> load "tut4data.txt"; Loading "L:\win\Magma\MATH2068\tut4data.txt" > Type(ct1); CryptTxt > sct1:=String(ct1); > Type(sct1); MonStgElt > /* > We had to do this because there are functions that we want to > use that can only be applied to strings (i.e. objects of type > "MonStgElt") and not to objects of type "CryptTxt". > However, sct1 is made up of exactly the same sequence of > letters as ct1. > I can look at the first 50 letters of ct1 as follows: > */ > sct1[1..50]; COMZBOIVVCHGTRPGUZLULIZVGTUZVAPLOXIGZBOISILCLNPYOX > /* > However ... > */ > ct1[1..50]; >> ct1[1..50]; ^ Runtime error in '[]': Bad argument types > sct2:=String(ct2); > sct3:=String(ct3); > sct4:=String(ct4); > sct5:=String(ct5); > sct6:=String(ct6); > sct7:=String(ct7); > CoincidenceIndex(sct1); 0.0694965088969106128825423590718 > CoincidenceIndex(sct2); 0.0415879787948780874621427836594 > CoincidenceIndex(sct3); 0.0416745922033904428145469104980 > CoincidenceIndex(sct4); 0.0652012312147048057406882815071 > CoincidenceIndex(sct5); 0.0407652125459580513021170486970 > CoincidenceIndex(sct6); 0.0651359214179901685384520145412 > CoincidenceIndex(sct7); 0.0650262272930852557825298140937 > /* > Since the coincidence index is usually about 0.065 for typical > English text, and since Vigenere ciphers reduce the coincidence > index (by making the distribution of the letters more balanced) > we deduce that ct2, ct3 and ct5 were the ones for which > Vigenere enciphering was used. We were told that only substitution > ciphers, transposition ciphers and Vigenere ciphers were used, > and substitution and transposition ciphers do not change the > coincidence index. > */ > /* > Now I used the Vigenere key finder and discovered that the deciphering > keys for ct2 and ct3 were, respectively, LIZECR and HBRNPKDH > */ > V2:=VigenereCryptosystem(6); > k2:=V2!"LIZECR"; > Enciphering(k2,Encoding(V2,sct2)); THEREWASONCEANEMPERORWHOHADAHORSESHODWITHGOLDHEHADAGOLDENSHOEONEACHFOOTANDWHYWASTHISHEWAS\ ABEAUTIFULCREATUREWITHSLENDERLEGSBRIGHTINTELLIGENTEYESANDAMANETHATHUNGDOWNOVERHISNECKLIKE\ AVEILHEHADCARRIEDHISMASTERTHROUGHFIREANDSMOKEINTHEBATTLEFIELDWITHTHEBULLETSWHISTLINGROUND\ HIMHEHADKICKEDANDBITTENANDTAKENPARTINTHEFIGHTWHENTHEENEMYADVANCEDANDWITHHISMASTERONHISBAC\ KHEHADDASHEDOVERTHEFALLENFOEANDSAVEDTHEGOLDENCROWNANDTHEEMPERORSLIFEWHICHWASOFMOREVALUETH\ ANTHEBRIGHTESTGOLDTHISISTHEREASONOFTHEEMPERORSHORSEWEARINGGOLDENSHOESABEETLECAMECREEPINGF\ ORTHFROMTHESTABLEWHERETHEFARRIERHADBEENSHOEINGTHEHORSEGREATONESFIRSTOFCOURSESAIDHEANDTHEN\ THELITTLEONESBUTSIZEISNOTALWAYSAPROOFOFGREATNESSHESTRETCHEDOUTHISTHINLEGASHESPOKEANDPRAYW\ HATDOYOUWANTASKEDTHEFARRIERGOLDENSHOESREPLIEDTHEBEETLEWHYYOUMUSTBEOUTOFYOURSENSESCRIEDTHE\ FARRIERGOLDENSHOESFORYOUINDEEDYESCERTAINLYGOLDENSHOESREPLIEDTHEBEETLEAMINOTJUSTASGOODASTH\ ATGREATCREATUREYONDERWHOISWAITEDUPONANDBRUSHEDANDHASFOODANDDRINKPLACEDBEFOREHIMANDDONTIBE\ LONGTOTHEROYALSTABLESBUTWHYDOESTHEHORSEHAVEGOLDENSHOESASKEDTHEFARRIEROFCOURSEYOUUNDERSTAN\ DTHEREASONUNDERSTANDWELLIUNDERSTANDTHATITISAPERSONALSLIGHTTOMECRIEDTHEBEETLEITISDONETOANN\ OYMESOIINTENDTOGOOUTINTOTHEWORLDANDSEEKMYFORTUNEGOALONGWITHYOUSAIDTHEFARRIERYOUREARUDEFEL\ LOWCRIEDTHEBEETLEASHEWALKEDOUTOFTHESTABLEANDTHENHEFLEWFORASHORTDISTANCETILLHEFOUNDHIMSELF\ INABEAUTIFULFLOWERGARDENALLFRAGRANTWITHROSESANDLAVENDERTHELADYBIRDSWITHREDANDBLACKSHELLSO\ NTHEIRBACKSANDDELICATEWINGSWEREFLYINGABOUTANDONEOFTHEMSAIDISITNOTSWEETANDLOVELYHEREOHHOWB\ EAUTIFULEVERYTHINGISIAMACCUSTOMEDTOBETTERTHINGSSAIDTHEBEETLEDOYOUCALLTHISBEAUTIFULWHYTHER\ EISNOTEVENADUNGHEAPTHENHEWENTONANDUNDERTHESHADOWOFALARGEHAYSTACKHEFOUNDACATERPILLARCRAWLI\ NGALONGHOWBEAUTIFULTHISWORLDISSAIDTHECATERPILLARTHESUNISSOWARMIQUITEENJOYITANDSOONISHALLG\ OTOSLEEPANDDIEASTHEYCALLITBUTISHALLWAKEUPWITHBEAUTIFULWINGSTOFLYWITHLIKEABUTTERFLYHOWCONC\ EITEDYOUAREEXCLAIMEDTHEBEETLEFLYABOUTASABUTTERFLYINDEEDWHATOFTHATIHAVECOMEOUTOFTHEEMPEROR\ SSTABLEANDNOONETHERENOTEVENTHEEMPERORSHORSEWHOINFACTWEARSMYCASTOFFGOLDENSHOESHASANYIDEAOF\ FLYINGEXCEPTINGMYSELFTOHAVEWINGSANDFLYWHYICANDOTHATALREADYANDSOSAYINGHESPREADHISWINGSANDF\ LEWAWAYIDONTWANTTOBEDISGUSTEDHESAIDTOHIMSELFANDYETICANTHELPITSOONAFTERHEFELLDOWNUPONANEXT\ ENSIVELAWNANDFORATIMEPRETENDEDTOSLEEPBUTATLASTFELLASLEEPINEARNESTSUDDENLYAHEAVYSHOWEROFRA\ INCAMEFALLINGFROMTHECLOUDSTHEBEETLEWOKEUPWITHTHENOISEANDWOULDHAVEBEENGLADTOCREEPINTOTHEEA\ RTHFORSHELTERBUTHECOULDNOTHEWASTUMBLEDOVERANDOVERWITHTHERAINSOMETIMESSWIMMINGONHISSTOMACH\ ANDSOMETIMESONHISBACKANDASFORFLYINGTHATWASOUTOFTHEQUESTIONHEBEGANTODOUBTWHETHERHESHOULDES\ CAPEWITHHISLIFESOHEREMAINEDQUIETLYLYINGWHEREHEWASAFTERAWHILETHEWEATHERCLEAREDUPALITTLEAND\ THEBEETLEWASABLETORUBTHEWATERFROMHISEYESANDLOOKABOUTHIMHESAWSOMETHINGGLEAMINGANDHEMANAGED\ TOMAKEHISWAYUPTOITITWASLINENWHICHHADBEENLAIDTOBLEACHONTHEGRASSHECREPTINTOAFOLDOFTHEDAMPLI\ NENWHICHCERTAINLYWASNOTSOCOMFORTABLEAPLACETOLIEINASTHEWARMSTABLEBUTTHEREWASNOTHINGBETTERS\ OHEREMAINEDLYINGTHEREFORAWHOLEDAYANDNIGHTANDTHERAINKEPTONALLTHETIMETOWARDSMORNINGHECREPTO\ UTOFHISHIDINGPLACEFEELINGINAVERYBADTEMPERWITHTHECLIMATETWOFROGSWERESITTINGONTHELINENANDTH\ EIRBRIGHTEYESACTUALLYGLISTENEDWITHPLEASUREWONDERFULWEATHERTHISCRIEDONEOFTHEMANDSOREFRESHI\ NGTHISLINENHOLDSTHEWATERTOGETHERSOBEAUTIFULLYTHATMYHINDLEGSQUIVERASIFIWEREGOINGTOSWIMISHO\ ULDLIKETOKNOWSAIDANOTHERIFTHESWALLOWWHOFLIESSOFARINHERMANYJOURNEYSTOFOREIGNLANDSEVERMETWI\ THABETTERCLIMATETHANTHISWHATDELICIOUSMOISTUREITISASPLEASANTASLYINGINAWETDITCHIAMSUREANYON\ EWHODOESNOTENJOYTHISHASNOLOVEFORHISFATHERLANDHAVEYOUEVERBEENINTHEEMPERORSSTABLEASKEDTHEBE\ ETLETHERETHEMOISTUREISWARMANDREFRESHINGTHATSTHECLIMATEFORMEBUTICOULDNOTTAKEITWITHMEONMYTR\ AVELSISTHERENOTEVENADUNGHILLHEREINTHISGARDENWHEREAPERSONOFRANKLIKEMYSELFCOULDTAKEUPHISABO\ DEANDFEELATHOMEBUTTHEFROGSEITHERDIDNOTORWOULDNOTUNDERSTANDHIMINEVERASKAQUESTIONTWICESAIDT\ HEBEETLEAFTERHEHADASKEDTHISONETHREETIMESANDRECEIVEDNOANSWERTHENHEWENTONALITTLEFARTHERANDS\ TUMBLEDAGAINSTAPIECEOFBROKENCROCKERYWAREWHICHCERTAINLYOUGHTNOTTOHAVEBEENLYINGTHEREBUTASIT\ WASTHEREITFORMEDAGOODSHELTERAGAINSTWINDANDWEATHERTOSEVERALFAMILIESOFEARWIGSWHODWELTINITTH\ EIRREQUIREMENTSWERENOTMANYTHEYWEREVERYSOCIABLEANDFULLOFAFFECTIONFORTHEIRCHILDRENSOMUCHSOT\ HATEACHMOTHERCONSIDEREDHEROWNCHILDTHEMOSTBEAUTIFULANDCLEVEROFTHEMALLOURDEARSONHASENGAGEDH\ IMSELFSAIDONEMOTHERDEARINNOCENTBOYHISGREATESTAMBITIONISTHATHEMAYONEDAYCREEPINTOACLERGYMAN\ SEARTHATISAVERYARTLESSANDLOVEABLEWISHANDBEINGENGAGEDWILLKEEPHIMSTEADYWHATHAPPINESSFORAMOT\ HEROURSONSAIDANOTHERHADSCARCELYCREPTOUTOFTHEEGGWHENHEWASOFFONHISTRAVELSHEISALLLIFEANDSPIR\ ITSIEXPECTHEWILLWEAROUTHISHORNSWITHRUNNINGHOWCHARMINGTHISISFORAMOTHERISITNOTMRBEETLEFORSH\ EKNEWTHESTRANGERBYHISHORNYCOATYOUAREBOTHQUITERIGHTSAIDHESOTHEYBEGGEDHIMTOWALKINTHATISTOCO\ MEASFARASHECOULDUNDERTHEBROKENPIECEOFEARTHENWARENOWYOUSHALLALSOSEEMYLITTLEEARWIGSSAIDATHI\ RDANDAFOURTHMOTHERTHEYARELOVELYLITTLETHINGSANDHIGHLYAMUSINGTHEYARENEVERILLBEHAVEDEXCEPTWH\ ENTHEYAREUNCOMFORTABLEINTHEIRINSIDEWHICHUNFORTUNATELYOFTENHAPPENSATTHEIRAGETHUSEACHMOTHER\ SPOKEOFHERBABYANDTHEIRBABIESTALKEDAFTERTHEIROWNFASHIONANDMADEUSEOFTHELITTLENIPPERSTHEYHAV\ EINTHEIRTAILSTONIPTHEBEARDOFTHEBEETLETHEYAREALWAYSBUSYABOUTSOMETHINGTHELITTLEROGUESSAIDTH\ EMOTHERBEAMINGWITHMATERNALPRIDEBUTTHEBEETLEFELTITABOREANDHETHEREFOREINQUIREDTHEWAYTOTHENE\ ARESTDUNGHEAPTHATISQUITEOUTINTHEGREATWORLDONTHEOTHERSIDEOFTHEDITCHANSWEREDANEARWIGIHOPENO\ NEOFMYCHILDRENWILLEVERGOSOFARITWOULDBETHEDEATHOFMEBUTISHALLTRYTOGETSOFARSAIDTHEBEETLEANDH\ EWALKEDOFFWITHOUTTAKINGANYFORMALLEAVEWHICHISCONSIDEREDAPOLITETHINGTODOWHENHEARRIVEDATTHED\ ITCHHEMETSEVERALFRIENDSALLTHEMBEETLESWELIVEHERETHEYSAIDANDWEAREVERYCOMFORTABLEMAYWEASKYOU\ TOSTEPDOWNINTOTHISRICHMUDYOUMUSTBEFATIGUEDAFTERYOURJOURNEYCERTAINLYSAIDTHEBEETLEISHALLBEM\ OSTHAPPYIHAVEBEENEXPOSEDTOTHERAINANDHAVEHADTOLIEUPONLINENANDCLEANLINESSISATHINGTHATGREATL\ YEXHAUSTSMEIHAVEALSOPAINSINONEOFMYWINGSFROMSTANDINGINTHEDRAUGHTUNDERAPIECEOFBROKENCROCKER\ YITISREALLYQUITEREFRESHINGTOBEWITHONESOWNKINDREDAGAINPERHAPSYOUCAMEFROMADUNGHEAPOBSERVEDT\ HEOLDESTOFTHEMNOINDEEDICAMEFROMAMUCHGRANDERPLACEREPLIEDTHEBEETLEICAMEFROMTHEEMPERORSSTABL\ EWHEREIWASBORNWITHGOLDENSHOESONMYFEETIAMTRAVELLINGONASECRETEMBASSYBUTYOUMUSTNOTASKMEANYQU\ ESTIONSFORICANNOTBETRAYMYSECRETTHENTHEBEETLESTEPPEDDOWNINTOTHERICHMUDWHERESATTHREEYOUNGLA\ DYBEETLESWHOTITTEREDBECAUSETHEYDIDNOTKNOWWHATTOSAYNONEOFTHEMAREENGAGEDYETSAIDTHEIRMOTHERA\ NDTHEBEETLEMAIDENSTITTEREDAGAINTHISTIMEQUITEINCONFUSIONIHAVENEVERSEENGREATERBEAUTIESEVENI\ NTHEROYALSTABLESEXCLAIMEDTHEBEETLEWHOWASNOWRESTINGHIMSELFDONTSPOILMYGIRLSSAIDTHEMOTHERAND\ DONTTALKTOTHEMPRAYUNLESSYOUHAVESERIOUSINTENTIONSBUTOFCOURSETHEBEETLESINTENTIONSWERESERIOU\ SANDAFTERAWHILEOURFRIENDWASENGAGEDTHEMOTHERGAVETHEMHERBLESSINGANDALLTHEOTHERBEETLESCRIEDH\ URRAHIMMEDIATELYAFTERTHEBETROTHALCAMETHEMARRIAGEFORTHEREWASNOREASONTODELAYTHEFOLLOWINGDAY\ PASSEDVERYPLEASANTLYANDTHENEXTWASTOLERABLYCOMFORTABLEBUTONTHETHIRDITBECAMENECESSARYFORHIM\ TOTHINKOFGETTINGFOODFORHISWIFEANDPERHAPSFORCHILDRENIHAVEALLOWEDMYSELFTOBETAKENINSAIDOURBE\ ETLETOHIMSELFANDNOWTHERESNOTHINGTOBEDONEBUTTOTAKETHEMININRETURNNOSOONERSAIDTHANDONEAWAYHE\ WENTANDSTAYEDAWAYALLDAYANDALLNIGHTANDHISWIFEREMAINEDBEHINDAFORSAKENWIDOWOHSAIDTHEOTHERBEE\ TLESTHISFELLOWTHATWEHAVERECEIVEDINTOOURFAMILYISNOTHINGBUTACOMPLETEVAGABONDHEHASGONEAWAYAN\ DLEFTHISWIFEABURDENUPONOURHANDSWELLSHECANBEUNMARRIEDAGAINANDREMAINHEREWITHMYOTHERDAUGHTER\ SSAIDTHEMOTHERFIEONTHEVILLAINTHATFORSOOKHERINTHEMEANTIMETHEBEETLEWHOHADSAILEDACROSSTHEDIT\ CHONACABBAGELEAFHADBEENJOURNEYINGONTHEOTHERSIDEINTHEMORNINGTWOPERSONSCAMEUPTOTHEDITCHWHEN\ THEYSAWHIMTHEYTOOKHIMUPANDTURNEDHIMOVERANDOVERLOOKINGVERYLEARNEDALLTHETIMEESPECIALLYONEWH\ OWASABOYALLAHSEESTHEBLACKBEETLEINTHEBLACKSTONEANDTHEBLACKROCKISNOTTHATWRITTENINTHEKORANHE\ ASKED > V3:=VigenereCryptosystem(8); > k3:=V3!"HBRNPKDH"; > Enciphering(k3,Encoding(V3,sct3)); IWILLTELLYOUASTORYTHATWASTOLDMEWHENIWASALITTLEBOYEVERYTIMEITHOUGHTOFTHISSTORYITSEEMEDTOME\ MOREANDMORECHARMINGFORITISWITHSTORIESASITISWITHMANYPEOPLETHEYBECOMEBETTERASTHEYGROWOLDERI\ HAVENODOUBTTHATYOUHAVEBEENINTHECOUNTRYANDSEENAVERYOLDFARMHOUSEWITHATHATCHEDROOFANDMOSSESA\ NDSMALLPLANTSGROWINGWILDUPONITTHEREISASTORKSNESTONTHERIDGEOFTHEGABLEFORWECANNOTDOWITHOUTT\ HESTORKTHEWALLSOFTHEHOUSEARESLOPINGANDTHEWINDOWSARELOWANDONLYONEOFTHELATTERISMADETOOPENTH\ EBAKINGOVENSTICKSOUTOFTHEWALLLIKEAGREATKNOBANELDERTREEHANGSOVERTHEPALINGSANDBENEATHITSBRA\ NCHESATTHEFOOTOFTHEPALINGISAPOOLOFWATERINWHICHAFEWDUCKSAREDISPORTINGTHEMSELVESTHEREISAYAR\ DDOGTOOWHOBARKSATALLCORNERSJUSTSUCHAFARMHOUSEASTHISSTOODINACOUNTRYLANEANDINITDWELTANOLDCO\ UPLEAPEASANTANDHISWIFESMALLASTHEIRPOSSESSIONSWERETHEYHADONEARTICLETHEYCOULDNOTDOWITHOUTAN\ DTHATWASAHORSEWHICHCONTRIVEDTOLIVEUPONTHEGRASSWHICHITFOUNDBYTHESIDEOFTHEHIGHROADTHEOLDPEA\ SANTRODEINTOTHETOWNUPONTHISHORSEANDHISNEIGHBORSOFTENBORROWEDITOFHIMANDPAIDFORTHELOANOFITB\ YRENDERINGSOMESERVICETOTHEOLDCOUPLEAFTERATIMETHEYTHOUGHTITWOULDBEASWELLTOSELLTHEHORSEOREX\ CHANGEITFORSOMETHINGWHICHMIGHTBEMOREUSEFULTOTHEMBUTWHATMIGHTTHISSOMETHINGBEYOULLKNOWBESTO\ LDMANSAIDTHEWIFEITISFAIRDAYTODAYSORIDEINTOTOWNANDGETRIDOFTHEHORSEFORMONEYORMAKEAGOODEXCHA\ NGEWHICHEVERYOUDOWILLBERIGHTTOMESORIDETOTHEFAIRANDSHEFASTENEDHISNECKERCHIEFFORHIMFORSHECO\ ULDDOTHATBETTERTHANHECOULDANDSHECOULDALSOTIEITVERYPRETTILYINADOUBLEBOWSHEALSOSMOOTHEDHISH\ ATROUNDANDROUNDWITHTHEPALMOFHERHANDANDGAVEHIMAKISSTHENHERODEAWAYUPONTHEHORSETHATWASTOBESO\ LDORBARTEREDFORSOMETHINGELSEYESTHEOLDMANKNEWWHATHEWASABOUTTHESUNSHONEWITHGREATHEATANDNOTA\ CLOUDWASTOBESEENINTHESKYTHEROADWASVERYDUSTYFORANUMBEROFPEOPLEALLGOINGTOTHEFAIRWEREDRIVING\ RIDINGORWALKINGUPONITTHEREWASNOSHELTERANYWHEREFROMTHEHOTSUNSHINEAMONGTHERESTAMANCAMETRUDG\ INGALONGANDDRIVINGACOWTOTHEFAIRTHECOWWASASBEAUTIFULACREATUREASANYCOWCOULDBESHEGIVESGOODMI\ LKIAMCERTAINSAIDTHEPEASANTTOHIMSELFTHATWOULDBEAVERYGOODEXCHANGETHECOWFORTHEHORSEHALLOTHER\ EYOUWITHTHECOWHESAIDITELLYOUWHATIDARESAYAHORSEISOFMOREVALUETHANACOWBUTIDONTCAREFORTHATACO\ WWILLBEMOREUSEFULTOMESOIFYOULIKEWELLEXCHANGETOBESUREIWILLSAIDTHEMANACCORDINGLYTHEEXCHANGE\ WASMADEANDASTHEMATTERWASSETTLEDTHEPEASANTMIGHTHAVETURNEDBACKFORHEHADDONETHEBUSINESSHECAME\ TODOBUTHAVINGMADEUPHISMINDTOGOTOTHEFAIRHEDETERMINEDTODOSOIFONLYTOHAVEALOOKATITSOONHEWENTT\ OTHETOWNWITHHISCOWLEADINGTHEANIMALHESTRODEONSTURDILYANDAFTERASHORTTIMEOVERTOOKAMANWHOWASD\ RIVINGASHEEPITWASAGOODFATSHEEPWITHAFINEFLEECEONITSBACKISHOULDLIKETOHAVETHATFELLOWSAIDTHEP\ EASANTTOHIMSELFTHEREISPLENTYOFGRASSFORHIMBYOURPALINGSANDINTHEWINTERWECOULDKEEPHIMINTHEROO\ MWITHUSPERHAPSITWOULDBEMOREPROFITABLETOHAVEASHEEPTHANACOWSHALLIEXCHANGETHEMANWITHTHESHEEP\ WASQUITEREADYANDTHEBARGAINWASQUICKLYMADEANDTHENOURPEASANTCONTINUEDHISWAYONTHEHIGHROADWITH\ HISSHEEPSOONAFTERTHISHEOVERTOOKANOTHERMANWHOHADCOMEINTOTHEROADFROMAFIELDANDWASCARRYINGALA\ RGEGOOSEUNDERHISARMWHATAHEAVYCREATUREYOUHAVETHERESAIDTHEPEASANTITHASPLENTYOFFEATHERSANDPL\ ENTYOFFATANDWOULDLOOKWELLTIEDTOASTRINGORPADDLINGINTHEWATERATOURPLACETHATWOULDBEVERYUSEFUL\ TOMYOLDWOMANSHECOULDMAKEALLSORTSOFPROFITSOUTOFITHOWOFTENSHEHASSAIDIFNOWWEONLYHADAGOOSENOW\ HEREISANOPPORTUNITYANDIFPOSSIBLEIWILLGETITFORHERSHALLWEEXCHANGEIWILLGIVEYOUMYSHEEPFORYOUR\ GOOSEANDTHANKSINTOTHEBARGAINTHEOTHERHADNOTTHELEASTOBJECTIONANDACCORDINGLYTHEEXCHANGEWASMA\ DEANDOURPEASANTBECAMEPOSSESSOROFTHEGOOSEBYTHISTIMEHEHADARRIVEDVERYNEARTHETOWNTHECROWDONTH\ EHIGHROADHADBEENGRADUALLYINCREASINGANDTHEREWASQUITEARUSHOFMENANDCATTLETHECATTLEWALKEDONTH\ EPATHANDBYTHEPALINGSANDATTHETURNPIKEGATETHEYEVENWALKEDINTOTHETOLLKEEPERSPOTATOFIELDWHEREO\ NEFOWLWASSTRUTTINGABOUTWITHASTRINGTIEDTOITSLEGFORFEARITSHOULDTAKEFRIGHTATTHECROWDANDRUNAW\ AYANDGETLOSTTHETAILFEATHERSOFTHEFOWLWEREVERYSHORTANDITWINKEDWITHBOTHITSEYESANDLOOKEDVERYC\ UNNINGASITSAIDCLUCKCLUCKWHATWERETHETHOUGHTSOFTHEFOWLASITSAIDTHISICANNOTTELLYOUBUTDIRECTLY\ OURGOODMANSAWITHETHOUGHTWHYTHATSTHEFINESTFOWLIEVERSAWINMYLIFEITSFINERTHANOURPARSONSBROODH\ ENUPONMYWORDISHOULDLIKETOHAVETHATFOWLFOWLSCANALWAYSPICKUPAFEWGRAINSTHATLIEABOUTANDALMOSTK\ EEPTHEMSELVESITHINKITWOULDBEAGOODEXCHANGEIFICOULDGETITFORMYGOOSESHALLWEEXCHANGEHEASKEDTHE\ TOLLKEEPEREXCHANGEREPEATEDTHEMANWELLITWOULDNOTBEABADTHINGANDSOTHEYMADEANEXCHANGETHETOLLKE\ EPERATTHETURNPIKEGATEKEPTTHEGOOSEANDTHEPEASANTCARRIEDOFFTHEFOWLNOWHEHADREALLYDONEAGREATDE\ ALOFBUSINESSONHISWAYTOTHEFAIRANDHEWASHOTANDTIREDHEWANTEDSOMETHINGTOEATANDAGLASSOFALETOREF\ RESHHIMSELFSOHETURNEDHISSTEPSTOANINNHEWASJUSTABOUTTOENTERWHENTHEOSTLERCAMEOUTANDTHEYMETAT\ THEDOORTHEOSTLERWASCARRYINGASACKWHATHAVEYOUINTHATSACKASKEDTHEPEASANTROTTENAPPLESANSWEREDT\ HEOSTLERAWHOLESACKFULOFTHEMTHEYWILLDOTOFEEDTHEPIGSWITHWHYTHATWILLBETERRIBLEWASTEHEREPLIED\ ISHOULDLIKETOTAKETHEMHOMETOMYOLDWOMANLASTYEARTHEOLDAPPLETREEBYTHEGRASSPLOTONLYBOREONEAPPL\ EANDWEKEPTITINTHECUPBOARDTILLITWASQUITEWITHEREDANDROTTENITWASALWAYSPROPERTYMYOLDWOMANSAID\ ANDHERESHEWOULDSEEAGREATDEALOFPROPERTYAWHOLESACKFULISHOULDLIKETOSHOWTHEMTOHERWHATWILLYOUG\ IVEMEFORTHESACKFULASKEDTHEOSTLERWHATWILLIGIVEWELLIWILLGIVEYOUMYFOWLINEXCHANGESOHEGAVEUPTH\ EFOWLANDRECEIVEDTHEAPPLESWHICHHECARRIEDINTOTHEINNPARLORHELEANEDTHESACKCAREFULLYAGAINSTTHE\ STOVEANDTHENWENTTOTHETABLEBUTTHESTOVEWASHOTANDHEHADNOTTHOUGHTOFTHATMANYGUESTSWEREPRESENTH\ ORSEDEALERSCATTLEDROVERSANDTWOENGLISHMENTHEENGLISHMENWERESORICHTHATTHEIRPOCKETSQUITEBULGE\ DOUTANDSEEMEDREADYTOBURSTANDTHEYCOULDBETTOOASYOUSHALLHEARHISSSSHISSSSWHATCOULDTHATBEBYTHE\ STOVETHEAPPLESWEREBEGINNINGTOROASTWHATISTHATASKEDONEWHYDOYOUKNOWSAIDOURPEASANTANDTHENHETO\ LDTHEMTHEWHOLESTORYOFTHEHORSEWHICHHEHADEXCHANGEDFORACOWANDALLTHERESTOFITDOWNTOTHEAPPLESWE\ LLYOUROLDWOMANWILLGIVEITYOUWELLWHENYOUGETHOMESAIDONEOFTHEENGLISHMENWONTTHEREBEANOISEWHATG\ IVEMEWHATSAIDTHEPEASANTWHYSHEWILLKISSMEANDSAYWHATTHEOLDMANDOESISALWAYSRIGHTLETUSLAYAWAGER\ ONITSAIDTHEENGLISHMENWELLWAGERYOUATONOFCOINEDGOLDAHUNDREDPOUNDSTOTHEHUNDREDWEIGHTNOABUSHE\ LWILLBEENOUGHREPLIEDTHEPEASANTICANONLYSETABUSHELOFAPPLESAGAINSTITANDILLTHROWMYSELFANDMYOL\ DWOMANINTOTHEBARGAINTHATWILLPILEUPTHEMEASUREIFANCYDONETAKENANDSOTHEBETWASMADETHENTHELANDL\ ORDSCOACHCAMETOTHEDOORANDTHETWOENGLISHMENANDTHEPEASANTGOTINANDAWAYTHEYDROVEANDSOONARRIVED\ ANDSTOPPEDATTHEPEASANTSHUTGOODEVENINGOLDWOMANGOODEVENINGOLDMANIVEMADETHEEXCHANGEAHWELLYOU\ UNDERSTANDWHATYOUREABOUTSAIDTHEWOMANTHENSHEEMBRACEDHIMANDPAIDNOATTENTIONTOTHESTRANGERSNOR\ DIDSHENOTICETHESACKIGOTACOWINEXCHANGEFORTHEHORSETHANKHEAVENSAIDSHENOWWESHALLHAVEPLENTYOFM\ ILKANDBUTTERANDCHEESEONTHETABLETHATWASACAPITALEXCHANGEYESBUTICHANGEDTHECOWFORASHEEPAHBETT\ ERSTILLCRIEDTHEWIFEYOUALWAYSTHINKOFEVERYTHINGWEHAVEJUSTENOUGHPASTUREFORASHEEPEWESMILKANDC\ HEESEWOOLLENJACKETSANDSTOCKINGSTHECOWCOULDNOTGIVEALLTHESEANDHERHAIRONLYFALLSOFFHOWYOUTHIN\ KOFEVERYTHINGBUTICHANGEDAWAYTHESHEEPFORAGOOSETHENWESHALLHAVEROASTGOOSETOEATTHISYEARYOUDEA\ ROLDMANYOUAREALWAYSTHINKINGOFSOMETHINGTOPLEASEMETHISISDELIGHTFULWECANLETTHEGOOSEWALKABOUT\ WITHASTRINGTIEDTOHERLEGSOSHEWILLBEFATTERSTILLBEFOREWEROASTHERBUTIGAVEAWAYTHEGOOSEFORAFOWL\ AFOWLWELLTHATWASAGOODEXCHANGEREPLIEDTHEWOMANTHEFOWLWILLLAYEGGSANDHATCHTHEMANDWESHALLHAVEC\ HICKENSWESHALLSOONHAVEAPOULTRYYARDOHTHISISJUSTWHATIWASWISHINGFORYESBUTIEXCHANGEDTHEFOWLFO\ RASACKOFSHRIVELLEDAPPLESWHATIREALLYMUSTGIVEYOUAKISSFORTHATEXCLAIMEDTHEWIFEMYDEARGOODHUSBA\ NDNOWILLTELLYOUSOMETHINGDOYOUKNOWALMOSTASSOONASYOULEFTMETHISMORNINGIBEGANTOTHINKOFWHATICO\ ULDGIVEYOUNICEFORSUPPERTHISEVENINGANDTHENITHOUGHTOFFRIEDEGGSANDBACONWITHSWEETHERBSIHADEGG\ SANDBACONBUTIWANTEDTHEHERBSSOIWENTOVERTOTHESCHOOLMASTERSIKNEWTHEYHADPLENTYOFHERBSBUTTHESC\ HOOLMISTRESSISVERYMEANALTHOUGHSHECANSMILESOSWEETLYIBEGGEDHERTOLENDMEAHANDFULOFHERBSLENDSH\ EEXCLAIMEDIHAVENOTHINGTOLENDNOTHINGATALLGROWSINOURGARDENNOTEVENASHRIVELLEDAPPLEICOULDNOTE\ VENLENDYOUASHRIVELLEDAPPLEMYDEARWOMANBUTNOWICANLENDHERTENORAWHOLESACKFULWHICHIMVERYGLADOF\ ITMAKESMELAUGHTOTHINKABOUTITANDTHENSHEGAVEHIMAHEARTYKISSWELLILIKEALLTHISSAIDBOTHTHEENGLIS\ HMENALWAYSGOINGDOWNTHEHILLANDYETALWAYSMERRYITSWORTHTHEMONEYTOSEEITSOTHEYPAIDAHUNDREDWEIGH\ TOFGOLDTOTHEPEASANTWHOWHATEVERHEDIDWASNOTSCOLDEDBUTKISSEDYESITALWAYSPAYSBESTWHENTHEWIFESE\ ESANDMAINTAINSTHATHERHUSBANDKNOWSBESTANDWHATEVERHEDOESISRIGHTTHATISASTORYWHICHIHEARDWHENI\ WASACHILDANDNOWYOUHAVEHEARDITTOOANDKNOWTHATWHATTHEOLDMANDOESISALWAYSRIGHT > V5:=VigenereCryptosystem(10); > k5:=V5!"IOAQSNFANY"; > Enciphering(k5,Encoding(V5,sct5)); MARLEYWASDEADTOBEGINWITHTHEREISNODOUBTWHATEVERABOUTTHATTHEREGISTEROFHISBURIALWASSIGNEDBYT\ HECLERGYMANTHECLERKTHEUNDERTAKERANDTHECHIEFMOURNERSCROOGESIGNEDITANDSCROOGESNAMEWASGOODUP\ ONCHANGEFORANYTHINGHECHOSETOPUTHISHANDTOOLDMARLEYWASASDEADASADOORNAILMINDIDONTMEANTOSAYTH\ ATIKNOWOFMYOWNKNOWLEDGEWHATTHEREISPARTICULARLYDEADABOUTADOORNAILIMIGHTHAVEBEENINCLINEDMYS\ ELFTOREGARDACOFFINNAILASTHEDEADESTPIECEOFIRONMONGERYINTHETRADEBUTTHEWISDOMOFOURANCESTORSI\ SINTHESIMILEANDMYUNHALLOWEDHANDSSHALLNOTDISTURBITORTHECOUNTRYSDONEFORYOUWILLTHEREFOREPERM\ ITMETOREPEATEMPHATICALLYTHATMARLEYWASASDEADASADOORNAILSCROOGEKNEWHEWASDEADOFCOURSEHEDIDHO\ WCOULDITBEOTHERWISESCROOGEANDHEWEREPARTNERSFORIDONTKNOWHOWMANYYEARSSCROOGEWASHISSOLEEXECU\ TORHISSOLEADMINISTRATORHISSOLEASSIGNHISSOLERESIDUARYLEGATEEHISSOLEFRIENDANDSOLEMOURNERAND\ EVENSCROOGEWASNOTSODREADFULLYCUTUPBYTHESADEVENTBUTTHATHEWASANEXCELLENTMANOFBUSINESSONTHEV\ ERYDAYOFTHEFUNERALANDSOLEMNISEDITWITHANUNDOUBTEDBARGAINTHEMENTIONOFMARLEYSFUNERALBRINGSME\ BACKTOTHEPOINTISTARTEDFROMTHEREISNODOUBTTHATMARLEYWASDEADTHISMUSTBEDISTINCTLYUNDERSTOODOR\ NOTHINGWONDERFULCANCOMEOFTHESTORYIAMGOINGTORELATEIFWEWERENOTPERFECTLYCONVINCEDTHATHAMLETS\ FATHERDIEDBEFORETHEPLAYBEGANTHEREWOULDBENOTHINGMOREREMARKABLEINHISTAKINGASTROLLATNIGHTINA\ NEASTERLYWINDUPONHISOWNRAMPARTSTHANTHEREWOULDBEINANYOTHERMIDDLEAGEDGENTLEMANRASHLYTURNING\ OUTAFTERDARKINABREEZYSPOTSAYSAINTPAULSCHURCHYARDFORINSTANCELITERALLYTOASTONISHHISSONSWEAK\ MINDSCROOGENEVERPAINTEDOUTOLDMARLEYSNAMETHEREITSTOODYEARSAFTERWARDSABOVETHEWAREHOUSEDOORS\ CROOGEANDMARLEYTHEFIRMWASKNOWNASSCROOGEANDMARLEYSOMETIMESPEOPLENEWTOTHEBUSINESSCALLEDSCRO\ OGESCROOGEANDSOMETIMESMARLEYBUTHEANSWEREDTOBOTHNAMESITWASALLTHESAMETOHIMOHBUTHEWASATIGHTF\ ISTEDHANDATTHEGRINDSTONESCROOGEASQUEEZINGWRENCHINGGRASPINGSCRAPINGCLUTCHINGCOVETOUSOLDSIN\ NERHARDANDSHARPASFLINTFROMWHICHNOSTEELHADEVERSTRUCKOUTGENEROUSFIRESECRETANDSELFCONTAINEDA\ NDSOLITARYASANOYSTERTHECOLDWITHINHIMFROZEHISOLDFEATURESNIPPEDHISPOINTEDNOSESHRIVELLEDHISC\ HEEKSTIFFENEDHISGAITMADEHISEYESREDHISTHINLIPSBLUEANDSPOKEOUTSHREWDLYINHISGRATINGVOICEAFRO\ STYRIMEWASONHISHEADANDONHISEYEBROWSANDHISWIRYCHINHECARRIEDHISOWNLOWTEMPERATUREALWAYSABOUT\ WITHHIMHEICEDHISOFFICEINTHEDOGDAYSANDDIDNTTHAWITONEDEGREEATCHRISTMASEXTERNALHEATANDCOLDHA\ DLITTLEINFLUENCEONSCROOGENOWARMTHCOULDWARMNOWINTRYWEATHERCHILLHIMNOWINDTHATBLEWWASBITTERE\ RTHANHENOFALLINGSNOWWASMOREINTENTUPONITSPURPOSENOPELTINGRAINLESSOPENTOENTREATYFOULWEATHER\ DIDNTKNOWWHERETOHAVEHIMTHEHEAVIESTRAINANDSNOWANDHAILANDSLEETCOULDBOASTOFTHEADVANTAGEOVERH\ IMINONLYONERESPECTTHEYOFTENCAMEDOWNHANDSOMELYANDSCROOGENEVERDIDNOBODYEVERSTOPPEDHIMINTHES\ TREETTOSAYWITHGLADSOMELOOKSMYDEARSCROOGEHOWAREYOUWHENWILLYOUCOMETOSEEMENOBEGGARSIMPLOREDH\ IMTOBESTOWATRIFLENOCHILDRENASKEDHIMWHATITWASOCLOCKNOMANORWOMANEVERONCEINALLHISLIFEINQUIRE\ DTHEWAYTOSUCHANDSUCHAPLACEOFSCROOGEEVENTHEBLINDMENSDOGSAPPEAREDTOKNOWHIMANDWHENTHEYSAWHIM\ COMINGONWOULDTUGTHEIROWNERSINTODOORWAYSANDUPCOURTSANDTHENWOULDWAGTHEIRTAILSASTHOUGHTHEYSA\ IDNOEYEATALLISBETTERTHANANEVILEYEDARKMASTERBUTWHATDIDSCROOGECAREITWASTHEVERYTHINGHELIKEDT\ OEDGEHISWAYALONGTHECROWDEDPATHSOFLIFEWARNINGALLHUMANSYMPATHYTOKEEPITSDISTANCEWASWHATTHEKN\ OWINGONESCALLNUTSTOSCROOGEONCEUPONATIMEOFALLTHEGOODDAYSINTHEYEARONCHRISTMASEVEOLDSCROOGES\ ATBUSYINHISCOUNTINGHOUSEITWASCOLDBLEAKBITINGWEATHERFOGGYWITHALANDHECOULDHEARTHEPEOPLEINTH\ ECOURTOUTSIDEGOWHEEZINGUPANDDOWNBEATINGTHEIRHANDSUPONTHEIRBREASTSANDSTAMPINGTHEIRFEETUPON\ THEPAVEMENTSTONESTOWARMTHEMTHECITYCLOCKSHADONLYJUSTGONETHREEBUTITWASQUITEDARKALREADYITHAD\ NOTBEENLIGHTALLDAYANDCANDLESWEREFLARINGINTHEWINDOWSOFTHENEIGHBOURINGOFFICESLIKERUDDYSMEAR\ SUPONTHEPALPABLEBROWNAIRTHEFOGCAMEPOURINGINATEVERYCHINKANDKEYHOLEANDWASSODENSEWITHOUTTHAT\ ALTHOUGHTHECOURTWASOFTHENARROWESTTHEHOUSESOPPOSITEWEREMEREPHANTOMSTOSEETHEDINGYCLOUDCOMED\ ROOPINGDOWNOBSCURINGEVERYTHINGONEMIGHTHAVETHOUGHTTHATNATURELIVEDHARDBYANDWASBREWINGONALAR\ GESCALETHEDOOROFSCROOGESCOUNTINGHOUSEWASOPENTHATHEMIGHTKEEPHISEYEUPONHISCLERKWHOINADISMAL\ LITTLECELLBEYONDASORTOFTANKWASCOPYINGLETTERSSCROOGEHADAVERYSMALLFIREBUTTHECLERKSFIREWASSO\ VERYMUCHSMALLERTHATITLOOKEDLIKEONECOALBUTHECOULDNTREPLENISHITFORSCROOGEKEPTTHECOALBOXINHI\ SOWNROOMANDSOSURELYASTHECLERKCAMEINWITHTHESHOVELTHEMASTERPREDICTEDTHATITWOULDBENECESSARYF\ ORTHEMTOPARTWHEREFORETHECLERKPUTONHISWHITECOMFORTERANDTRIEDTOWARMHIMSELFATTHECANDLEINWHIC\ HEFFORTNOTBEINGAMANOFASTRONGIMAGINATIONHEFAILEDAMERRYCHRISTMASUNCLEGODSAVEYOUCRIEDACHEERF\ ULVOICEITWASTHEVOICEOFSCROOGESNEPHEWWHOCAMEUPONHIMSOQUICKLYTHATTHISWASTHEFIRSTINTIMATIONH\ EHADOFHISAPPROACHBAHSAIDSCROOGEHUMBUG > /* > Transposition ciphers do not change the frequencies of letters at all. > So if we find that E is the most common letter, followed by T or A, and > then things like O, I, N, S etc., with very few Q's, J's or Z's, then > it is likely that a transposition cipher was used. > We can used SortedFreqDist: > */ > SortedFreqDist(sct1); [ <0.132410107180476188659667968750, I>, <0.0947521869093179702758789062500, O>, <0.0889212824404239654541015625000, X>, <0.0792031101882457733154296875000, Z>, <0.0711856167763471603393554687500, P>, <0.0685131195932626724243164062500, L>, <0.0658406224101781845092773437500, V>, <0.0568513120524585247039794921875, B>, <0.0532069969922304153442382812500, C>, <0.0522351795807480812072753906250, U>, <0.0500485906377434730529785156250, G>, <0.0291545188520103693008422851562, M>, <0.0242954324930906295776367187500, N>, <0.0225947522558271884918212890625, E>, <0.0196793002542108297348022460938, F>, <0.0194363459013402462005615234375, Y>, <0.0189504374284297227859497070312, R>, <0.0140913508366793394088745117188, H>, <0.0121477162465453147888183593750, T>, <0.0114188533043488860130310058594, Q>, <0.00680272106546908617019653320312, S>, <0.00631681241793558001518249511719, A>, <0.000971817295067012310028076171875, J>, <0.000728862971300259232521057128906, K>, <0.000242954323766753077507019042969, W>, <0.000000000000000000000000000000, D> ] > /* > All those X's and Z's! Definitely not a transposition cipher! > */ > SortedFreqDist(sct4); [ <0.127444546669721603393554687500, U>, <0.101719385944306850433349609375, J>, <0.0756004722788929939270019531250, X>, <0.0752067202702164649963378906250, T>, <0.0651004072278738021850585937500, O>, <0.0641816509887576103210449218750, Z>, <0.0602441267110407352447509765625, F>, <0.0601128758862614631652832031250, L>, <0.0509253181517124176025390625000, E>, <0.0467252922244369983673095703125, D>, <0.0406877542845904827117919921875, A>, <0.0360939754173159599304199218750, Y>, <0.0278251739218831062316894531250, S>, <0.0261189131997525691986083984375, N>, <0.0232313952874392271041870117188, H>, <0.0217876362148672342300415039062, G>, <0.0216563853900879621505737304688, Q>, <0.0175876098219305276870727539062, W>, <0.0170626067556440830230712890625, P>, <0.0160126001574099063873291015625, R>, <0.0126000787131488323211669921875, K>, <0.00813755090348422527313232421875, I>, <0.00236251475871540606021881103516, V>, <0.000787504919571802020072937011719, B>, <0.000656254102068487554788589477539, M>, <0.000131250821141293272376060485840, C> ] > /* > Lots of J's and X's .... not a transposition cipher > */ > SortedFreqDist(sct6); [ <0.128529144451022148132324218750, E>, <0.0935792345553636550903320312500, T>, <0.0775273228064179420471191406250, A>, <0.0757058290764689445495605468750, I>, <0.0737704914063215255737304687500, O>, <0.0677367942407727241516113281250, N>, <0.0566939888522028923034667968750, S>, <0.0555555555038154125213623046875, H>, <0.0549863385967910289764404296875, R>, <0.0397313297726213932037353515625, D>, <0.0374544626101851463317871093750, L>, <0.0350637524388730525970458984375, M>, <0.0311930782627314329147338867188, C>, <0.0306238615885376930236816406250, F>, <0.0274362477939575910568237304688, U>, <0.0215163934044539928436279296875, Y>, <0.0214025501627475023269653320312, W>, <0.0211748634465038776397705078125, P>, <0.0171903460286557674407958984375, G>, <0.0144581056665629148483276367188, B>, <0.00979052821639925241470336914062, V>, <0.00421220401767641305923461914062, K>, <0.00216302368789911270141601562500, X>, <0.00125227686658035963773727416992, J>, <0.000910746814042795449495315551758, Q>, <0.000341530056175542995333671569824, Z> ] > /* > Now this looks like a transposition cipher! > */ > SortedFreqDist(sct7); [ <0.110627178102731704711914062500, E>, <0.0927700344473123550415039062500, A>, <0.0831881528720259666442871093750, T>, <0.0814459929242730140686035156250, N>, <0.0788327530026435852050781250000, H>, <0.0714285718277096748352050781250, O>, <0.0653310101479291915893554687500, I>, <0.0627177702262997627258300781250, D>, <0.0522648082114756107330322265625, S>, <0.0500871078111231327056884765625, L>, <0.0391986062750220298767089843750, R>, <0.0339721255004405975341796875000, M>, <0.0331010455265641212463378906250, W>, <0.0248257839120924472808837890625, C>, <0.0213414633180946111679077148438, G>, <0.0204703833442181348800659179688, U>, <0.0187282229308038949966430664062, Y>, <0.0139372822595760226249694824219, P>, <0.0130662020528689026832580566406, F>, <0.0121951219625771045684814453125, K>, <0.00958188157528638839721679687500, B>, <0.00479094078764319419860839843750, J>, <0.00391986063914373517036437988281, V>, <0.00217770034214481711387634277344, X>, <0.000000000000000000000000000000, Q>, <0.000000000000000000000000000000, Z> ] > /* > Another transposition cipher > */ > d:=[pt6[i]*pt6[i+1]: i in [1..#pt6-1]]; > d[1..7]; [ FO, OR, RT, TH, HE, EM, MO ] > pt6[1..8]; FORTHEMO > CoincidenceIndex(d); 0.00706865940193723755646563970225 > d1:=[pt6[i]*pt6[i+2]: i in [1..#pt6-2]]; > d1[1..7]; [ FR, OT, RH, TE, HM, EO, MS ] > /* > Now we are not looking at pairs of letters that are adjacent in the > plaintext, but at pairs of letters that are almost adjacent: exactly > one letter in between. > */ > CoincidenceIndex(d1); 0.00492849992288115286698359180142 > /* > Much lower than the coincidence index of d, but still quite a bit > larger than (1/26)^2 > */ > (1.0/26)^2; 0.00147928994082840236686390532544 > d2:=[pt6[i]*pt6[i+3]: i in [1..#pt6-3]]; > CoincidenceIndex(d2); 0.00453643051535737104781264373094 > d3:=[pt6[i]*pt6[i+4]: i in [1..#pt6-4]]; > CoincidenceIndex(d3); 0.00424101727538355793658557216551 > /* > It is never going to get anywhere near (1/26)^2, because we are > still taking pairs made up of letters that occur in the text, > and some pairs (like XX) will obviously be rare. But the sequence > made from pairs of adjacent letters has a much higher coincidence > index, because the frequency distribution of the pairs is much > more unbalanced in this case. Some pairs of letters have a very > strong tendency to occur together as digraphs, and others have > a very strong tendency not to. For example, although A is a > very common letter, AA is a very uncommon digraph. > */ > CoincidenceIndex(Decimation(sct6,[1,8],9)); 0.00471836906263135771332492643968 > CoincidenceIndex(Decimation(sct6,[8,1],9)); 0.00471836906263135771332492643968 > /* > The sequence Decimation(sct6,[8,1],9) is the same as the sequence > Decimation(sct6,[1,8],9), except that all the pairs are reversed: > */ > Decimation(sct6,[8,1],9)[1..20]; [ SR, MI, YT, ER, AI, NU, EE, SE, LI, DF, ID, CT, ST, VH, SY, EJ, DO, AC, NM, EE ] > Decimation(sct6,[1,8],9)[1..20]; [ RS, IM, TY, RE, IA, UN, EE, ES, IL, FD, DI, TC, TS, HV, YS, JE, OD, CA, MN, EE ] > /* > Obviously the probability that two randomly chosen terms of are equal > is the same for the second of these two sequences as it is for the first. > */ > for i:=2 to 9 do for> "i =",i,": CI=",CoincidenceIndex(Decimation(sct6,[1,i],9)); for> end for; i = 2 : CI= 0.00441361916771752837326607818411 i = 3 : CI= 0.00457755359394703656998738965952 i = 4 : CI= 0.00496847414880201765447667087011 i = 5 : CI= 0.00805380411937788986969314838168 i = 6 : CI= 0.00434846574190836485918453131568 i = 7 : CI= 0.00733711643547709121479613282892 i = 8 : CI= 0.00471836906263135771332492643968 i = 9 : CI= 0.00490752416981925178646490121900 > /* > There are two cases where the value is noticeably higher than usual, > namely i=5 