A Mathematical Jamboree

This page intentionally left blank A Mathematical Jamboree 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/9780521485890 © Cambridge University Press 1995 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 1995 ISBN-13 978-0-511-41356-8 eBook (EBL) ISBN-13 paperback 978-0-521-48589-0 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 activities. The second page number refers to the commentary. Introduction 1 Complete the cube 7 68 2 Jasmine's friends 7 68 3 Building to order! 7 68 4 Matchstick mansions 8 68 5 Make 24 8 69 6 Symbolic interpretations! 8 69 7 Sort out the symbols! 9 69 8 Journey to St Ives! 9 70 9 Punishing perambulations! 10 70 10 Sale bargains? 10 70 11 Three in a line 11 71 12 Age related! 11 71 13 Cross out! 12 71 14 What scores are possible? 12 72 15 Triangular trios 13 72 16 Cubical configurations 13 73 17 Crosswords 13 73 18 Counter change! 14 74 19 All things being equal 14 74 20 Safe cracking! 15 75 21 Donald's success? 15 75 22 Manufacturing squares! 15 75 23 Motorway machinations! 16 75 24 Turnabout! 16 76 25 The open prison! 17 76 26 Ayesha's offcuts 18 77 27 A triple prime! 18 77 28 Coin magic! 19 78 29 Mustafa's mosaics 19 78 30 Lord Fearful's fortifications 20 79 31 Norman's radio aerial 20 79 32 The three dice trick 21 79 33 The scouts' initiative test! 21 80 34 The rugger tournament 22 80 35 Do your eyes deceive you? 22 36 A cubical crawl 23 80 37 Only'takes'and'adds'! 23 80 38 Striking the hour 23 80 39 A frog he would a-wooing go! 23 81 40 A fishy connection! 24 81 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 Pool-ball triangles 24 82 Magic squares to magic tetrahedra 25 82 All ten digits! 25 83 By a whisker! 26 83 Pythagorean perimeters! 26 83 Magic circles 26 83 Armchair football 27 84 Commercialising Catch! 27 84 Squaring squares! 28 84 Seasonal visiting 28 85 Lunar areas 28 85 Cable connections 29 86 A matter of relative speed! 29 86 Party politics! 30 86 Bridge building? 30 86 Formation flying 31 87 The robotic mouse! 31 87 Finding the centre 32 87 Number wheels! 32 88 Equal products! 32 88 More insights into magic squares 33 Where is the shopping centre? 34 89 Negotiating the corridor 34 89 Marti's many routes! 35 89 Fancy that! 35 90 Which route to follow? 36 90 Triangular number tiles 36 90 Panoramic possibilities! 37 90 Prime magic! 37 91 Traffic management 38 91 1089 and the rest! 38 92 A magical eye! 39 92 Devious Diana's dice 39 93 Square sisters! 40 93 Shunt your way out of this! 40 93 Map folding 41 94 Spot check! 41 94 Neighbourliness! 42 95 The communicative sisters 42 95 Marvellou