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Publié par | mijec |
Nombre de lectures | 42 |
Langue | English |
Extrait
2
E
A B C D E F
A X X X AB
13
B X X X X
C X X
D X X X
21
C DE X X
F X X
F
1
3
3 3
9×8×7×6×5 = 15120
4 10 8
3
4× 10× 8 = 320
5 4×10×5 = 200
50
(50×49)/2 = 1225
?tainersstMathconeofMidtermerofbdesserts.umdessertsnisminimalhasthecreateisywhatoers;hoicesndscouercomphotheserforthesfromrctainebconmaosaledisp(b)ofenhoiceyccantheisfacilitateIftotheusedwehber.ouldhwThethatcgraphrthetowcanDraUrbana-Champreactions.wAnswshoer.enThestategraphumiseabOneocvrestauranesoups,;andawvtertex-coloringaofcustomerthisonegraphfromwillcategoryatofleastpieusewillthreepie,colorsysincecanthecustomergraph?cononetainsfroma,tareriangCorrection.ldierene;,nevandpie,theGroupchoolorithnegSpringabdiereno(c)YvtemileageshothewswthaterysacolorsHoisyenough.ersSohathecompucAnswhromatictonofumhoices.bAertofshothewgraphtreesiselodangerouHo,manwhicdierenhcmeansforthatmealtheaminimalmaknifumselectionbmadeereaofhcon?tainersbneedtheedareisandausingcustomer.nev2.order(a)hoInmandesigningdierenamealssecurittyesystemcforoseitsAnswaccounIfts,selectionamadebankeacacategorysthekseeactableh1.customer2.toF1cthohoicesoseifacustomervee-digitordersnheumonlycdessertswithoutcneededoseumandersusdivisimakn181y2007comesaignthethoicetwhichoices.capitalouconsidersanmantoyacgridhoiceswingcandistanceaetcustomeremakevepair?theAnswU.Ser.capitals.Therewarenmixednebbwillcannotouhvwhictooundstcomp?hemicaler.cneedswscomputepIllinoiossiblebUniversityer,allnthebdigit(thesotobb2efromdistinctcandofnonzero.hHoonewrst).3! = 6
32× = 62
13
4 5
2 3
4 5= 6 = 102 3
1
1 1
1 2 1 4C
21 3 3 1 5C
1 4 6 4 1 3
1 5 10 10 5 1
5
52 = 32 5
aredierentyalternativjoritpeossibleeingchapphoiceconditions.ifIfwtieserseareballohwved,toneandmendustsatisaddcantheforcasethewheredthereer.isjoritajoritthree-wyaareyIrrelevtcie,tandptheactcaseassAwhenIAtherecandidateareonetawvo-wrankingaExplainynottiesto;fourtherethatarecandidatetherevties,noCArrowingmallodesirableWithoutofer.Criterion,ofIndepthosees(depx.endingxonedwhetherwiththevrst(thettwooororantheAnswlastotingteswtheoyarehimtied),fromsotoowinnervelectionerallleasttheretoareorAnswApwinner.ossibleywruleagoysaofhorankingwthreees.candidatesproblemifmatiesthatareaalloofwined.there(b)usingUserule.Pimpascal'sortrianglethattoconditioncompautsystem.ehCCondorcet?PedndandceCtw(e)alloChair's.er,Answparader.yFscriromthetheatpicturevbcandidates,elowithw,wonehair)obtainsvCrareintiesself-inifwithAndleast-preferredandelectionCt?es.tieser.wingvallosystem.withoutIcandidates,ifthreeonlyrankaoterav(callaA)cangoyslosingaelectionwbya(c)ofHonewwismanatyonedierenotertrevcomhisbinationsherofofYESandandpreviousNO(c)vwhotesmacanythereisbaeowithwmanyvcotersose?etAnsweener.alternativThereAnswareThewisoithyInenotingnocanobtainsemaoutcomes.yAnswtheFote,anwhicvcasesystem,isiswinnerossiblemandyset(d)vw'spreferenceossibilitthatthecauseevstatessystemanviolatevdierensystemtgivcundesirableomExplain.binationser.oforYESyandotingNOitvpototaeofsoters'withballots3.(a)willvtheoters.oting4.to(a)aExpdeemedlforafairiotingnExamplesthesucPconditionsaretothecondition.WinnerAnswtheer.aretoAavtheotingendensystemofsatisesanthisAlternativconditioncondition.proExplainvidedhethatparadoifAnswevTheeryhairvoomatbederbprefersasafactcandidatehto,another,threethenotersitthreeistheimpoterossibletie-breakingforotheerlatterccandidacan,talleotoewinstherationallyelection.their(b)wnExplainterest,indupephisendherencecandidateoftheirrelevwinner.Number of voters
12 8 6 3
First choice B C A C
Second choice C A B B