and i=7 give high values. This means that maybe the block > length is 9 and the 1st letter in each block was adjacent to the 5th > letter in the block before the block was reordered, and also maybe the > first letter was adjacent to the 7th letter before the reordering. > The original order might have been ..517.. or ..715.. . > */ > for j:=1 to 8 do for> for i:=j+1 to 9 do for|for> j,i,": CI=",CoincidenceIndex(Decimation(sct6,[j,i],9)); for|for> end for; for> end for; 1 2 : CI= 0.00441361916771752837326607818411 1 3 : CI= 0.00457755359394703656998738965952 1 4 : CI= 0.00496847414880201765447667087011 1 5 : CI= 0.00805380411937788986969314838168 1 6 : CI= 0.00434846574190836485918453131568 1 7 : CI= 0.00733711643547709121479613282892 1 8 : CI= 0.00471836906263135771332492643968 1 9 : CI= 0.00490752416981925178646490121900 2 3 : CI= 0.00458806221101303068516183270282 2 4 : CI= 0.00414459857082807902480033627574 2 5 : CI= 0.00405212274064733081126523749474 2 6 : CI= 0.00652585119798234552332912988651 2 7 : CI= 0.00424337957124842370744010088272 2 8 : CI= 0.00778898696931483816729718369063 2 9 : CI= 0.00434636401849516603614964270702 3 4 : CI= 0.00420975199663724253888188314418 3 5 : CI= 0.00493484657419083648591845313157 3 6 : CI= 0.00680958385876418663303909205548 3 7 : CI= 0.00429171920975199663724253888188 3 8 : CI= 0.00492013451029844472467423287096 3 9 : CI= 0.00701555275325767129045817570408 4 5 : CI= 0.00427490542244640605296343001261 4 6 : CI= 0.00418873476250525430853299705759 4 7 : CI= 0.00674232870954182429592265657839 4 8 : CI= 0.00428331231609920134510298444725 4 9 : CI= 0.00402900378310214375788146279950 5 6 : CI= 0.00457124842370744010088272383354 5 7 : CI= 0.00479823455233291298865069356873 5 8 : CI= 0.00423917612442202606137032366541 5 9 : CI= 0.00643757881462799495586380832282 6 7 : CI= 0.00459016393442622950819672131147 6 8 : CI= 0.00532576712904581757040773434216 6 9 : CI= 0.00488650693568726355611601513241 7 8 : CI= 0.00463219840269020596889449348466 7 9 : CI= 0.00447667087011349306431273644388 8 9 : CI= 0.00420134510298444724674232870954 > /* > The possible adjacencies seem to be (1,5), (1,7), (2,6) (?), (2,8), (3,6), (3,9), > (4,7), (5,9). This gives a possible original order of 471593628 or its reverse. > */ > T:=TranspositionCryptosystem(9); > key:=T![4,7,1,5,9,3,6,2,8]; > Enciphering(key,Encoding(T,sct6)); FORTHEMOSTWILDYETMOSTHOMELYNARRATIVEWHICHIAMABOUTTOPENINEITHEREXPECTNORSOLICITBELIEFMADIN\ DEEDWOULDIBETOEXPECTITINACASEWHEREMYVERYSENSESREJECTTHEIROWNEVIDENCEYETMADAMINOTANDVERYSU\ RELYDOINOTDREAMBUTTOMORROWIDIEANDTODAYIWOULDUNBURTHENMYSOULMYIMMEDIATEPURPOSEISTOPLACEBEF\ ORETHEWORLDPLAINLYSUCCINCTLYANDWITHOUTCOMMENTASERIESOFMEREHOUSEHOLDEVENTSINTHEIRCONSEQUEN\ CESTHESEEVENTSHAVETERRIFIEDHAVETORTUREDHAVEDESTROYEDMEYETIWILLNOTATTEMPTTOEXPOUNDTHEMTOME\ THEYHAVEPRESENTEDLITTLEBUTHORRORTOMANYTHEYWILLSEEMLESSTERRIBLETHANBAROQUESHEREAFTERPERHAP\ SSOMEINTELLECTMAYBEFOUNDWHICHWILLREDUCEMYPHANTASMTOTHECOMMONPLACESOMEINTELLECTMORECALMMOR\ ELOGICALANDFARLESSEXCITABLETHANMYOWNWHICHWILLPERCEIVEINTHECIRCUMSTANCESIDETAILWITHAWENOTH\ INGMORETHANANORDINARYSUCCESSIONOFVERYNATURALCAUSESANDEFFECTSFROMMYINFANCYIWASNOTEDFORTHED\ OCILITYANDHUMANITYOFMYDISPOSITIONMYTENDERNESSOFHEARTWASEVENSOCONSPICUOUSASTOMAKEMETHEJEST\ OFMYCOMPANIONSIWASESPECIALLYFONDOFANIMALSANDWASINDULGEDBYMYPARENTSWITHAGREATVARIETYOFPETS\ WITHTHESEISPENTMOSTOFMYTIMEANDNEVERWASSOHAPPYASWHENFEEDINGANDCARESSINGTHEMTHISPECULIAROFC\ HARACTERGREWWITHMYGROWTHANDINMYMANHOODIDERIVEDFROMITONEOFMYPRINCIPALSOURCESOFPLEASURETOTH\ OSEWHOHAVECHERISHEDANAFFECTIONFORAFAITHFULANDSAGACIOUSDOGINEEDHARDLYBEATTHETROUBLEOFEXPLA\ ININGTHENATUREORTHEINTENSITYOFTHEGRATIFICATIONTHUSDERIVABLETHEREISSOMETHINGINTHEUNSELFISH\ ANDSELFSACRIFICINGLOVEOFABRUTEWHICHGOESDIRECTLYTOTHEHEARTOFHIMWHOHASHADFREQUENTOCCASIONTO\ TESTTHEPALTRYFRIENDSHIPANDGOSSAMERFIDELITYOFMEREMANIMARRIEDEARLYANDWASHAPPYTOFINDINMYWIFE\ ADISPOSITIONNOTUNCONGENIALWITHMYOWNOBSERVINGMYPARTIALITYFORDOMESTICPETSSHELOSTNOOPPORTUNI\ TYOFPROCURINGTHOSEOFTHEMOSTAGREEABLEKINDWEHADBIRDSGOLDFISHAFINEDOGRABBITSASMALLMONKEYANDA\ CATTHISLATTERWASAREMARKABLYLARGEANDBEAUTIFULANIMALENTIRELYBLACKANDSAGACIOUSTOANASTONISHIN\ GDEGREEINSPEAKINGOFHISINTELLIGENCEMYWIFEWHOATHEARTWASNOTALITTLETINCTUREDWITHSUPERSTITIONM\ ADEFREQUENTALLUSIONTOTHEANCIENTPOPULARNOTIONWHICHREGARDEDALLBLACKCATSASWITCHESINDISGUISEN\ OTTHATSHEWASEVERSERIOUSUPONTHISPOINTANDIMENTIONTHEMATTERATALLFORNOBETTERREASONTHANTHATITH\ APPENSJUSTNOWTOBEREMEMBEREDPLUTOTHISWASTHECATSNAMEWASMYFAVORITEPETANDPLAYMATEIALONEFEDHIM\ ANDHEATTENDEDMEWHEREVERIWENTABOUTTHEHOUSEITWASEVENWITHDIFFICULTYTHATICOULDPREVENTHIMFROMF\ OLLOWINGMETHROUGHTHESTREETSOURFRIENDSHIPLASTEDINTHISMANNERFORSEVERALYEARSDURINGWHICHMYGEN\ ERALTEMPERAMENTANDCHARACTERTHROUGHTHEINSTRUMENTALITYOFTHEFIENDINTEMPERANCEHADIBLUSHTOCONF\ ESSITEXPERIENCEDARADICALALTERATIONFORTHEWORSEIGREWDAYBYDAYMOREMOODYMOREIRRITABLEMOREREGAR\ DLESSOFTHEFEELINGSOFOTHERSISUFFEREDMYSELFTOUSEINTEMPERATELANGUAGETOMYATLENGTHIEVENOFFERED\ HERPERSONALVIOLENCEMYPETSOFCOURSEWEREMADETOFEELTHECHANGEINMYDISPOSITIONINOTONLYNEGLECTEDB\ UTILLUSEDTHEMFORPLUTOHOWEVERISTILLRETAINEDSUFFICIENTREGARDTORESTRAINMEFROMMALTREATINGHIMA\ SIMADENOSCRUPLEOFMALTREATINGTHERABBITSTHEMONKEYOREVENTHEDOGWHENBYACCIDENTORTHROUGHAFFECTI\ ONTHEYCAMEINMYWAYBUTMYDISEASEGREWUPONMEFORWHATDISEASEISLIKEALCOHOLANDATLENGTHEVENPLUTOWHO\ WASNOWBECOMINGOLDANDCONSEQUENTLYSOMEWHATPEEVISHEVENPLUTOBEGANTOEXPERIENCETHEEFFECTSOFMYIL\ LTEMPERONENIGHTRETURNINGHOMEMUCHINTOXICATEDFROMONEOFMYHAUNTSABOUTTOWNIFANCIEDTHATTHECATAV\ OIDEDMYPRESENCEISEIZEDHIMWHENINHISFRIGHTATMYVIOLENCEHEINFLICTEDASLIGHTWOUNDUPONMYHANDWITH\ HISTEETHTHEFURYOFADEMONINSTANTLYPOSSESSEDMEIKNEWMYSELFNOLONGERMYORIGINALSOULSEEMEDATONCET\ OTAKEITSFLIGHTFROMMYBODYANDAMORETHANFIENDISHMALEVOLENCEGINNURTUREDTHRILLEDEVERYFIBREOFMYF\ RAMEITOOKFROMMYWAISTCOATPOCKETAPENKNIFEOPENEDITGRASPEDTHEPOORBEASTBYTHETHROATANDDELIBERAT\ ELYCUTONEOFITSEYESFROMTHESOCKETIBLUSHIBURNISHUDDERWHILEIPENTHEDAMNABLEATROCITYWHENREASONR\ ETURNEDWITHTHEMORNINGWHENIHADSLEPTOFFTHEFUMESOFTHENIGHTSDEBAUCHIEXPERIENCEDASENTIMENTHALF\ OFHORRORHALFOFREMORSEFORTHECRIMEOFWHICHIHADBEENGUILTYBUTITWASATBESTAFEEBLEANDEQUIVOCALFEE\ LINGANDTHESOULREMAINEDUNTOUCHEDIAGAINPLUNGEDINTOEXCESSANDSOONDROWNEDINWINEALLMEMORYOFTHED\ EEDINTHEMEANTIMETHECATSLOWLYRECOVEREDTHESOCKETOFTHELOSTEYEPRESENTEDITISTRUEAFRIGHTFULAPPE\ ARANCEBUTHENOLONGERAPPEAREDTOSUFFERANYPAINHEWENTABOUTTHEHOUSEASUSUALBUTASMIGHTBEEXPECTEDF\ LEDINEXTREMETERRORATMYAPPROACHIHADSOMUCHOFMYOLDHEARTLEFTASTOBEATFIRSTGRIEVEDBYTHISEVIDENT\ DISLIKEONTHEPARTOFACREATUREWHICHHADONCESOLOVEDMEBUTTHISFEELINGSOONGAVEPLACETOIRRITATIONAN\ DTHENCAMEASIFTOMYFINALANDIRREVOCABLEOVERTHROWTHESPIRITOFPERVERSENESSOFTHISSPIRITPHILOSOPH\ YTAKESNOACCOUNTYETIAMNOTMORESURETHATMYSOULLIVESTHANIAMTHATPERVERSENESSISONEOFTHEPRIMITIVE\ IMPULSESOFTHEHUMANHEARTONEOFTHEINDIVISIBLEPRIMARYFACULTIESORSENTIMENTSWHICHGIVEDIRECTIONT\ OTHECHARACTEROFMANWHOHASNOTAHUNDREDTIMESFOUNDHIMSELFCOMMITTINGAVILEORASILLYACTIONFORNOOTH\ ERREASONTHANBECAUSEHEKNOWSHESHOULDNOTHAVEWENOTAPERPETUALINCLINATIONINTHETEETHOFOURBESTJUD\ GMENTTOVIOLATETHATWHICHISLAWMERELYBECAUSEWEUNDERSTANDITTOBESUCHTHISSPIRITOFPERVERSENESSIS\ AYCAMETOMYFINALOVERTHROWITWASTHISUNFATHOMABLELONGINGOFTHESOULTOVEXITSELFTOOFFERVIOLENCETO\ ITSOWNNATURETODOWRONGFORTHEWRONGSSAKEONLYTHATURGEDMETOCONTINUEANDFINALLYTOCONSUMMATETHEIN\ JURYIHADINFLICTEDUPONTHEUNOFFENDINGBRUTEONEMORNINGINCOOLBLOODISLIPPEDANOOSEABOUTITSNECKAN\ DHUNGITTOTHELIMBOFATREEHUNGITWITHTHETEARSSTREAMINGFROMMYEYESANDWITHTHEBITTERESTREMORSEATM\ YHEARTHUNGITBECAUSEIKNEWTHATITHADLOVEDMEANDBECAUSEIFELTITHADGIVENMENOREASONOFOFFENCEHUNGI\ TBECAUSEIKNEWTHATINSODOINGIWASCOMMITTINGASINADEADLYSINTHATWOULDSOJEOPARDIZEMYIMMORTALSOUL\ ASTOPLACEITIFSUCHATHINGWEREPOSSIBLEEVENBEYONDTHEREACHOFTHEINFINITEMERCYOFTHEMOSTMERCIFULA\ NDMOSTTERRIBLEGODONTHENIGHTOFTHEDAYONWHICHTHISCRUELDEEDWASDONEIWASAROUSEDFROMSLEEPBYTHECR\ YOFFIRETHECURTAINSOFMYBEDWEREINFLAMESTHEWHOLEHOUSEWASBLAZINGITWASWITHGREATDIFFICULTYTHATM\ YWIFEASERVANTANDMYSELFMADEOURESCAPEFROMTHECONFLAGRATIONTHEDESTRUCTIONWASCOMPLETEMYENTIREW\ ORLDLYWEALTHWASSWALLOWEDUPANDIRESIGNEDMYSELFTHENCEFORWARDTODESPAIRIAMABOVETHEWEAKNESSOFSE\ EKINGTOESTABLISHASEQUENCEOFCAUSEANDEFFECTBETWEENTHEDISASTERANDTHEATROCITYBUTIAMDETAILINGA\ CHAINOFFACTSANDWISHNOTTOLEAVEEVENAPOSSIBLELINKIMPERFECTONTHEDAYSUCCEEDINGTHEFIREIVISITEDT\ HERUINSTHEWALLSWITHONEEXCEPTIONHADFALLENINTHISEXCEPTIONWASFOUNDINACOMPARTMENTWALLNOTVERYT\ HICKWHICHSTOODABOUTTHEMIDDLEOFTHEHOUSEANDAGAINSTWHICHHADRESTEDTHEHEADOFMYBEDTHEPLASTERING\ HADHEREINGREATMEASURERESISTEDTHEACTIONOFTHEFIREAFACTWHICHIATTRIBUTEDTOITSHAVINGBEENRECENT\ LYSPREADABOUTTHISWALLADENSECROWDWERECOLLECTEDANDMANYPERSONSSEEMEDTOBEEXAMININGAPARTICULAR\ PORTIONOFITWITHEVERYMINUTEANDEAGERATTENTIONTHEWORDSSTRANGESINGULARANDOTHERSIMILAREXPRESSI\ ONSEXCITEDMYCURIOSITYIAPPROACHEDANDSAWASIFGRAVENINBASRELIEFUPONTHEWHITESURFACETHEFIGUREOF\ AGIGANTICCATTHEIMPRESSIONWASGIVENWITHANACCURACYTRULYMARVELLOUSTHEREWASAROPEABOUTTHEANIMAL\ SNECKWHENIFIRSTBEHELDTHISAPPARITIONFORICOULDSCARCELYREGARDITASLESSMYWONDERANDMYTERRORWERE\ EXTREMEBUTATLENGTHREFLECTIONCAMETOMYAIDTHECATIREMEMBEREDHADBEENHUNGINAGARDENADJACENTTOTHE\ HOUSEUPONTHEALARMOFFIRETHISGARDENHADBEENIMMEDIATELYFILLEDBYTHECROWDBYSOMEONEOFWHOMTHEANIM\ ALMUSTHAVEBEENCUTFROMTHETREEANDTHROWNTHROUGHANOPENWINDOWINTOMYCHAMBERTHISHADPROBABLYBEEND\ ONEWITHTHEVIEWOFAROUSINGMEFROMSLEEPTHEFALLINGOFOTHERWALLSHADCOMPRESSEDTHEVICTIMOFMYCRUELT\ YINTOTHESUBSTANCEOFTHEFRESHLYSPREADPLASTERTHELIMEOFWHICHHADTHENWITHTHEFLAMESANDTHEAMMONIA\ FROMTHECARCASSACCOMPLISHEDTHEPORTRAITUREASISAWITALTHOUGHITHUSREADILYACCOUNTEDTOMYREASONIF\ NOTALTOGETHERTOMYCONSCIENCEFORTHESTARTLINGFACTJUSTDETAILEDITDIDNOTTHELESSFALLTOMAKEADEEPI\ MPRESSIONUPONMYFANCYFORMONTHSICOULDNOTRIDMYSELFOFTHEPHANTASMOFTHECATANDDURINGTHISPERIODTH\ ERECAMEBACKINTOMYSPIRITAHALFSENTIMENTTHATSEEMEDBUTWASNOTREMORSEIWENTSOFARASTOREGRETTHELOS\ SOFTHEANIMALANDTOLOOKABOUTMEAMONGTHEVILEHAUNTSWHICHINOWHABITUALLYFREQUENTEDFORANOTHERPETO\ FTHESAMESPECIESANDOFSOMEWHATSIMILARAPPEARANCEWITHWHICHTOSUPPLYITSPLACEONENIGHTASISATHALFS\ TUPEFIEDINADENOFMORETHANINFAMYMYATTENTIONWASSUDDENLYDRAWNTOSOMEBLACKOBJECTREPOSINGUPONTHE\ HEADOFONEOFTHEIMMENSEHOGSHEADSOFGINOROFRUMWHICHCONSTITUTEDTHECHIEFFURNITUREOFTHEAPARTMENT\ IHADBEENLOOKINGSTEADILYATTHETOPOFTHISHOGSHEADFORSOMEMINUTESANDWHATNOWCAUSEDMESURPRISEWAST\ HEFACTTHATIHADNOTSOONERPERCEIVEDTHEOBJECTTHEREUPONIAPPROACHEDITANDTOUCHEDITWITHMYHANDITWA\ SABLACKCATAVERYLARGEONEFULLYASLARGEASPLUTOANDCLOSELYRESEMBLINGHIMINEVERYRESPECTBUTONEPLUT\ OHADNOTAWHITEHAIRUPONANYPORTIONOFHISBODYBUTTHISCATHADALARGEALTHOUGHINDEFINITESPLOTCHOFWHI\ TECOVERINGNEARLYTHEWHOLEREGIONOFTHEBREASTUPONMYTOUCHINGHIMHEIMMEDIATELYAROSEPURREDLOUDLYR\ UBBEDAGAINSTMYHANDANDAPPEAREDDELIGHTEDWITHMYNOTICETHISTHENWASTHEVERYCREATUREOFWHICHIWASIN\ SEARCHIATONCEOFFEREDTOPURCHASEITOFTHELANDLORDBUTTHISPERSONMADENOCLAIMTOITKNEWNOTHINGOFITH\ ADNEVERSEENITBEFOREICONTINUEDMYCARESSESANDWHENIPREPAREDTOGOHOMETHEANIMALEVINCEDADISPOSITI\ ONTOACCOMPANYMEIPERMITTEDITTODOSOOCCASIONALLYSTOOPINGANDPATTINGITASIPROCEEDEDWHENITREACHE\ DTHEHOUSEITDOMESTICATEDITSELFATONCEANDBECAMEIMMEDIATELYAGREATFAVORITEWITHMYWIFEFORMYOWNPA\ RTISOONFOUNDADISLIKETOITARISINGWITHINMETHISWASJUSTTHEREVERSEOFWHATIHADANTICIPATEDBUTIKNOW\ NOTHOWORWHYITWASITSEVIDENTFONDNESSFORMYSELFRATHERDISGUSTEDANDA > /* > "For the most wild yet most homely narrative ...". This is from the story > "The Black Cat" by Edgar Allen Poe. > It looks like the lowest the CI gets for sequences of digraphs from > English text is about 0.0064. The figure 0.01 that I gave on the question sheet > appears to be a bit higher than it should have been. > > Let's try the same method on ct7. > The first step is to try to find the block length by finding an i and an m > such that Decimation(sct7,[1,i],m) has a high CI. > */ > for m:=2 to 20 do for> for i:=2 to m do for|for> CoincidenceIndex(Decimation(sct7,[1,i],m)); for|for> end for; for> end for; 0.00535102934788221963674363359650 0.00554015672586661191527221708928 0.00426034288060774047839030900318 0.00532073383561060741497467330694 0.00432347629385044785376799168141 0.00489507512876175882177669944239 0.00582241630276564774381368267831 0.00440486723558904396304858673212 0.00453805976539087250620772326398 0.00412896842385668483793323248756 0.00535927773426227480727212763326 0.00410877959626774401890863118550 0.00457599868079317310467081667148 0.00425993871184950048783169119567 0.00395762048068598754998557117533 0.00939807563213246811367196240770 0.00934213470575072723204296263146 0.00749608413515327813828597001566 0.00453121503692101141194898187514 0.00488550757067203699559931379130 0.00585515029462221227716864324607 0.00579907896981067712775029848200 0.00438585804439462976048341902000 0.00494627323895616578543407811701 0.00382544284983309373553275992300 0.00480007797080967812675129748300 0.00428839453229697132136156526400 0.00460515094661436124850758997101 0.00626833410529566157171530029335 0.00441562451752354485101127065000 0.00463177396943029180176007410838 0.00450825999691215068704647213216 0.00361278369615562760537285780454 0.00463177396943029180176007410838 0.00444650301065308012968967114405 0.00426123205187586845761926817971 0.00601394315483030720907071171378 0.00402206389335784877039760974488 0.00490308741285528231057994330805 0.00352409407798973416072933425266 0.00482647667202941852447713169386 0.00452003370872596338006588523711 0.00425189611583544012870604458745 0.00402206389335784877039760974488 0.00363901018922852983988355167395 0.00594574507617985878855444072835 0.00459866220735785953177257525083 0.00431995540691192865105908584169 0.00455221107395020438498699368265 0.00483091787439613526570048309178 0.00478446674098848011891490152360 0.00422705314009661835748792270532 0.00380899293942772203641768859160 0.00348383500557413600891861761427 0.00510962467484206614641397250093 0.00507026729126481124276660236980 0.00473959768531275833562965004133 0.00484982088729677597134196748415 0.00507026729126481124276660236980 0.00512537889225682006062276109121 0.00429870487737668779278038027005 0.00545604849820887296775971341968 0.00363736566547258197850647561312 0.00589694130614494351060898319096 0.00440892807936070542849269771287 0.00540093689721686414990355469826 0.00512987012987012987012987012987 0.00370129870129870129870129870130 0.00584415584415584415584415584416 0.00441558441558441558441558441558 0.00441558441558441558441558441558 0.00474025974025974025974025974026 0.00590909090909090909090909090909 0.00363636363636363636363636363636 0.00441558441558441558441558441558 0.00383116883116883116883116883117 0.00396103896103896103896103896104 0.00487012987012987012987012987013 0.0108484213676492593146790363609 0.00830465359868322609606464162801 0.00950172078407900643423612150231 0.00546161903336824779290737692653 0.00471345204249588508155020200509 0.00546161903336824779290737692653 0.00418973514888523118360017956008 0.00448900194523417626814304952866 0.00389046835253628609905730959150 0.00441418524614693999700733203651 0.00404010175071075864132874457579 0.00553643573245548406404309441868 0.00463863534340864881041448451294 0.00593395252837977296181630546955 0.00343997248022015823873409012728 0.00498796009631922944616443068456 0.00352597179222566219470244238046 0.00412796697626418988648090815273 0.00472996216030271757825937392501 0.00455796353629170966632266941865 0.00464396284829721362229102167182 0.00395596835225318197454420364637 0.00464396284829721362229102167182 0.00524595803233574131406948744410 0.00472996216030271757825937392501 0.00421396628826969384244926040592 0.00447196422428620571035431716546 0.00689451393676745789421845759874 0.00364424308086279917265832758791 0.00443218753077908007485472274205 0.00344725696838372894710922879937 0.00492465281197675563872746971339 0.00453068058701861518762927213631 0.00443218753077908007485472274205 0.00502314586821629075150201910765 0.00393972224958140451098197577071 0.00413670836206047473653107455924 0.00472766669949768541317837092485 0.00443218753077908007485472274205 0.00374273613710233428543287698217 0.00610656948685117699202206244460 0.00551561114941396631537476607899 0.00619126589275843007186290768381 0.00287451630735212824765063571034 0.00386954118297401879491431730238 0.00508568269762299613045881702598 0.00409065782200110558319513543394 0.00420121614151464897733554449973 0.00530679933665008291873963515754 0.00420121614151464897733554449973 0.00552791597567716970702045328911 0.00386954118297401879491431730238 0.00276395798783858485351022664456 0.00552791597567716970702045328911 0.00353786622443338861249309010503 0.00420121614151464897733554449973 0.00508568269762299613045881702598 0.00353786622443338861249309010503 0.00549931258592675915510561179853 0.00424946881639795025621797275341 0.00562429696287964004499437570304 0.00449943757030371203599550056243 0.00324959380077490313710786151731 0.00449943757030371203599550056243 0.00462442194725659292588426446694 0.00287464066991626046744156980377 0.00449943757030371203599550056243 0.00387451568553930758655168103987 0.00437445319335083114610673665792 0.00412448443944506936632920884890 0.00437445319335083114610673665792 0.00312460942382202224721909761280 0.00424946881639795025621797275341 0.00587426571678540182477190351206 0.00437445319335083114610673665792 0.00378151260504201680672268907563 0.00602240896358543417366946778711 0.00462184873949579831932773109243 0.00490196078431372549019607843137 0.00392156862745098039215686274510 0.00560224089635854341736694677871 0.00546218487394957983193277310924 0.00392156862745098039215686274510 0.00378151260504201680672268907563 0.00434173669467787114845938375350 0.00364145658263305322128851540616 0.00490196078431372549019607843137 0.00434173669467787114845938375350 0.00490196078431372549019607843137 0.00448179271708683473389355742297 0.00546218487394957983193277310924 0.00518207282913165266106442577031 0.00406162464985994397759103641456 0.00652072659524918490917559385189 0.00434715106349945660611706256792 0.00683123738549914609532681260674 0.00434715106349945660611706256792 0.00481291724887439838534389070020 0.00605496040987424312994876571961 0.00419189566837447601304145319050 0.00434715106349945660611706256792 0.00357087408787455364073901568080 0.00465766185374941779226828132278 0.00450240645862443719919267194535 0.00403664027324949541996584381307 0.00388138487812451482689023443565 0.00465766185374941779226828132278 0.00434715106349945660611706256792 0.00372612948299953423381462505822 0.00589970501474926253687315634218 0.00543393882937432075764632820991 0.00512342803912435957149510945505 > /* > I see some 0.093's there. But I should have printed out m and i > at each stage so that I can see which values of m and i > gave thos high values for the coincidence index. > So let's do it again, a bit better this time! > */ > for m:=2 to 20 do for> for i:=2 to m do for|for> "m=",m,"i=",i,CoincidenceIndex(Decimation(sct7,[1,i],m)); for|for> end for; for> end for; m= 2 i= 2 0.00535102934788221963674363359650 m= 3 i= 2 0.00554015672586661191527221708928 m= 3 i= 3 0.00426034288060774047839030900318 m= 4 i= 2 0.00532073383561060741497467330694 m= 4 i= 3 0.00432347629385044785376799168141 m= 4 i= 4 0.00489507512876175882177669944239 m= 5 i= 2 0.00582241630276564774381368267831 m= 5 i= 3 0.00440486723558904396304858673212 m= 5 i= 4 0.00453805976539087250620772326398 m= 5 i= 5 0.00412896842385668483793323248756 m= 6 i= 2 0.00535927773426227480727212763326 m= 6 i= 3 0.00410877959626774401890863118550 m= 6 i= 4 0.00457599868079317310467081667148 m= 6 i= 5 0.00425993871184950048783169119567 m= 6 i= 6 0.00395762048068598754998557117533 m= 7 i= 2 0.00939807563213246811367196240770 m= 7 i= 3 0.00934213470575072723204296263146 m= 7 i= 4 0.00749608413515327813828597001566 m= 7 i= 5 0.00453121503692101141194898187514 m= 7 i= 6 0.00488550757067203699559931379130 m= 7 i= 7 0.00585515029462221227716864324607 m= 8 i= 2 0.00579907896981067712775029848200 m= 8 i= 3 0.00438585804439462976048341902000 m= 8 i= 4 0.00494627323895616578543407811701 m= 8 i= 5 0.00382544284983309373553275992300 m= 8 i= 6 0.00480007797080967812675129748300 m= 8 i= 7 