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1、2929DifferentDifferentWaysWaysToToLaceLaceShoesShoesMyMylacinglacingdiagramsdiagramsareareallallcolourcodedcolourcodedtotomakemakeititeasiereasiertotofollowfollowwherewherethethelacelaceruns.runs.GenerallyGenerallythethe

2、greygreysectionsectionisisthethestartstartofofthethelacinglacingwhilstwhilstthetheblueblueendendofofthethelacelacestartsstartsononthetheleftleftsidesidethetheyellowyellowendendstartsstartsononthetherightrightside.side.Th

3、eThecolourscolourswerewerechosenchosentotomakemakeititrelativelyrelativelyeasyeasyevenevenffcolourblindcolourblindvisitsvisitsasasblueblueisisdarkerdarkerthanthanyellow.yellow.HowHowmanymanypossiblepossiblewayswaysareare

4、theretheretotolacelaceananaverageaverageshoeshoeThisThissimplesimplequestionquestionwhenwhenansweredansweredwithwithmathematicsmathematicsresultsresultsininsomesomesurprisinglysurprisinglybigbignumbersnumbersononananaver

5、ageaverageshoeshoewithwithsixsixpairspairsofofeyeletseyeletstherethereareare19619905536001961990553600wayswaystotofeedfeedashoelaceshoelacethoughthoughthosethose1212eyelets.eyelets.ThatsThatsalmostalmost2TRILLIONTRILLION

6、possibilities!possibilities!HoweverHowevermanymanyofofthesethesecantcantbebeconsideredconsidered“Lacing“LacingMethods“Methods“becausebecausetheytheydontdontevenevenfulfilfulfilthetheprimaryprimarypurposepurposeofofholdin

7、gholdingthetheshoeshoeclosedclosedwhilstwhilstmanymanyarearehopelesslyhopelesslytangledtangledmessesmessesmanymanyareareminminirrelevantirrelevantvariations.variations.NohelessNohelessevenevenwithwithrealwldrealwldconstr

8、aintsconstraints(see(seebelow)below)theretherearearecountlesscountlesspossiblepossiblelacinglacingmethods.methods.InInthisthissectionsectionIllIllpresentpresenta(somewhat(somewhatmemerealistic)realistic)fewfewmethodsmeth

9、odsthatthatIconsiderconsiderwthywthyofofdevotingdevotingthethetimetimerequiredrequiredtotocreatecreateinstructionsinstructionseithereitherbecausebecausetheytheyhavehaveaparticularparticularbenefitbenefitjustjustbecausebe

10、causeIlikelikethethewaywaytheytheylook.look.PackedPackedupupbybyWooWooFrom::2TrillionTrillionPossibilitiesPossibilitiesIthardlyseemspossiblethattherecouldbequitethatmanywaystofeedalacethrough12eyelets!Soletslookatthemath

11、ematics:Feedthroughoneof12eyeletsfromeitherinsideoutside.Thats24possiblewaystostart.Continuethroughoneof11remainingeyeletsfromeitherinsideoutside(x22meways).Then10remainingeyelets(x20meways).Weveonlygonethroughthreeeyele

12、tswerealreadyupto24x22x20=10560ways!Bythetimewereachthelasteyelet(x2meways)thepossiblewayshavemultipliedto24x22x20x18x16x14x12x10x8x6x4x2waysastaggeringtotalofalmost2TRILLIONpossibilities!Thisnumbercanbehalvedfthosepaths

13、thataremirrimagesofotherpathshalvedagainfthosethatfollowtheidenticalpathfromoppositedirections.Howeverwecanmultiplybythemanydifferentwaysthelacescanbecrossedinterwovenpritopassingthroughthoseeyeletsmultiplyagainifweallow

14、thelacestoeitherpassthroughanyeyeletmethanonceskipanyeyeletevenmeifweusetwomelacespershoe.Thisresultsinalmostinfinitepossibilitieslimitedmainlybylacelength.Intherealwldhoweverwecanplacesomesensibleconstraintssuchas:Thela

15、ceshouldgenerallystartfinishfromthetoppairofeyelets.Thelaceshouldpassthrougheacheyeletonlyonce.Eacheyeletshouldcontributetopullingtogetherthesidesoftheshoe.Thelacingshouldnotbetoodifficulttotightenloosen.Anypatternfmedsh

16、ouldberelativelystable.Igneirrelevantvariations(eg.changingthedirectionthroughoneeyelet).Aboveallthefinishedresultshouldbevisuallypleasing.EvenwiththeseconstraintsImsurethattheabovelistoflacingmethodsisdestinedtogrowasId

17、iscovermewthwhilemethodsfromthecountlesspossibilitiesthatIhaventyetexpled.NOTE:IftheshoehasanODDnumberofeyeletpairs(eg.7pairs=14eyeletslikemyshoeatleft)startwiththebottom(greysection)underneathinderfthelastcrossovertoals

18、obeunderneathwhenyoureachthetopeyelets.3StraightStraight(European)(European)LacingLacingSometimesreferredtoas“LadderLacing“ThismethodofStraightLacingshoesappearstobemecommoninEurope.Thelacesrunstraightacrosspairsofeyelet

19、sgivinganeatresult.LacingTechnique:1.Thelacerunsstraightacrossthebottom(greysection)theendsarefedintobothbottomeyelets.2.Oneendofthelace(yellowend)crossesdiagonallyunderneathemergesrunsstraightacrossthesecondsetofeyelets

20、.3.Theotherend(blueend)crossesdiagonallyemergesrunsstraightacrossthenextset.4.Continueuptheshoealternatelyfeedinginoneendthentheother.IansRating:ShtensendsNeatontopMessyunderneathNOTE:Theunderlyingmessoflacesismainlynoti

21、ceablewhenthesidesthatarebeinglacedtogetherarewidelyspacedsuchasintheseimages.Thoughvisuallymessythiscrisscrossmakesthelacingverytight&secure.MilitaryAdvice:Straightlacingmethodsareoftenrecommendedfmilitaryusenotonlybeca

22、useofthesecuritybutbecausethestraightsectionsoflacecanbequicklycutthroughwithaknifescisssindertoeasilyremoveabootfromaninjuredfoot.HoweverIvebeentoldthattheU.S.Armywhichhasregulationsfjustabouteverythingstatesthefollowin

23、gftheirstardblackleathercombatboots:“Thebootsarelaceddiagonallywithblacklaceswiththeexcesslacetuckedintothetopofthebootundertheblousedtrousersslackswrappedaroundthetopoftheboot.“IguessthatwouldmakeStraight(European)Lacin

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