Third choice A B C A
8×1+6×2 = 20 12×2+6×1+3×1 = 33
12×1+8×2+3×2 = 34
18
C 11
Number of voters
20 14 10 6
First choice A B B C
Second choice C A A D
Third choice E D C B
Fourth choice B C D A
Fifth choice D E E E
50 0 44 6 D 44 6 30 20 26
24
20−30 24 26 36−14 50−0
andthenoshomethoscorevofBCbis),threeA,Bamong(iffrompluralitoseyho.cwithustrmheduleotershedulesvusedy-ninepluralittsoenSame.bHence?thebwinningatalternativSameeAistheC.E(b)rCanelothevvofotersw.who(a)leastbprefer?therstwinningbalternatiwvforeAcBordahangeandtheirBpreferencewinninglistytocprocandidateduceforantialoutcomeagendathey(likseCbanettEethernce(explainwnwhesy/whC.ypreferencenot)is?theAnswber.methoYAesh:y)ifelectedtvher.esethevvoterswreplaceelectedtheirvballotused.boyCondtheAnswballoteatsB,A,Cscore(inCthattoorder),btheneBeatswinsalternativ;andactuallyBittoiseacenougloseshonethattherejustwinneoneelection.offorthesevvhoAnswttoe(a)rBsCcBohangesDhis/hercounballotCint.thathaweaprefeyetoschashovbew.B:bandecomeThetheoterswinner.sc(c)areWhicBhscorealternativ;ewnwelooTheulddhaisvofeWhicwcandidateonanifwilltheeHareusingsystemyhadotingbAnsweenCandidateusedhas?mostAnsw-placeer.otesCandidatehe/sheAouldisedeletedifrsty,otingleadingasto(b)aquestirunonbtheetorcetwd.eener.BbandECyintowhic,hbBTheobtainser.wAnswrst-placeyvtootes;abndATywtomak,candidateCwineatsAnswbYthe:isoneSothehB,C,A,D,E,andidatehetoofleastoneotherfrom:(a)iswCondorcetAr(thethisalternativ(c),questionSosequenthispairwisedaotingCt(d)eyA,B,C,D,E.nderagendalosesused.B6.WhatFiftisythenvloseoterstowho(elec-t),onedefeatsof(thedav)edcandidatesdefeatsA,B,C,D(orcandidatewhom).loseswithB,agenBcandidatetowins.bCanmeetingoueeannthatobtainsould5.ers-placeAv?oter.eessif;usessoagendacandidatetBresultswone-oneouldduelshaquestionvshoethatwwinsononlyiftotAhiseandHarelosessystemChadeforebA).Approval ballots
A X X X X X X X
B X X X X X
C X X X X X
D X X X X X X
87.5 62.5 75
A A C C B
B B A A C
C C B B A
C
B C
4
4
alvapproanrunoethatindicatesoutcomewColoreloduels,bcvthatiote.otablethelinAnswXTR(a)ofWhicC,hotercandidateywillisbveer.cgraphhosenpluralitbUEybuttheebinoardtheifwinnjustagendaonetheofwthemThibsetorbwhicerunoelectedrue?grapAnsw-cer.eTheALSEcthatandidateawithethesystemmoster.approlvotingalBordaballotssatisesistA,Fsovidehe/pairwisesAnswhthereewinsisnotheEvoneCondorcetthatelection,wbouldBbBeancofhosenaifyjutosistdonevofshothempluralitisotingto9.bfeAnelected.admits(b)eWhicinghorcandidatess.wisoutheleoremdybdmiteertex-coloringcorhosens.ifv75notpulable.ercenisttheapprorvyaliswmanipulable.astneededing?indepAnswirrelever.esCandidateThisA(thehas5AnexampleD.SequenandotingpdorcetercenThist:approavthenalhis/her;he/sheBwhicandusedCseboters'othotinghanewvtheeisA,B,Cetcandidateseenfourandpandercenwins.t,us,andunilateralDhangehasballotnypvercenmat.lSoadAanandthatDprefeweouldbbthateoter,chhosen.ws8.theUseythevfollosystemwingmanipulable.electionTtoorshoalsw?thatythehpluralitayertrunoxvolorotingusingsystemcolorsislmanipuslAnswaThisble.Fo;oting4vThalstatesvanapproplanaryabsotevvusingerscolorsblmemsoardThebyAnswotinger.isInmanthepelectionAnswabThisoTRv:e,ptheurunoaisitbvetsystemwgroup-manipulableeennotATheandcounC,vandttsystemwins.theHoendencwofevaner,alternativthecriterion.leftmoster.visoterALSEwballotsoexerciseuldpropreferanEighofce!).protialavwinner.satiseser.Coniscriterion.ALSEer.wissaUEiifinislCondorcetserandhe/shehallsone-on-onethesowwinsymatterehtoisv.systemserywtbvthanpreferentoballotswinducesoCondorcetvAnswerThis7.F,;andehewctancacahievs,etthatioutcomeisbreasonyhcwhangingtriedisndballototingtothatB,A,Cere(inetterthattheorder).vInsystem.