The Mathematical Funfair

This page intentionally left blank THE MATHEMATICAL FUNFAIR Brian Bolt CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521377430 © Cambridge University Press 1989 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 1989 ISBN-13 978-0-511-41359-9 eBook (EBL) ISBN-13 paperback 978-0-521-37743-0 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. CONTENTS Page numbers in bold refer to the puzzles; the second page number to the commentary. Introduction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Matchstick magic 1,67 The car jam 1,67 Who nobbled the racehorse? 2,67 The car importer 3,68 Number pyramids 3,68 The triangular building site 4,68 Ring the triangle 4,69 The j eweller's chain 5,69 The anti-litter campaign 6,69 The railcar terminus 6,70 Paving the patio 7,71 Mind stretching 7,71 The chapel hymnboard 8,71 One step forward, march! 8,72 Sim 9 Complete the set 9,72 The Old Girls'reunion 10,72 The chocolate manufacturers' dilemma 10,73 The Ruby wedding 11,73 The flight controller's nightmare 11,74 Threeofakind 11,74 Coin contortions 12,74 An elephantine hole 12,75 Loading the ferry 13,75 Postage due 14,75 Ann's tower 14,76 Seeing is believing! 15 Reafforestation! 16,76 Find the route 16,76 The tournament draw 17,77 The police officer's beat 17,77 Gale 18 The stamp machine 18,78 Billy Bunter's bargain 19,78 All touching 19,79 1984 revisited 20,79 Identical twins, quads and triplets 20,79 Rhyme around 20,79 Touching coins 21,80 Two wrongs make a right 21,80 in 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 IV Narcissistic numbers 22,80 Inside and out 22,81 Matchstick manoeuvres 22,81 Micro millions 23,81 The economy cut 23,82 The variable menu 24,82 Not in her prime 24,83 Loop-line limitations 25,83 As easy as abc! 25,83 Magic polygons 26,84 Factors galore 27,85 Fascinating fractions 27,86 How large a number can you make? 27,86 Food for thought 27,87 How many will you take? 28,87 The dishonest gold exporter 28,87 Do you know your birthday? 29 Ten Tors training 30,88 Alphameric puzzles 30,88 K9 or One man and his dog 31,89 Quadreels 32 Topsy-turvy 32,89 Which was the winning strategy? 33,90 A topological trick 33,91 The blanket box 34,91 Divisibility 34,92 Calculator challenge 34,92 Toasting efficiently 35,92 Playing safe! 35,93 Odds on winning 35,93 Tangrams 36,94 Number the sectors 37,94 Rearranging the hospital ward 37,95 One hundred up! 37,95 Hidden shapes 38,95 Always one short 38,96 Amoeboid patterns 39, 9^ The Embassy reception 39,98 Quartering a circle 40,98 Sweeping the park efficiently 40,98 Pentomino parcels 41,99 A stamp book with a difference 42,99 Some curious number relations 42,100 Concentric magic squares 43,100 Connecting the fire hydrants 44,100 To set you thinking 44,100 Kirkman's schoolgirls problem 45,101 Spot the pattern 45,102 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115