointed star-9 rows with oaks in each-but a true forester might object to the three isolated trees An oak loves sunshine from above, but on its sides it prefers greenery As the saying goes, it likes to wear a coat but no hat Diagram the 27 oaks in rows with oaks per row, preserving symmetry, but with all the oaks in three clustered groups 40 Difficult Problems 106 GEOMETRICAL GAMES (A) Place 10 checkers (or coins, buttons, etc.) in rows of each on a table, as shown Shift checkers from one row and checker from the other (without moving the other checkers and without putting one checker on top of another) so that straight rows with checkers each are formed Don't move the other checkers and don't pile checkers vertically-but a symmetrical pattern is not required The five solutions shown all have different shapes And, there are many more solutions The same checkers can be selected and moved in different ways (a and d), or different sets of checkers can be selected Simply selecting the checkers gives fifty solutions: ten ways to select checkers from the top 5, times five ways to select checker from the bottom (a) (c) (d) (e) 41 The Moscow Puzzles Here is an expansion of the game: In front of each player put 10 checkers in rows Each player, while alone, shifts checkers (3 from one row and from the other) to form rows with checkers per row Then they compare solutions Players with identical configurations get pOint A player with a unique pattern gets pOints Those not finishing within the time limit get no points The game can also be played on paper Also, you can permit taking checkers from each row, and permit putting checkers on top of each other This makes many solutions possible like the two shown in diagrams e and f y (e) (f) (B) Punch 49 small holes in a piece of cardboard, in a square grille Stick matches in 10 holes, then try to solve problems such as this: Take matches and stick them in other holes so as to form rows of matches each First solve the problem set up in the diagram below, then vary it by changing the starting pattern and number of rows to be formed " i J 107 f i f i 1 EVEN AND ODD Number checkers and pile them up as shown Use a minimum of moves to shift checkers 1, 3, 5, and from the center to the "Odd" side circles and checkers 2,4, 42 Difficult Problems 6,and to the "Even" side circles To move, shift the top checker from one pile to the top of another It is against the rules to put a checker with a higher number on a checker with a lower one, or to place an odd-numbered checker on an evennumbered checker or vice versa Thus you can put checker I on 3, on 7, or on 6-not on I or I on 108 A PATTERN Place 25 numbered checkers in 25 cells, as shown By exchanging pairs of checkers put them in numerical order: checkers 1,2,3,4, and in the first row, left to right; 6,7,8,9, and 10 in the second row, and so on G @ @ @) (1) @@@@ @ @ @> @ @ @@0 @ @ @ ® 0) What is the minimum number of moves? What basic method should be used? 109 A PUZZLE GIFT The well-known Chinese box has a smaller box inside; inside, there is a still smaller box and so on for many boxes Make a toy out of four boxes Put pieces of candy in each of the three smallest boxes and candies in the largest 43 The Moscow Puzzles Give this collection of 21 candies as a birthday present and tell your friend not to eat any until he redistributes them so as to have an even number of pairs of candies plus in each box Naturally, you should first solve the puzzle yourself 110 KNIGHT'S MOVE To solve this problem you need not be a chess player You need only know the way a knight moves on the chessboard: two squares in one direction and one square at right angles to the first direction The diagram shows 16 black pawns on a board Can a knight capture all 16 pawns in 16 moves? 111 SHIFTING THE CHECKERS (A) Number checkers, and place them as shown in the first diagram 44 Difficult Problems Can you shift checker I to cell I in 75 moves, with checkers to again in cells to 9? Checkers move vertically and horizontally into empty cells No jumps (B) In the second diagram, exchange the black and white checkers in 46 moves (Q) (Q) (0) ©) (Q) (Q) (Q) (Q) (I) (I) •••••• Checkers move horizontally and vertically into the empty cell You can jump one checker over another and you need not alternate white and black moves 112 A GROUPING OF INTEGERS See how elegantly the integers progressions of integers: I 8} 15 d= 7; } d = 5; 14 THROUGH 15 through IS can be arranged in five arithmetic } d 10 II = 4; ~ } d= 2; 12} d=l 13 For example, - I = 15 - = 7, so d (difference) is for the first triplet Now, keeping the first triplet, make four new triplets, still with d = 5, 4, 2, and On your own, try arranging the integers from I through 15 with other values of d 113 EIGHT STARS I have placed a star in one of the white squares of the board shown 45 The Moscow Puzzles Place more stars in white squares so that no of the stars are in line horizontally, vertically, or diagonally 114 TWO PROBLEMS IN PLACING LETTERS (A) Place letters in a 4-by-4 square so that there is only I letter in each row, each column, and each of the two main diagonals How many solutions are there if the letters are identical? If they are different? (B) Now place a's, b's, c's, and d's in the 4-by-4 square so that there are no identical letters in any row, column, or main diagonal How many solutions are there? 115 CELLS OF DIFFERENT COLORS Make 16 square cells of four different colors, say, white, black, red, and green Write 1,2, 3,4 on the white cells, and on the black cells, and so on Arrange the cells in a 4-by-4 square so that in each row, column, and main diagonal you will find all the colors and all the numbers There are many solutions How many? 116 THE LAST PIECE Take a piece of cardboard, cut 32 little pieces from it, and place the pieces in circles to 33 of an enlarged copy of the diagram Circle I remains vacant In each move, a piece jumps horizontally or vertically over a second piece into a vacant circle, and the second piece is removed Make 31 moves so that the last piece jumps into circle I (There are many solutions.) 46 Difficult Problems 117 A RING OF DISKS Take equal-sized coins or disks and place them as shown in a In moves, form them into a new position, ring (b) To move, slide a disk to a new position where it touches at least other disks (a) (b) Can you discover the 24 basic solutions of the problem? (The same moves in a different order is not a basic solution.) Here is one, showing the notation I to 2, 3, which means slide disk I until it touches and 3; to 6,5, which means slide disk until it touches and 5; to 1,3; I to 6, 118 FIGURE SKATERS Pupils of a "ballet school on ice" are rehearsing at a Moscow rink One area is decorated with a square of 64 flowers (a), another with a chessboard (b) i!) (:) 1:1 (:)