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Multiple Win Covers or Wheels
 LottoPoster Forums : NUMBER SETS TO PLAY FROM DIFFERENT METHODS : Multiple Win Covers or Wheels
Message Icon Topic: Multiple Prize Wins in Lotto and C(22,6,3,3,1)=77 Post Reply Post New Topic
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
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To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
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Posts: 678
Quote Colin F Replybullet Topic: Multiple Prize Wins in Lotto and C(22,6,3,3,1)=77
    Posted: May 22 2009 at 9:56am

Covers or Wheels with Guarantees as applied to Lotto have concentrated on a single lowest value prize guarantee but are they giving you the best return? Follow this link multiple prize wins in Lotto for an article on the best way of achieving multiple prizes with particular attention to the remarkable attributes for pool 22.

The table below shows the amazing Steiner C(22,6,3,3,1)=77 where for a Pool of 22 distinct objects (they don't have to be integers) all the possible 1540 combinations of 3 of the objects are included in 77 lines without repetition. In this case I have used the first 22 lower case alphabetical characters and displayed the combination in alphabetical order - but this is only convention as it is a combination and therefore 5 other orders are applicable eg abc, acb, bac, bca, cab, cba.
 
Of note is the fact that removal of 1 line and its effect on coverage is the same for all 77 lines. While there is no Pick 6 Lotto game with a Pool of 22 the nearest being 25 (the extra 3 integers more than doubles the possible winning combinations from 74,613 to 177,100) there is a lot to learn from it as it sets limits on what is possible.
 
Trivia: For the combinations shown there are at least 30 English words excluding the usual place and family names, abreviations and acronyms. Question: How many for the other 8470 permutations? Do we get another 150 words ie 180 in all?
 
Triples for C(22,6,3,3,1)=77 enumerated.