0.00428839453229697132136156526400 m= 8 i= 8 0.00460515094661436124850758997101 m= 9 i= 2 0.00626833410529566157171530029335 m= 9 i= 3 0.00441562451752354485101127065000 m= 9 i= 4 0.00463177396943029180176007410838 m= 9 i= 5 0.00450825999691215068704647213216 m= 9 i= 6 0.00361278369615562760537285780454 m= 9 i= 7 0.00463177396943029180176007410838 m= 9 i= 8 0.00444650301065308012968967114405 m= 9 i= 9 0.00426123205187586845761926817971 m= 10 i= 2 0.00601394315483030720907071171378 m= 10 i= 3 0.00402206389335784877039760974488 m= 10 i= 4 0.00490308741285528231057994330805 m= 10 i= 5 0.00352409407798973416072933425266 m= 10 i= 6 0.00482647667202941852447713169386 m= 10 i= 7 0.00452003370872596338006588523711 m= 10 i= 8 0.00425189611583544012870604458745 m= 10 i= 9 0.00402206389335784877039760974488 m= 10 i= 10 0.00363901018922852983988355167395 m= 11 i= 2 0.00594574507617985878855444072835 m= 11 i= 3 0.00459866220735785953177257525083 m= 11 i= 4 0.00431995540691192865105908584169 m= 11 i= 5 0.00455221107395020438498699368265 m= 11 i= 6 0.00483091787439613526570048309178 m= 11 i= 7 0.00478446674098848011891490152360 m= 11 i= 8 0.00422705314009661835748792270532 m= 11 i= 9 0.00380899293942772203641768859160 m= 11 i= 10 0.00348383500557413600891861761427 m= 11 i= 11 0.00510962467484206614641397250093 m= 12 i= 2 0.00507026729126481124276660236980 m= 12 i= 3 0.00473959768531275833562965004133 m= 12 i= 4 0.00484982088729677597134196748415 m= 12 i= 5 0.00507026729126481124276660236980 m= 12 i= 6 0.00512537889225682006062276109121 m= 12 i= 7 0.00429870487737668779278038027005 m= 12 i= 8 0.00545604849820887296775971341968 m= 12 i= 9 0.00363736566547258197850647561312 m= 12 i= 10 0.00589694130614494351060898319096 m= 12 i= 11 0.00440892807936070542849269771287 m= 12 i= 12 0.00540093689721686414990355469826 m= 13 i= 2 0.00512987012987012987012987012987 m= 13 i= 3 0.00370129870129870129870129870130 m= 13 i= 4 0.00584415584415584415584415584416 m= 13 i= 5 0.00441558441558441558441558441558 m= 13 i= 6 0.00441558441558441558441558441558 m= 13 i= 7 0.00474025974025974025974025974026 m= 13 i= 8 0.00590909090909090909090909090909 m= 13 i= 9 0.00363636363636363636363636363636 m= 13 i= 10 0.00441558441558441558441558441558 m= 13 i= 11 0.00383116883116883116883116883117 m= 13 i= 12 0.00396103896103896103896103896104 m= 13 i= 13 0.00487012987012987012987012987013 m= 14 i= 2 0.0108484213676492593146790363609 m= 14 i= 3 0.00830465359868322609606464162801 m= 14 i= 4 0.00950172078407900643423612150231 m= 14 i= 5 0.00546161903336824779290737692653 m= 14 i= 6 0.00471345204249588508155020200509 m= 14 i= 7 0.00546161903336824779290737692653 m= 14 i= 8 0.00418973514888523118360017956008 m= 14 i= 9 0.00448900194523417626814304952866 m= 14 i= 10 0.00389046835253628609905730959150 m= 14 i= 11 0.00441418524614693999700733203651 m= 14 i= 12 0.00404010175071075864132874457579 m= 14 i= 13 0.00553643573245548406404309441868 m= 14 i= 14 0.00463863534340864881041448451294 m= 15 i= 2 0.00593395252837977296181630546955 m= 15 i= 3 0.00343997248022015823873409012728 m= 15 i= 4 0.00498796009631922944616443068456 m= 15 i= 5 0.00352597179222566219470244238046 m= 15 i= 6 0.00412796697626418988648090815273 m= 15 i= 7 0.00472996216030271757825937392501 m= 15 i= 8 0.00455796353629170966632266941865 m= 15 i= 9 0.00464396284829721362229102167182 m= 15 i= 10 0.00395596835225318197454420364637 m= 15 i= 11 0.00464396284829721362229102167182 m= 15 i= 12 0.00524595803233574131406948744410 m= 15 i= 13 0.00472996216030271757825937392501 m= 15 i= 14 0.00421396628826969384244926040592 m= 15 i= 15 0.00447196422428620571035431716546 m= 16 i= 2 0.00689451393676745789421845759874 m= 16 i= 3 0.00364424308086279917265832758791 m= 16 i= 4 0.00443218753077908007485472274205 m= 16 i= 5 0.00344725696838372894710922879937 m= 16 i= 6 0.00492465281197675563872746971339 m= 16 i= 7 0.00453068058701861518762927213631 m= 16 i= 8 0.00443218753077908007485472274205 m= 16 i= 9 0.00502314586821629075150201910765 m= 16 i= 10 0.00393972224958140451098197577071 m= 16 i= 11 0.00413670836206047473653107455924 m= 16 i= 12 0.00472766669949768541317837092485 m= 16 i= 13 0.00443218753077908007485472274205 m= 16 i= 14 0.00374273613710233428543287698217 m= 16 i= 15 0.00610656948685117699202206244460 m= 16 i= 16 0.00551561114941396631537476607899 m= 17 i= 2 0.00619126589275843007186290768381 m= 17 i= 3 0.00287451630735212824765063571034 m= 17 i= 4 0.00386954118297401879491431730238 m= 17 i= 5 0.00508568269762299613045881702598 m= 17 i= 6 0.00409065782200110558319513543394 m= 17 i= 7 0.00420121614151464897733554449973 m= 17 i= 8 0.00530679933665008291873963515754 m= 17 i= 9 0.00420121614151464897733554449973 m= 17 i= 10 0.00552791597567716970702045328911 m= 17 i= 11 0.00386954118297401879491431730238 m= 17 i= 12 0.00276395798783858485351022664456 m= 17 i= 13 0.00552791597567716970702045328911 m= 17 i= 14 0.00353786622443338861249309010503 m= 17 i= 15 0.00420121614151464897733554449973 m= 17 i= 16 0.00508568269762299613045881702598 m= 17 i= 17 0.00353786622443338861249309010503 m= 18 i= 2 0.00549931258592675915510561179853 m= 18 i= 3 0.00424946881639795025621797275341 m= 18 i= 4 0.00562429696287964004499437570304 m= 18 i= 5 0.00449943757030371203599550056243 m= 18 i= 6 0.00324959380077490313710786151731 m= 18 i= 7 0.00449943757030371203599550056243 m= 18 i= 8 0.00462442194725659292588426446694 m= 18 i= 9 0.00287464066991626046744156980377 m= 18 i= 10 0.00449943757030371203599550056243 m= 18 i= 11 0.00387451568553930758655168103987 m= 18 i= 12 0.00437445319335083114610673665792 m= 18 i= 13 0.00412448443944506936632920884890 m= 18 i= 14 0.00437445319335083114610673665792 m= 18 i= 15 0.00312460942382202224721909761280 m= 18 i= 16 0.00424946881639795025621797275341 m= 18 i= 17 0.00587426571678540182477190351206 m= 18 i= 18 0.00437445319335083114610673665792 m= 19 i= 2 0.00378151260504201680672268907563 m= 19 i= 3 0.00602240896358543417366946778711 m= 19 i= 4 0.00462184873949579831932773109243 m= 19 i= 5 0.00490196078431372549019607843137 m= 19 i= 6 0.00392156862745098039215686274510 m= 19 i= 7 0.00560224089635854341736694677871 m= 19 i= 8 0.00546218487394957983193277310924 m= 19 i= 9 0.00392156862745098039215686274510 m= 19 i= 10 0.00378151260504201680672268907563 m= 19 i= 11 0.00434173669467787114845938375350 m= 19 i= 12 0.00364145658263305322128851540616 m= 19 i= 13 0.00490196078431372549019607843137 m= 19 i= 14 0.00434173669467787114845938375350 m= 19 i= 15 0.00490196078431372549019607843137 m= 19 i= 16 0.00448179271708683473389355742297 m= 19 i= 17 0.00546218487394957983193277310924 m= 19 i= 18 0.00518207282913165266106442577031 m= 19 i= 19 0.00406162464985994397759103641456 m= 20 i= 2 0.00652072659524918490917559385189 m= 20 i= 3 0.00434715106349945660611706256792 m= 20 i= 4 0.00683123738549914609532681260674 m= 20 i= 5 0.00434715106349945660611706256792 m= 20 i= 6 0.00481291724887439838534389070020 m= 20 i= 7 0.00605496040987424312994876571961 m= 20 i= 8 0.00419189566837447601304145319050 m= 20 i= 9 0.00434715106349945660611706256792 m= 20 i= 10 0.00357087408787455364073901568080 m= 20 i= 11 0.00465766185374941779226828132278 m= 20 i= 12 0.00450240645862443719919267194535 m= 20 i= 13 0.00403664027324949541996584381307 m= 20 i= 14 0.00388138487812451482689023443565 m= 20 i= 15 0.00465766185374941779226828132278 m= 20 i= 16 0.00434715106349945660611706256792 m= 20 i= 17 0.00372612948299953423381462505822 m= 20 i= 18 0.00589970501474926253687315634218 m= 20 i= 19 0.00543393882937432075764632820991 m= 20 i= 20 0.00512342803912435957149510945505 > /* > So I think that the block length m is 7. Note that this also causes there > to be high values when m=14. > */ > for j:=1 to 6 do for> for i:=j+1 to 7 do for|for> j,i,": CI=",CoincidenceIndex(Decimation(sct7,[j,i],7)); for|for> end for; for> end for; 1 2 : CI= 0.00939807563213246811367196240770 1 3 : CI= 0.00934213470575072723204296263146 1 4 : CI= 0.00749608413515327813828597001566 1 5 : CI= 0.00453121503692101141194898187514 1 6 : CI= 0.00488550757067203699559931379130 1 7 : CI= 0.00585515029462221227716864324607 2 3 : CI= 0.00738420228238979637502797046319 2 4 : CI= 0.00842843290818229283210263295293 2 5 : CI= 0.00551950473633176698739464458865 2 6 : CI= 0.00443798015961810994256731558141 2 7 : CI= 0.00520250615350190199149697918997 3 4 : CI= 0.00509062430073842022823897963750 3 5 : CI= 0.00427015738047288729768031625270 3 6 : CI= 0.00639591258297904079958230774968 3 7 : CI= 0.0101439546505556798687252927575 4 5 : CI= 0.0109457745953606325054076228836 4 6 : CI= 0.00484821361975087640784664727381 4 7 : CI= 0.00501603639889609905273364660252 5 6 : CI= 0.00413962855224882524054598344148 5 7 : CI= 0.00410233460132766465279331692400 6 7 : CI= 0.00846572685910345341985529947043 > /* > Likely adjacencies: (1,2),(1,3),(2,4),(3,7),(4,5),(6,7). > This gives the order 6731245 or its reverse. > */ > T2:=TranspositionCryptosystem(7); > key2:=T2![6,7,3,1,2,4,5]; > Enciphering(key2,Encoding(T2,sct7)); NOWTHISISTHENEXTTALEANDITTELLSHOWTHECAMELGOTHISBIGHUMPINTHEBEGINNINGOFYEARSWHENTHEWORLDWA\ SSONEWANDALLANDTHEANIMALSWEREJUSTBEGINNINGTOWORKFORMANTHEREWASACAMELANDHELIVEDINTHEMIDDLE\ OFAHOWLINGDESERTBECAUSEHEDIDNOTWANTTOWORKANDBESIDESHEWASAHOWLERHIMSELFSOHEATESTICKSANDTHO\ RNSANDTAMARISKSANDMILKWEEDANDPRICKLESMOSTSCRUCIATINGIDLEANDWHENANYBODYSPOKETOHIMHESAIDHUM\ PHJUSTHUMPHANDNOMOREPRESENTLYTHEHORSECAMETOHIMONMONDAYMORNINGWITHASADDLEONHISBACKANDABITI\ NHISMOUTHANDSAIDCAMELOCAMELCOMEOUTANDTROTLIKETHERESTOFUSHUMPHSAIDTHECAMELANDTHEHORSEWENTA\ WAYANDTOLDTHEMANPRESENTLYTHEDOGCAMETOHIMWITHASTICKINHISMOUTHANDSAIDCAMELOCAMELCOMEANDFETC\ HANDCARRYLIKETHERESTOFUSHUMPHSAIDTHECAMELANDTHEDOGWENTAWAYANDTOLDTHEMANPRESENTLYTHEOXCAME\ TOHIMWITHTHEYOKEONHISNECKANDSAIDCAMELOCAMELCOMEANDPLOUGHLIKETHERESTOFUSHUMPHSAIDTHECAMELA\ NDTHEOXWENTAWAYANDTOLDTHEMANATTHEENDOFTHEDAYTHEMANCALLEDTHEHORSEANDTHEDOGANDTHEOXTOGETHER\ ANDSAIDTHREEOTHREEIMVERYSORRYFORYOUWITHTHEWORLDSONEWANDALLBUTTHATHUMPHTHINGINTHEDESERTCAN\ TWORKORHEWOULDHAVEBEENHEREBYNOWSOIAMGOINGTOLEAVEHIMALONEANDYOUMUSTWORKDOUBLETIMETOMAKEUPF\ ORITTHATMADETHETHREEVERYANGRYWITHTHEWORLDSONEWANDALLANDTHEYHELDAPALAVERANDANINDABAANDAPUN\ CHAYETANDAPOWWOWONTHEEDGEOFTHEDESERTANDTHECAMELCAMECHEWINGONMILKWEEDMOSTSCRUCIATINGIDLEAN\ DLAUGHEDATTHEMTHENHESAIDHUMPHANDWENTAWAYAGAINPRESENTLYTHERECAMEALONGTHEDJINNINCHARGEOFALL\ DESERTSROLLINGINACLOUDOFDUSTDJINNSALWAYSTRAVELTHATWAYBECAUSEITISMAGICANDHESTOPPEDTOPALAVE\ RANDPOWPOWWITHTHETHREEDJINNOFALLDESERTSSAIDTHEHORSEISITRIGHTFORANYONETOBEIDLEWITHTHEWORLD\ SONEWANDALLCERTAINLYNOTSAIDTHEDJINNWELLSAIDTHEHORSETHERESATHINGINTHEMIDDLEOFYOURHOWLINGDE\ SERTANDHESAHOWLERHIMSELFWITHALONGNECKANDLONGLEGSANDHEHASNTDONEASTROKEOFWORKSINCEMONDAYMOR\ NINGHEWONTTROTWHEWSAIDTHEDJINNWHISTLINGTHATSMYCAMELFORALLTHEGOLDINARABIAWHATDOESHESAYABOU\ TITHESAYSHUMPHSAIDTHEDOGANDHEWONTFETCHANDCARRYDOESHESAYANYTHINGELSEONLYHUMPHANDHEWONTPLOU\ GHSAIDTHEOXVERYGOODSAIDTHEDJINNILLHUMPHHIMIFYOUWILLKINDLYWAITAMINUTETHEDJINNROLLEDHIMSELF\ UPINHISDUSTCLOAKANDTOOKABEARINGACROSSTHEDESERTANDFOUNDTHECAMELMOSTSCRUCIATINGLYIDLELOOKIN\ GATHISOWNREFLECTIONINAPOOLOFWATERMYLONGANDBUBBLINGFRIENDSAIDTHEDJINNWHATSTHISIHEAROFYOURD\ OINGNOWORKWITHTHEWORLDSONEWANDALLHUMPHSAIDTHECAMELTHEDJINNSATDOWNWITHHISCHININHISHANDANDB\ EGANTOTHINKAGREATMAGICWHILETHECAMELLOOKEDATHISOWNREFLECTIONINTHEPOOLOFW > /* How the Camel got his Hump" by Rudyard Kipling. */ > /* The substitution ciphers (ct1, ct4) are more time-consuming. */ > S:=SubstitutionCryptosystem(); > t1:=Encoding(S,sct1); > fk:=S!freqkey(t1); > fk; KHRZMWLYEJXNUCTIBGVPDSQAFO > p1:=String(Enciphering(fk,t1)); > PolygraphFrequencyDistribution(p1,3,0.01); {@ OND, TAE, AES @} [ 0.0143482490272373540856031128405, 0.0277237354085603112840466926070, 0.0158073929961089494163424124514 ] > swap("A","H",~fk); > p1:=String(Enciphering(fk,t1)); > PolygraphFrequencyDistribution(p1,3,0.01); {@ THE, OND, HES @} [ 0.0277237354085603112840466926070, 0.0143482490272373540856031128405, 0.0158073929961089494163424124514 ] > swap("A","O",~fk); > swap("S","R",~fk); > p1:=String(Enciphering(fk,t1)); > PolygraphFrequencyDistribution(p1,3,0.01); {@ THE, HER, AND @} [ 0.0277237354085603112840466926070, 0.0158073929961089494163424124514, 0.0143482490272373540856031128405 ] > p1[1..70]; STUAOTERRSYLPGILDANDNEARLPDARKINTHELAOTEVENSNCIFTHEILDPEARANDTHEONIUUA > /* There are words! The NSN I can see suggests to me that S should > be swapped with some vowel. Maybe the first word is "It"*/ > swap("S","I",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ITUAOTERRIYLPGSLDANDNEARLPDARKSNTHELAOTEVENINCSFTHESLDPEARANDTHEONSUUA > swap("S","O",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ITUASTERRIYLPGOLDANDNEARLPDARKONTHELASTEVENINCOFTHEOLDPEARANDTHESNOUUA > swap("P","Y",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ITUASTERRIPLYGOLDANDNEARLYDARKONTHELASTEVENINCOFTHEOLDYEARANDTHESNOUUA > swap("U","W",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ITWASTERRIPLYGOLDANDNEARLYDARKONTHELASTEVENINCOFTHEOLDYEARANDTHESNOWWA > swap("P","B",~fk); > swap("G","C",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ITWASTERRIBLYCOLDANDNEARLYDARKONTHELASTEVENINGOFTHEOLDYEARANDTHESNOWWA > p1[1..300]; ITWASTERRIBLYCOLDANDNEARLYDARKONTHELASTEVENINGOFTHEOLDYEARANDTHESNOWWASFALLINGFASTINTHECO\ LDANDTHEDARKNESSAPOORLITTLEGIRLWITHBAREHEADANDNAKEDFEETROAUEDTHROMGHTHESTREETSITISTRMESHE\ HADONAPAIROFSLIPPERSWHENSHELEFTHOUEBMTTHEYWERENOTOFUMCHMSETHEYWEREVERYLARGESOLARGEINDEEDT\ HATTHEYHADBELONGEDTOHERUOTHERANDT > swap("M","U",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ITWASTERRIBLYCOLDANDNEARLYDARKONTHELASTEVENINGOFTHEOLDYEARANDTHESNOWWASFALLINGFASTINTHECO\ LDANDTHEDARKNESSAPOORLITTLEGIRLWITHBAREHEADANDNAKEDFEETROAMEDTHROUGHTHESTREETSITISTRUESHE\ HADONAPAIROFSLIPPERSWHENSHELEFTHOMEBUTTHEYWERENOTOFMUCHUSETHEYWEREVERYLARGESOLARGEINDEEDT\ HATTHEYHADBELONGEDTOHERMOTHERANDT > p1; ITWASTERRIBLYCOLDANDNEARLYDARKONTHELASTEVENINGOFTHEOLDYEARANDTHESNOWWASFALLINGFASTINTHECO\ LDANDTHEDARKNESSAPOORLITTLEGIRLWITHBAREHEADANDNAKEDFEETROAMEDTHROUGHTHESTREETSITISTRUESHE\ HADONAPAIROFSLIPPERSWHENSHELEFTHOMEBUTTHEYWERENOTOFMUCHUSETHEYWEREVERYLARGESOLARGEINDEEDT\ HATTHEYHADBELONGEDTOHERMOTHERANDTHEPOORLITTLECREATUREHADLOSTTHEMINRUNNINGACROSSTHESTREETT\ OAVOIDTWOCARRIAGESTHATWEREROLLINGALONGATATERRIBLERATEONEOFTHESLIPPERSSHECOULDNOTFINDANDAB\ OYSEIXEDUPONTHEOTHERANDRANAWAYWITHITSAYINGTHATHECOULDUSEITASACRADLEWHENHEHADCHILDRENOFHIS\ OWNSOTHELITTLEGIRLWENTONWITHHERLITTLENAKEDFEETWHICHWEREQUITEREDANDBLUEWITHTHECOLDINANOLDA\ PRONSHECARRIEDANUMBEROFMATCHESANDHADABUNDLEOFTHEMINHERHANDSNOONEHADBOUGHTANYTHINGOFHERTHE\ WHOLEDAYNORHADANYONEGIVENHEREVENAPENNYSHIVERINGWITHCOLDANDHUNGERSHECREPTALONGPOORLITTLECH\ ILDSHELOOKEDTHEPICTUREOFMISERYTHESNOWFLAKESFELLONHERLONGFAIRHAIRWHICHHUNGINCURLSONHERSHOU\ LDERSBUTSHEREGARDEDTHEMNOTLIGHTSWERESHININGFROMEVERYWINDOWANDTHEREWASASAVORYSMELLOFROASTG\ OOSEFORITWASNEWYEARSEVEYESSHEREMEMBEREDTHATINACORNERBETWEENTWOHOUSESONEOFWHICHPROJECTEDBE\ YONDTHEOTHERSHESANKDOWNANDHUDDLEDHERSELFTOGETHERSHEHADDRAWNHERLITTLEFEETUNDERHERBUTSHECOU\ LDNOTKEEPOFFTHECOLDANDSHEDAREDNOTGOHOMEFORSHEHADSOLDNOMATCHESANDCOULDNOTTAKEHOMEEVENAPENN\ YOFMONEYHERFATHERWOULDCERTAINLYBEATHERBESIDESITWASALMOSTASCOLDATHOMEASHEREFORTHEYHADONLYT\ HEROOFTOCOVERTHEMTHROUGHWHICHTHEWINDHOWLEDALTHOUGHTHELARGESTHOLESHADBEENSTOPPEDUPWITHSTRA\ WANDRAGSHERLITTLEHANDSWEREALMOSTFROXENWITHTHECOLDAHPERHAPSABURNINGMATCHMIGHTBESOMEGOODIFS\ HECOULDDRAWITFROMTHEBUNDLEANDSTRIKEITAGAINSTTHEWALLJUSTTOWARMHERFINGERSSHEDREWONEOUTSCRAT\ CHHOWITSPUTTEREDASITBURNTITGAVEAWARMBRIGHTLIGHTLIKEALITTLECANDLEASSHEHELDHERHANDOVERITITW\ ASREALLYAWONDERFULLIGHTITSEEMEDTOTHELITTLEGIRLTHATSHEWASSITTINGBYALARGEIRONSTOVEWITHPOLIS\ HEDBRASSFEETANDABRASSORNAMENTHOWTHEFIREBURNEDANDSEEMEDSOBEAUTIFULLYWARMTHATTHECHILDSTRETC\ HEDOUTHERFEETASIFTOWARMTHEMWHENLOTHEFLAMEOFTHEMATCHWENTOUTTHESTOVEVANISHEDANDSHEHADONLYTH\ EREMAINSOFTHEHALFBURNTMATCHINHERHANDSHERUBBEDANOTHERMATCHONTHEWALLITBURSTINTOAFLAMEANDWHE\ REITSLIGHTFELLUPONTHEWALLITBECAMEASTRANSPARENTASAVEILANDSHECOULDSEEINTOTHEROOMTHETABLEWAS\ COVEREDWITHASNOWYWHITETABLECLOTHONWHICHSTOODASPLENDIDDINNERSERVICEANDASTEAMINGROASTGOOSES\ TUFFEDWITHAPPLESANDDRIEDPLUMSANDWHATWASSTILLMOREWONDERFULTHEGOOSEJUMPEDDOWNFROMTHEDISHAND\ WADDLEDACROSSTHEFLOORWITHAKNIFEANDFORKINITSBREASTTOTHELITTLEGIRLTHENTHEMATCHWENTOUTANDTHE\ REREMAINEDNOTHINGBUTTHETHICKDAMPCOLDWALLBEFOREHERSHELIGHTEDANOTHERMATCHANDTHENSHEFOUNDHER\ SELFSITTINGUNDERABEAUTIFULCHRISTMASTREEITWASLARGERANDMOREBEAUTIFULLYDECORATEDTHANTHEONEWH\ ICHSHEHADSEENTHROUGHTHEGLASSDOORATTHERICHMERCHANTSTHOUSANDSOFTAPERSWEREBURNINGUPONTHEGREE\ NBRANCHESANDCOLOREDPICTURESLIKETHOSESHEHADSEENINTHESHOWWINDOWSLOOKEDDOWNUPONITALLTHELITTL\ EONESTRETCHEDOUTHERHANDTOWARDSTHEMANDTHEMATCHWENTOUTTHECHRISTMASLIGHTSROSEHIGHERANDHIGHER\ TILLTHEYLOOKEDTOHERLIKETHESTARSINTHESKYTHENSHESAWASTARFALLLEAVINGBEHINDITABRIGHTSTREAKOFF\ IRESOMEONEISDYINGTHOUGHTTHELITTLEGIRLFORHEROLDGRANDMOTHERTHEONLYONEWHOHADEVERLOVEDHERANDW\ HOWASNOWDEADHADTOLDHERTHATWHENASTARFALLSASOULWASGOINGUPTOGODSHEAGAINRUBBEDAMATCHONTHEWALL\ ANDTHELIGHTSHONEROUNDHERINTHEBRIGHTNESSSTOODHEROLDGRANDMOTHERCLEARANDSHININGYETMILDANDLOV\ INGINHERAPPEARANCEGRANDMOTHERCRIEDTHELITTLEONEOTAKEMEWITHYOUIKNOWYOUWILLGOAWAYWHENTHEMATC\ HBURNSOUTYOUWILLVANISHLIKETHEWARMSTOVETHEROASTGOOSEANDTHELARGEGLORIOUSCHRISTMASTREEANDSHE\ MADEHASTETOLIGHTTHEWHOLEBUNDLEOFMATCHESFORSHEWISHEDTOKEEPHERGRANDMOTHERTHEREANDTHEMATCHES\ GLOWEDWITHALIGHTTHATWASBRIGHTERTHANTHENOONDAYANDHERGRANDMOTHERHADNEVERAPPEAREDSOLARGEORSO\ BEAUTIFULSHETOOKTHELITTLEGIRLINHERARMSANDTHEYBOTHFLEWUPWARDSINBRIGHTNESSANDJOYFARABOVETHE\ EARTHWHERETHEREWASNEITHERCOLDNORHUNGERNORPAINFORTHEYWEREWITHGODINTHEDAWNOFMORNINGTHERELAY\ THEPOORLITTLEONEWITHPALECHEEKSANDSMILINGMOUTHLEANINGAGAINSTTHEWALLSHEHADBEENFROXENTODEATH\ ONTHELASTEVENINGOFTHEYEARANDTHENEWYEARSSUNROSEANDSHONEUPONALITTLECORPSETHECHILDSTILLSATIN\ THESTIFFNESSOFDEATHHOLDINGTHEMATCHESINHERHANDONEBUNDLEOFWHICHWASBURNTSHETRIEDTOWARMHERSEL\ FSAIDSOMENOONEIMAGINEDWHATBEAUTIFULTHINGSSHEHADSEENNORINTOWHATGLORYSHEHADENTEREDWITHHERGR\ ANDMOTHERONNEWYEARSDAY > swap("X","Z",~fk); > p1:=String(Enciphering(fk,t1)); > p1; ITWASTERRIBLYCOLDANDNEARLYDARKONTHELASTEVENINGOFTHEOLDYEARANDTHESNOWWASFALLINGFASTINTHECO\ LDANDTHEDARKNESSAPOORLITTLEGIRLWITHBAREHEADANDNAKEDFEETROAMEDTHROUGHTHESTREETSITISTRUESHE\ HADONAPAIROFSLIPPERSWHENSHELEFTHOMEBUTTHEYWERENOTOFMUCHUSETHEYWEREVERYLARGESOLARGEINDEEDT\ HATTHEYHADBELONGEDTOHERMOTHERANDTHEPOORLITTLECREATUREHADLOSTTHEMINRUNNINGACROSSTHESTREETT\ OAVOIDTWOCARRIAGESTHATWEREROLLINGALONGATATERRIBLERATEONEOFTHESLIPPERSSHECOULDNOTFINDANDAB\ OYSEIZEDUPONTHEOTHERANDRANAWAYWITHITSAYINGTHATHECOULDUSEITASACRADLEWHENHEHADCHILDRENOFHIS\ OWNSOTHELITTLEGIRLWENTONWITHHERLITTLENAKEDFEETWHICHWEREQUITEREDANDBLUEWITHTHECOLDINANOLDA\ PRONSHECARRIEDANUMBEROFMATCHESANDHADABUNDLEOFTHEMINHERHANDSNOONEHADBOUGHTANYTHINGOFHERTHE\ WHOLEDAYNORHADANYONEGIVENHEREVENAPENNYSHIVERINGWITHCOLDANDHUNGERSHECREPTALONGPOORLITTLECH\ ILDSHELOOKEDTHEPICTUREOFMISERYTHESNOWFLAKESFELLONHERLONGFAIRHAIRWHICHHUNGINCURLSONHERSHOU\ LDERSBUTSHEREGARDEDTHEMNOTLIGHTSWERESHININGFROMEVERYWINDOWANDTHEREWASASAVORYSMELLOFROASTG\ OOSEFORITWASNEWYEARSEVEYESSHEREMEMBEREDTHATINACORNERBETWEENTWOHOUSESONEOFWHICHPROJECTEDBE\ YONDTHEOTHERSHESANKDOWNANDHUDDLEDHERSELFTOGETHERSHEHADDRAWNHERLITTLEFEETUNDERHERBUTSHECOU\ LDNOTKEEPOFFTHECOLDANDSHEDAREDNOTGOHOMEFORSHEHADSOLDNOMATCHESANDCOULDNOTTAKEHOMEEVENAPENN\ YOFMONEYHERFATHERWOULDCERTAINLYBEATHERBESIDESITWASALMOSTASCOLDATHOMEASHEREFORTHEYHADONLYT\ HEROOFTOCOVERTHEMTHROUGHWHICHTHEWINDHOWLEDALTHOUGHTHELARGESTHOLESHADBEENSTOPPEDUPWITHSTRA\ WANDRAGSHERLITTLEHANDSWEREALMOSTFROZENWITHTHECOLDAHPERHAPSABURNINGMATCHMIGHTBESOMEGOODIFS\ HECOULDDRAWITFROMTHEBUNDLEANDSTRIKEITAGAINSTTHEWALLJUSTTOWARMHERFINGERSSHEDREWONEOUTSCRAT\ CHHOWITSPUTTEREDASITBURNTITGAVEAWARMBRIGHTLIGHTLIKEALITTLECANDLEASSHEHELDHERHANDOVERITITW\ ASREALLYAWONDERFULLIGHTITSEEMEDTOTHELITTLEGIRLTHATSHEWASSITTINGBYALARGEIRONSTOVEWITHPOLIS\ HEDBRASSFEETANDABRASSORNAMENTHOWTHEFIREBURNEDANDSEEMEDSOBEAUTIFULLYWARMTHATTHECHILDSTRETC\ HEDOUTHERFEETASIFTOWARMTHEMWHENLOTHEFLAMEOFTHEMATCHWENTOUTTHESTOVEVANISHEDANDSHEHADONLYTH\ EREMAINSOFTHEHALFBURNTMATCHINHERHANDSHERUBBEDANOTHERMATCHONTHEWALLITBURSTINTOAFLAMEANDWHE\ REITSLIGHTFELLUPONTHEWALLITBECAMEASTRANSPARENTASAVEILANDSHECOULDSEEINTOTHEROOMTHETABLEWAS\ COVEREDWITHASNOWYWHITETABLECLOTHONWHICHSTOODASPLENDIDDINNERSERVICEANDASTEAMINGROASTGOOSES\ TUFFEDWITHAPPLESANDDRIEDPLUMSANDWHATWASSTILLMOREWONDERFULTHEGOOSEJUMPEDDOWNFROMTHEDISHAND\ WADDLEDACROSSTHEFLOORWITHAKNIFEANDFORKINITSBREASTTOTHELITTLEGIRLTHENTHEMATCHWENTOUTANDTHE\ REREMAINEDNOTHINGBUTTHETHICKDAMPCOLDWALLBEFOREHERSHELIGHTEDANOTHERMATCHANDTHENSHEFOUNDHER\ SELFSITTINGUNDERABEAUTIFULCHRISTMASTREEITWASLARGERANDMOREBEAUTIFULLYDECORATEDTHANTHEONEWH\ ICHSHEHADSEENTHROUGHTHEGLASSDOORATTHERICHMERCHANTSTHOUSANDSOFTAPERSWEREBURNINGUPONTHEGREE\ NBRANCHESANDCOLOREDPICTURESLIKETHOSESHEHADSEENINTHESHOWWINDOWSLOOKEDDOWNUPONITALLTHELITTL\ EONESTRETCHEDOUTHERHANDTOWARDSTHEMANDTHEMATCHWENTOUTTHECHRISTMASLIGHTSROSEHIGHERANDHIGHER\ TILLTHEYLOOKEDTOHERLIKETHESTARSINTHESKYTHENSHESAWASTARFALLLEAVINGBEHINDITABRIGHTSTREAKOFF\ IRESOMEONEISDYINGTHOUGHTTHELITTLEGIRLFORHEROLDGRANDMOTHERTHEONLYONEWHOHADEVERLOVEDHERANDW\ HOWASNOWDEADHADTOLDHERTHATWHENASTARFALLSASOULWASGOINGUPTOGODSHEAGAINRUBBEDAMATCHONTHEWALL\ ANDTHELIGHTSHONEROUNDHERINTHEBRIGHTNESSSTOODHEROLDGRANDMOTHERCLEARANDSHININGYETMILDANDLOV\ INGINHERAPPEARANCEGRANDMOTHERCRIEDTHELITTLEONEOTAKEMEWITHYOUIKNOWYOUWILLGOAWAYWHENTHEMATC\ HBURNSOUTYOUWILLVANISHLIKETHEWARMSTOVETHEROASTGOOSEANDTHELARGEGLORIOUSCHRISTMASTREEANDSHE\ MADEHASTETOLIGHTTHEWHOLEBUNDLEOFMATCHESFORSHEWISHEDTOKEEPHERGRANDMOTHERTHEREANDTHEMATCHES\ GLOWEDWITHALIGHTTHATWASBRIGHTERTHANTHENOONDAYANDHERGRANDMOTHERHADNEVERAPPEAREDSOLARGEORSO\ BEAUTIFULSHETOOKTHELITTLEGIRLINHERARMSANDTHEYBOTHFLEWUPWARDSINBRIGHTNESSANDJOYFARABOVETHE\ EARTHWHERETHEREWASNEITHERCOLDNORHUNGERNORPAINFORTHEYWEREWITHGODINTHEDAWNOFMORNINGTHERELAY\ THEPOORLITTLEONEWITHPALECHEEKSANDSMILINGMOUTHLEANINGAGAINSTTHEWALLSHEHADBEENFROZENTODEATH\ ONTHELASTEVENINGOFTHEYEARANDTHENEWYEARSSUNROSEANDSHONEUPONALITTLECORPSETHECHILDSTILLSATIN\ THESTIFFNESSOFDEATHHOLDINGTHEMATCHESINHERHANDONEBUNDLEOFWHICHWASBURNTSHETRIEDTOWARMHERSEL\ FSAIDSOMENOONEIMAGINEDWHATBEAUTIFULTHINGSSHEHADSEENNORINTOWHATGLORYSHEHADENTEREDWITHHERGR\ ANDMOTHERONNEWYEARSDAY > /* I can't bear to read it all to see if there are still things to fix! */ > t1:=Encoding(S,sct4); > fk:=S!freqkey(t1); > p1:=String(Enciphering(fk,t1)); > p1[1..70]; ODUWVAHWEORRIKEDPRAFBARTUGOLYUTTNERECERESAFECNASOIDSNEWOFEPRAFSBOIHCNI > PolygraphFrequencyDistribution(p1,3,0.01); {@ TNE @} [ 0.0245567957977675640183847669074 ] > swap("N","H",~fk); > p1:=String(Enciphering(fk,t1)); > PolygraphFrequencyDistribution(p1,3,0.009); {@ ING, THE @} [ 0.00998030203545633617859487852921, 0.0245567957977675640183847669074 ] > PolygraphFrequencyDistribution(p1,3,0.008); {@ ING, THE, OND @} [ 0.00998030203545633617859487852921, 0.0245567957977675640183847669074, 0.00814182534471437951411687458963 ] > swap("A","O",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ADUWVONWEARRIKEDPROFBORTUGALYUTTHERECERESOFECHOSAIDSHEWAFEPROFSBAINCHIWHISALFOSTTHESAFETH\ INGATALLEKENTSSHECASWALLEDTHEBORTUGUESEANDSHELAIDEGGSCASVILLEDANDWOOVEDANDTHERECASANENDOP\ HERYUTTHEDUWVLINGSCHIWHWREBTPORTHPROFTHEEGGSCEREALSOWALLEDBORTUGUESEANDAYOUTTHATTHEREFAMY\ ESOFEJUESTIONYUTOPALLTHEPAFILMONE > /* Maybe THERECERE should be THEREWERE */ > swap("C","W",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ADUCVONCEARRIKEDPROFBORTUGALYUTTHEREWERESOFEWHOSAIDSHECAFEPROFSBAINWHICHISALFOSTTHESAFETH\ INGATALLEKENTSSHEWASCALLEDTHEBORTUGUESEANDSHELAIDEGGSWASVILLEDANDCOOVEDANDTHEREWASANENDOP\ HERYUTTHEDUCVLINGSWHICHCREBTPORTHPROFTHEEGGSWEREALSOCALLEDBORTUGUESEANDAYOUTTHATTHEREFAMY\ ESOFEJUESTIONYUTOPALLTHEPAFILMONE > /* THEREWERESOFEWHOSAID should be THEREWERESOMEWHOSAID */ > swap("F","M",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ADUCVONCEARRIKEDPROMBORTUGALYUTTHEREWERESOMEWHOSAIDSHECAMEPROMSBAINWHICHISALMOSTTHESAMETH\ INGATALLEKENTSSHEWASCALLEDTHEBORTUGUESEANDSHELAIDEGGSWASVILLEDANDCOOVEDANDTHEREWASANENDOP\ HERYUTTHEDUCVLINGSWHICHCREBTPORTHPROMTHEEGGSWEREALSOCALLEDBORTUGUESEANDAYOUTTHATTHEREMAFY\ ESOMEJUESTIONYUTOPALLTHEPAMILFONE > /* YUTTHEREWERESOMEWHOSAIDSHECAMEPROM -> BUT THERE WERE SOME WHO SAID SHE CAME FROM */ > swap("Y","B",~fk); > swap("P","F",~fk); > p1[1..300]; ADUCVONCEARRIKEDPROMBORTUGALYUTTHEREWERESOMEWHOSAIDSHECAMEPROMSBAINWHICHISALMOSTTHESAMETH\ INGATALLEKENTSSHEWASCALLEDTHEBORTUGUESEANDSHELAIDEGGSWASVILLEDANDCOOVEDANDTHEREWASANENDOP\ HERYUTTHEDUCVLINGSWHICHCREBTPORTHPROMTHEEGGSWEREALSOCALLEDBORTUGUESEANDAYOUTTHATTHEREMAFY\ ESOMEJUESTIONYUTOPALLTHEPAMILFONE > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ADUCVONCEARRIKEDFROMYORTUGALBUTTHEREWERESOMEWHOSAIDSHECAMEFROMSYAINWHICHISALMOSTTHESAMETH\ INGATALLEKENTSSHEWASCALLEDTHEYORTUGUESEANDSHELAIDEGGSWASVILLEDANDCOOVEDANDTHEREWASANENDOF\ HERBUTTHEDUCVLINGSWHICHCREYTFORTHFROMTHEEGGSWEREALSOCALLEDYORTUGUESEANDABOUTTHATTHEREMAPB\ ESOMEJUESTIONBUTOFALLTHEFAMILPONE > swap("P","Y",~fk); > swap("K","V",~fk); > p1:=String(Enciphering(fk,t1)); > p1[1..300]; ADUCKONCEARRIVEDFROMPORTUGALBUTTHEREWERESOMEWHOSAIDSHECAMEFROMSPAINWHICHISALMOSTTHESAMETH\ INGATALLEVENTSSHEWASCALLEDTHEPORTUGUESEANDSHELAIDEGGSWASKILLEDANDCOOKEDANDTHEREWASANENDOF\ HERBUTTHEDUCKLINGSWHICHCREPTFORTHFROMTHEEGGSWEREALSOCALLEDPORTUGUESEANDABOUTTHATTHEREMAYB\ ESOMEJUESTIONBUTOFALLTHEFAMILYONE > swap("J","Q",~fk); > p1:=String(Enciphering(fk,t1)); > p1; ADUCKONCEARRIVEDFROMPORTUGALBUTTHEREWERESOMEWHOSAIDSHECAMEFROMSPAINWHICHISALMOSTTHESAMETH\ INGATALLEVENTSSHEWASCALLEDTHEPORTUGUESEANDSHELAIDEGGSWASKILLEDANDCOOKEDANDTHEREWASANENDOF\ HERBUTTHEDUCKLINGSWHICHCREPTFORTHFROMTHEEGGSWEREALSOCALLEDPORTUGUESEANDABOUTTHATTHEREMAYB\ ESOMEQUESTIONBUTOFALLTHEFAMILYONEONLYREMAINEDINTHEDUCKYARDWHICHMAYBECALLEDAFARMYARDASTHEC\ HICKENSWEREADMITTEDANDTHECOCKSTRUTTEDABOUTINAVERYHOSTILEMANNERHEANNOYSMEWITHHISLOUDCROWIN\ GSAIDTHEPORTUGUESEDUCKBUTSTILLHESAHANDSOMEBIRDTHERESNODENYINGTHATALTHOUGHHESNOTADRAKEHEOU\ GHTTOMODERATEHISVOICELIKETHOSELITTLEBIRDSWHOARESINGINGINTHELIMETREESOVERTHEREINOURNEIGHBO\ RSGARDENBUTTHATISANARTONLYACQUIREDINPOLITESOCIETYHOWSWEETLYTHEYSINGTHEREITISQUITEAPLEASUR\ ETOLISTENTOTHEMICALLITPORTUGUESESINGINGIFIHADONLYSUCHALITTLESINGINGBIRDIDBEKINDANDGOODASA\ MOTHERTOHIMFORITSINMYNATUREINMYPORTUGUESEBLOODWHILESHEWASSPEAKINGONEOFTHELITTLESINGINGBIR\ DSCAMETUMBLINGHEADOVERHEELSFROMTHEROOFINTOTHEYARDTHECATWASAFTERHIMBUTHEHADESCAPEDFROMHERW\ ITHABROKENWINGANDSOCAMETUMBLINGINTOTHEYARDTHATSJUSTLIKETHECATSHESAVILLAINSAIDTHEPORTUGUES\ EDUCKIREMEMBERHERWAYSWHENIHADCHILDRENOFMYOWNHOWCANSUCHACREATUREBEALLOWEDTOLIVEANDWANDERAB\ OUTUPONTHEROOFSIDONTTHINKTHEYALLOWSUCHTHINGSINPORTUGALSHEPITIEDTHELITTLESINGINGBIRDANDSOD\ IDALLTHEOTHERDUCKSWHOWERENOTPORTUGUESEPOORLITTLECREATURETHEYSAIDONEAFTERANOTHERASTHEYCAME\ UPWECANTSINGCERTAINLYBUTWEHAVEASOUNDINGBOARDORSOMETHINGOFTHEKINDWITHINUSWECANFEELTHATTHOU\ GHWEDONTTALKABOUTITBUTICANTALKSAIDTHEPORTUGUESEDUCKANDILLDOSOMETHINGFORTHELITTLEFELLOWITS\ MYDUTYANDSHESTEPPEDINTOTHEWATERTROUGHANDBEATHERWINGSUPONTHEWATERSOSTRONGLYTHATTHEBIRDWASN\ EARLYDROWNEDBYASHOWERBATHBUTTHEDUCKMEANTITKINDLYTHATISAGOODDEEDSHESAIDIHOPETHEOTHERSWILLT\ AKEEXAMPLEBYITTWEETTWEETSAIDTHELITTLEBIRDFORONEOFHISWINGSBEINGBROKENHEFOUNDITDIFFICULTTOS\ HAKEHIMSELFBUTHEQUITEUNDERSTOODTHATTHEBATHWASMEANTKINDLYANDHESAIDYOUAREVERYKINDHEARTEDMAD\ AMBUTHEDIDNOTWISHFORASECONDBATHIHAVENEVERTHOUGHTABOUTMYHEARTREPLIEDTHEPORTUGUESEDUCKBUTIK\ NOWTHATILOVEALLMYFELLOWCREATURESEXCEPTTHECATANDNOBODYCANEXPECTMETOLOVEHERFORSHEATEUPTWOOF\ MYDUCKLINGSBUTPRAYMAKEYOURSELFATHOMEITISEASYTOMAKEONESSELFCOMFORTABLEIAMMYSELFFROMAFOREIG\ NCOUNTRYASYOUMAYSEEBYMYFEATHERYDRESSMYDRAKEISANATIVEOFTHESEPARTSHESNOTOFMYRACEBUTIAMNOTPR\ OUDONTHATACCOUNTIFANYONEHERECANUNDERSTANDYOUIMAYSAYPOSITIVELYIAMTHATPERSONSHESQUITEFULLOF\ PORTULAKSAIDALITTLECOMMONDUCKWHOWASWITTYALLTHECOMMONDUCKSCONSIDEREDTHEWORDPORTULAKAGOODJO\ KEFORITSOUNDEDLIKEPORTUGALTHEYNUDGEDEACHOTHERANDSAIDQUACKTHATWASWITTYTHENTHEOTHERDUCKSBEG\ ANTONOTICETHELITTLEBIRDTHEPORTUGUESEHADCERTAINLYAGREATFLOWOFLANGUAGETHEYSAIDTOTHELITTLEBI\ RDFOROURPARTWEDONTCARETOFILLOURBEAKSWITHSUCHLONGWORDSBUTWESYMPATHIZEWITHYOUQUITEASMUCHIFW\ EDONTDOANYTHINGELSEWECANWALKABOUTWITHYOUEVERYWHEREANDWETHINKTHATISTHEBESTTHINGWECANDOYOUH\ AVEALOVELYVOICESAIDONEOFTHEELDESTDUCKSITMUSTBEGREATSATISFACTIONTOYOUTOBEABLETOGIVESOMUCHP\ LEASUREASYOUDOIAMCERTAINLYNOJUDGEOFYOURSINGINGSOIKEEPMYBEAKSHUTWHICHISBETTERTHANTALKINGNO\ NSENSEASOTHERSDODONTPLAGUEHIMSOINTERPOSEDTHEPORTUGUESEDUCKHEREQUIRESRESTANDNURSINGMYLITTL\ ESINGINGBIRDDOYOUWISHMETOPREPAREANOTHERBATHFORYOUOHNONOPRAYLETMEDRYIMPLOREDTHELITTLEBIRDT\ HEWATERCUREISTHEONLYREMEDYFORMEWHENIAMNOTWELLSAIDTHEPORTUGUESEAMUSEMENTTOOISVERYBENEFICIA\ LTHEFOWLSFROMTHENEIGHBORHOODWILLSOONBEHERETOPAYYOUAVISITTHEREARETWOCOCHINCHINESEAMONGSTTH\ EMTHEYWEARFEATHERSONTHEIRLEGSANDAREWELLEDUCATEDTHEYHAVEBEENBROUGHTFROMAGREATDISTANCEANDCO\ NSEQUENTLYITREATTHEMWITHGREATERRESPECTTHANIDOTHEOTHERSTHENTHEFOWLSARRIVEDANDTHECOCKWASPOL\ ITEENOUGHTODAYTOKEEPFROMBEINGRUDEYOUAREAREALSONGSTERHESAIDYOUDOASMUCHWITHYOURLITTLEVOICEA\ SITISPOSSIBLETODOBUTTHEREREQUIRESMORENOISEANDSHRILLNESSINANYONEWHOWISHESITTOBEKNOWNWHOHEI\ STHETWOCHINESEWEREQUITEENCHANTEDWITHTHEAPPEARANCEOFTHESINGINGBIRDHISFEATHERSHADBEENMUCHRU\ FFLEDBYHISBATHSOTHATHESEEMEDTOTHEMQUITELIKEATINYCHINESEFOWLHESCHARMINGTHEYSAIDTOEACHOTHER\ ANDBEGANACONVERSATIONWITHHIMINWHISPERSUSINGTHEMOSTARISTOCRATICCHINESEDIALECTWEAREOFTHESAM\ ERACEASYOURSELFTHEYSAIDTHEDUCKSEVENTHEPORTUGUESEAREALLAQUATICBIRDSASYOUMUSTHAVENOTICEDYOU\ DONOTKNOWUSYETVERYFEWKNOWUSORGIVETHEMSELVESTHETROUBLETOMAKEOURACQUAINTANCENOTEVENANYOFTHE\ FOWLSTHOUGHWEAREBORNTOOCCUPYAHIGHERGRADEINSOCIETYTHANMOSTOFTHEMBUTTHATDOESNOTDISTURBUSWEQ\ UIETLYGOONINOUROWNWAYAMONGTHERESTWHOSEIDEASARECERTAINLYNOTOURSFORWELOOKATTHEBRIGHTSIDEOFT\ HINGSANDONLYSPEAKWHATISGOODALTHOUGHTHATISSOMETIMESVERYDIFFICULTTOFINDWHERENONEEXISTSEXCEP\ TOURSELVESANDTHECOCKTHEREISNOTONEINTHEYARDWHOCANBECALLEDTALENTEDORPOLITEITCANNOTEVENBESAI\ DOFTHEDUCKSANDWEWARNYOULITTLEBIRDNOTTOTRUSTTHATONEYONDERWITHTHESHORTTAILFEATHERSFORSHEISC\ 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