a1 a2 a3 a4 a5 a6 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20
a b c d e f abc abd abe abf acd ace acf ade adf aef bcd bce bcf bde bdf bef cde cdf cef def
a b g h i j abg abh abi abj agh agi agj ahi ahj aij bgh bgi bgj bhi bhj bij ghi ghj gij hij
c d g h k l cdg cdh cdk cdl cgh cgk cgl chk chl ckl dgh dgk dgl dhk dhl dkl ghk ghl gkl hkl
e f i j k l efi efj efk efl eij eik eil ejk ejl ekl fij fik fil fjk fjl fkl ijk ijl ikl jkl
e f g h m n efg efh efm efn egh egm egn ehm ehn emn fgh fgm fgn fhm fhn fmn ghm ghn gmn hmn
c d i j m n cdi cdj cdm cdn cij cim cin cjm cjn cmn dij dim din djm djn dmn ijm ijn imn jmn
a b k l m n abk abl abm abn akl akm akn alm aln amn bkl bkm bkn blm bln bmn klm kln kmn lmn
c e g i o p ceg cei ceo cep cgi cgo cgp cio cip cop egi ego egp eio eip eop gio gip gop iop
d f h j o p dfh dfj dfo dfp dhj dho dhp djo djp dop fhj fho fhp fjo fjp fop hjo hjp hop jop
a f g k o q afg afk afo afq agk ago agq ako akq aoq fgk fgo fgq fko fkq foq gko gkq goq koq
b e h l o q beh bel beo beq bhl bho bhq blo blq boq ehl eho ehq elo elq eoq hlo hlq hoq loq
b d i k p q bdi bdk bdp bdq bik bip biq bkp bkq bpq dik dip diq dkp dkq dpq ikp ikq ipq kpq
a c j l p q acj acl acp acq ajl ajp ajq alp alq apq cjl cjp cjq clp clq cpq jlp jlq jpq lpq
b c j k o r bcj bck bco bcr bjk bjo bjr bko bkr bor cjk cjo cjr cko ckr cor jko jkr jor kor
a d i l o r adi adl ado adr ail aio air alo alr aor dil dio dir dlo dlr dor ilo ilr ior lor
a e h k p r aeh aek aep aer ahk ahp ahr akp akr apr ehk ehp ehr ekp ekr epr hkp hkr hpr kpr
b f g l p r bfg bfl bfp bfr bgl bgp bgr blp blr bpr fgl fgp fgr flp flr fpr glp glr gpr lpr
c f h i q r cfh cfi cfq cfr chi chq chr ciq cir cqr fhi fhq fhr fiq fir fqr hiq hir hqr iqr
d e g j q r deg dej deq der dgj dgq dgr djq djr dqr egj egq egr ejq ejr eqr gjq gjr gqr jqr
m n o p q r mno mnp mnq mnr mop moq mor mpq mpr mqr nop noq nor npq npr nqr opq opr oqr pqr
b d g m o s bdg bdm bdo bds bgm bgo bgs bmo bms bos dgm dgo dgs dmo dms dos gmo gms gos mos
a c h n o s ach acn aco acs ahn aho ahs ano ans aos chn cho chs cno cns cos hno hns hos nos
a f i m p s afi afm afp afs aim aip ais amp ams aps fim fip fis fmp fms fps imp ims ips mps
b e j n p s bej ben bep bes bjn bjp bjs bnp bns bps ejn ejp ejs enp ens eps jnp jns jps nps
c e k m q s cek cem ceq ces ckm ckq cks cmq cms cqs ekm ekq eks emq ems eqs kmq kms kqs mqs
d f l n q s dfl dfn dfq dfs dln dlq dls dnq dns dqs fln flq fls fnq fns fqs lnq lns lqs nqs
h j l m r s hjl hjm hjr hjs hlm hlr hls hmr hms hrs jlm jlr jls jmr jms jrs lmr lms lrs mrs
g i k n r s gik gin gir gis gkn gkr gks gnr gns grs ikn ikr iks inr ins irs knr kns krs nrs
a e j m o t aej aem aeo aet ajm ajo ajt amo amt aot ejm ejo ejt emo emt eot jmo jmt jot mot
b f i n o t bfi bfn bfo bft bin bio bit bno bnt bot fin fio fit fno fnt fot ino int iot not
b c h m p t bch bcm bcp bct bhm bhp bht bmp bmt bpt chm chp cht cmp cmt cpt hmp hmt hpt mpt
a d g n p t adg adn adp adt agn agp agt anp ant apt dgn dgp dgt dnp dnt dpt gnp gnt gpt npt
g i l m q t gil gim giq git glm glq glt gmq gmt gqt ilm ilq ilt imq imt iqt lmq lmt lqt mqt
h j k n q t hjk hjn hjq hjt hkn hkq hkt hnq hnt hqt jkn jkq jkt jnq jnt jqt knq knt kqt nqt
d f k m r t dfk dfm dfr dft dkm dkr dkt dmr dmt drt fkm fkr fkt fmr fmt frt kmr kmt krt mrt
c e l n r t cel cen cer cet cln clr clt cnr cnt crt eln elr elt enr ent ert lnr lnt lrt nrt
d e h i s t deh dei des det dhi dhs dht dis dit dst ehi ehs eht eis eit est his hit hst ist
c f g j s t cfg cfj cfs cft cgj cgs cgt cjs cjt cst fgj fgs fgt fjs fjt fst gjs gjt gst jst
k l o p s t klo klp kls klt kop kos kot kps kpt kst lop los lot lps lpt lst ops opt ost pst
a b q r s t abq abr abs abt aqr aqs aqt ars art ast bqr bqs bqt brs brt bst qrs qrt qst rst
h i k m o u hik him hio hiu hkm hko hku hmo hmu hou ikm iko iku imo imu iou kmo kmu kou mou
g j l n o u gjl gjn gjo gju gln glo glu gno gnu gou jln jlo jlu jno jnu jou lno lnu lou nou
d e l m p u del dem dep deu dlm dlp dlu dmp dmu dpu elm elp elu emp emu epu lmp lmu lpu mpu
c f k n p u cfk cfn cfp cfu ckn ckp cku cnp cnu cpu fkn fkp fku fnp fnu fpu knp knu kpu npu
b f j m q u bfj bfm bfq bfu bjm bjq bju bmq bmu bqu fjm fjq fju fmq fmu fqu jmq jmu jqu mqu
a e i n q u aei aen aeq aeu ain aiq aiu anq anu aqu ein eiq eiu enq enu equ inq inu iqu nqu
a c g m r u acg acm acr acu agm agr agu amr amu aru cgm cgr cgu cmr cmu cru gmr gmu gru mru
b d h n r u bdh bdn bdr bdu bhn bhr bhu bnr bnu bru dhn dhr dhu dnr dnu dru hnr hnu hru nru
a d j k s u adj adk ads adu ajk ajs aju aks aku asu djk djs dju dks dku dsu jks jku jsu ksu
b c i l s u bci bcl bcs bcu bil bis biu bls blu bsu cil cis ciu cls clu csu ils ilu isu lsu
g h p q s u ghp ghq ghs ghu gpq gps gpu gqs gqu gsu hpq hps hpu hqs hqu hsu pqs pqu psu qsu
e f o r s u efo efr efs efu eor eos eou ers eru esu for fos fou frs fru fsu ors oru osu rsu
b e g k t u beg bek bet beu bgk bgt bgu bkt bku btu egk egt egu ekt eku etu gkt gku gtu ktu
a f h l t u afh afl aft afu ahl aht ahu alt alu atu fhl fht fhu flt flu ftu hlt hlu htu ltu
c d o q t u cdo cdq cdt cdu coq cot cou cqt cqu ctu doq dot dou dqt dqu dtu oqt oqu otu qtu
i j p r t u ijp ijr ijt iju ipr ipt ipu irt iru itu jpr jpt jpu jrt jru jtu prt pru ptu rtu
c f l m o v cfl cfm cfo cfv clm clo clv cmo cmv cov flm flo flv fmo fmv fov lmo lmv lov mov
d e k n o v dek den deo dev dkn dko dkv dno dnv dov ekn eko ekv eno env eov kno knv kov nov
g j k m p v gjk gjm gjp gjv gkm gkp gkv gmp gmv gpv jkm jkp jkv jmp jmv jpv kmp kmv kpv mpv
h i l n p v hil hin hip hiv hln hlp hlv hnp hnv hpv iln ilp ilv inp inv ipv lnp lnv lpv npv
a d h m q v adh adm adq adv ahm ahq ahv amq amv aqv dhm dhq dhv dmq dmv dqv hmq hmv hqv mqv
b c g n q v bcg bcn bcq bcv bgn bgq bgv bnq bnv bqv cgn cgq cgv cnq cnv cqv gnq gnv gqv nqv
b e i m r v bei bem ber bev bim bir biv bmr bmv brv eim eir eiv emr emv erv imr imv irv mrv
a f j n r v afj afn afr afv ajn ajr ajv anr anv arv fjn fjr fjv fnr fnv frv jnr jnv jrv nrv
b f h k s v bfh bfk bfs bfv bhk bhs bhv bks bkv bsv fhk fhs fhv fks fkv fsv hks hkv hsv ksv
a e g l s v aeg ael aes aev agl ags agv als alv asv egl egs egv els elv esv gls glv gsv lsv
i j o q s v ijo ijq ijs ijv ioq ios iov iqs iqv isv joq jos jov jqs jqv jsv oqs oqv osv qsv
c d p r s v cdp cdr cds cdv cpr cps cpv crs crv csv dpr dps dpv drs drv dsv prs prv psv rsv
a c i k t v aci ack act acv aik ait aiv akt akv atv cik cit civ ckt ckv ctv ikt ikv itv ktv
b d j l t v bdj bdl bdt bdv bjl bjt bjv blt blv btv djl djt djv dlt dlv dtv jlt jlv jtv ltv
e f p q t v efp efq eft efv epq ept epv eqt eqv etv fpq fpt fpv fqt fqv ftv pqt pqv ptv qtv
g h o r t v gho ghr ght ghv gor got gov grt grv gtv hor hot hov hrt hrv htv ort orv otv rtv
d f g i u v dfg dfi dfu dfv dgi dgu dgv diu div duv fgi fgu fgv fiu fiv fuv giu giv guv iuv
c e h j u v ceh cej ceu cev chj chu chv cju cjv cuv ehj ehu ehv eju ejv euv hju hjv huv juv
a b o p u v abo abp abu abv aop aou aov apu apv auv bop bou bov bpu bpv buv opu opv ouv puv
k l q r u v klq klr klu klv kqr kqu kqv kru krv kuv lqr lqu lqv lru lrv luv qru qrv quv ruv
m n s t u v mns mnt mnu mnv mst msu msv mtu mtv muv nst nsu nsv ntu ntv nuv stu stv suv tuv

Regards

Colin Fairbrother
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