山水娱乐

  • Jason Doucette / Xona Games
     
    hometown – Yarmouth, NS, Canada
    residence – Seattle, WA, USA
    university – Acadia University
    college – COGS
    contact – (other methods)
        social networks
        tech – Project/Games · Graphics Tech · Artificial Intelligence · World Records/Number Theory
    personal – Home · Resume · Transcripts · Contact
    twin – Matthew Doucette of Xona Games
    old – Petzold's Programming Windows 5th ed Errata · Domain Hacks · Wallpapers



    196 Palindrome Quest

    Back to Main Resume Page

    196 Iterated 200 Times via Reversal-Addition

    This page shows 196 Palindrome Quest (a.k.a. 196 Algorithm, or 196 Problem) iterated 200 times via reverse-addition. This is a sub page of my World Records (Palindrome) Page, which fully explains my involvement in The 196 Palindrome Quest / Algorithm / Problem, among others. It also shows another one of my palindrome records, The Most Delayed Palindromic Number. Please visit these pages, if you wish to learn more. The page you are currently reading was meant only to show the initial 200 iterations of the 196 Palindrome Quest, and to give an idea of the magnitude of calculations required to take this quest into millions of digits.

    Back to World Records page

    The 196 Algorithm:
    1. Take a number.
    2. Reverse its digits, and add.
    3. If the result is not a palindrome (i.e. reads forwards as it does backwards), then repeat.
    Sounds easy? Let's try it for 196:

    196
    + 691
    step 1: 887
    + 788
    step 2: 1675
    + 5761
    step 3: 7436
    + 6347
    step 4: 13783
    + 38731
    step 5: 52514
    + 41525
    step 6: 94039
    + 93049
    step 7: 187088
    + 880781
    step 8: 1067869
    + 9687601
    step 9: 10755470
    + 07455701
    step 10: 18211171
    + 17111281
    step 11: 35322452
    + 25422353
    step 12: 60744805
    + 50844706
    step 13: 111589511
    + 115985111
    step 14: 227574622
    + 226475722
    step 15: 454050344
    + 443050454
    step 16: 897100798
    + 897001798
    step 17: 1794102596
    + 6952014971
    step 18: 8746117567
    + 7657116478
    step 19: 16403234045
    + 54043230461
    step 20: 70446464506
    + 60546464407
    step 21: 130992928913
    + 319829299031
    step 22: 450822227944
    + 449722228054
    step 23: 900544455998
    + 899554445009
    step 24: 1800098901007
    + 7001098900081
    step 25: 8801197801088
    + 8801087911088
    step 26: 17602285712176
    + 67121758220671
    step 27: 84724043932847
    + 74823934042748
    step 28: 159547977975595
    + 595579779745951
    step 29: 755127757721546
    + 645127757721557
    step 30: 1400255515443103
    + 3013445155520041
    step 31: 4413700670963144
    + 4413690760073144
    step 32: 8827391431036288
    + 8826301341937288
    step 33: 17653692772973576
    + 67537927729635671
    step 34: 85191620502609247
    + 74290620502619158
    step 35: 159482241005228405
    + 504822500142284951
    step 36: 664304741147513356
    + 653315741147403466
    step 37: 1317620482294916822
    + 2286194922840267131
    step 38: 3603815405135183953
    + 3593815315045183063
    step 39: 7197630720180367016
    + 6107630810270367917
    step 40: 13305261530450734933
    + 33943705403516250331
    step 41: 47248966933966985264
    + 46258966933966984274
    step 42: 93507933867933969538
    + 83596933976833970539
    step 43: 177104867844767940077
    + 770049767448768401771
    step 44: 947154635293536341848
    + 848143635392536451749
    step 45: 1795298270686072793597
    + 7953972706860728925971
    step 46: 9749270977546801719568
    + 8659171086457790729479
    step 47: 18408442064004592449047
    + 74094429540046024480481
    step 48: 92502871604050616929528
    + 82592961605040617820529
    step 49: 175095833209091234750057
    + 750057432190902338590571
    step 50: 925153265399993573340628
    + 826043375399993562351529
    step 51: 1751196640799987135692157
    + 7512965317899970466911571
    step 52: 9264161958699957602603728
    + 8273062067599968591614629
    step 53: 17537224026299926194218357
    + 75381249162999262042273571
    step 54: 92918473189299188236491928
    + 82919463288199298137481929
    step 55: 175837936477498486373973857
    + 758379373684894774639738571
    step 56: 934217310162393261013712428
    + 824217310162393261013712439
    step 57: 1758434620324786522027424867
    + 7684247202256874230264348571
    step 58: 9442681822581660752291773438
    + 8343771922570661852281862449
    step 59: 17786453745152322604573635887
    + 78853637540622325154735468771
    step 60: 96640091285774647759309104658
    + 85640190395774647758219004669
    step 61: 182280281681549295517528109327
    + 723901825715592945186182082281
    step 62: 906182107397142240703710191608
    + 806191017307042241793701281609
    step 63: 1712373124704184482497411473217
    + 7123741147942844814074213732171
    step 64: 8836114272647029296571625205388
    + 8835025261756929207462724116388
    step 65: 17671139534403958504034349321776
    + 67712394343040585930443593117671
    step 66: 85383533877444544434477942439447
    + 74493424977443444544477833538358
    step 67: 159876958854887988978955775977805
    + 508779577559879889788458859678951
    step 68: 668656536414767878767414635656756
    + 657656536414767878767414635656866
    step 69: 1326313072829535757534829271313622
    + 2263131729284357575359282703136231
    step 70: 3589444802113893332894111974449853
    + 3589444791114982333983112084449853
    step 71: 7178889593228875666877224058899706
    + 6079988504227786665788223959888717
    step 72: 13258878097456662332665448018788423
    + 32488781084456623326665479087885231
    step 73: 45747659181913285659330927106673654
    + 45637660172903395658231918195674754
    step 74: 91385319354816681317562845302348408
    + 80484320354826571318661845391358319
    step 75: 171869639709643252636224690693706727
    + 727607396096422636252346907936968171
    step 76: 899477035806065888888571598630674898
    + 898476036895175888888560608530774998
    step 77: 1797953072701241777777132207161449896
    + 6989441617022317777771421072703597971
    step 78: 8787394689723559555548553279865047867
    + 7687405689723558455559553279864937878
    step 79: 16474800379447118011108106559729985745
    + 54758992795560180111081174497300847461
    step 80: 71233793175007298122189281057030833206
    + 60233803075018298122189270057139733217
    step 81: 131467596250025596244378551114170566423
    + 324665071411155873442695520052695764131
    step 82: 456132667661181469687074071166866330554
    + 455033668661170470786964181166766231654
    step 83: 911166336322351940474038252333632562208
    + 802265236333252830474049153223633661119
    step 84: 1713431572655604770948087405557266223327
    + 7233226627555047808490774065562751343171
    step 85: 8946658200210652579438861471120017566498
    + 8946657100211741688349752560120028566498
    step 86: 17893315300422394267788614031240046132996
    + 69923164004213041688776249322400351339871
    step 87: 87816479304635435956564863353640397472867
    + 76827479304635336846565953453640397461878
    step 88: 164643958609270772803130816807280794934745
    + 547439497082708618031308277072906859346461
    step 89: 712083455691979390834439093880187654281206
    + 602182456781088390934438093979196554380217
    step 90: 1314265912473067781768877187859384208661423
    + 3241668024839587817788671877603742195624131
    step 91: 4555933937312655599557549065463126404285554
    + 4555824046213645609457559955562137393395554
    step 92: 9111757983526301209015109021025263797681108
    + 8011867973625201209015109021036253897571119
    step 93: 17123625957151502418030218042061517695252227
    + 72225259671516024081203081420515175952632171
    step 94: 89348885628667526499233299462576693647884398
    + 89348874639667526499233299462576682658884398
    step 95: 178697760268335052998466598925153376306768796
    + 697867603673351529895664899250533862067796871
    step 96: 876565363941686582894131498175687238374565667
    + 766565473832786571894131498285686149363565678
    step 97: 1643130837774473154788262996461373387738131345
    + 5431318377833731646992628874513744777380313461
    step 98: 7074449215608204801780891870975118165118444806
    + 6084448115618115790781980871084028065129444707
    step 99: 13158897331226320592562872742059146230247889513
    + 31598874203264195024727826529502362213379885131
    step 100: 44757771534490515617290699271561508443627774644
    + 44647772634480516517299609271651509443517775744
    step 101: 89405544168971032134590308543213017887145550388
    + 88305554178871031234580309543123017986144550498
    step 102: 177711098347842063369170618086336035873290100886
    + 688001092378530633680816071963360248743890117771
    step 103: 865712190726372697049986690049696284617180218657
    + 756812081716482696940096689940796273627091217568
    step 104: 1622524272442855393990083379990492558244271436225
    + 5226341724428552940999733800993935582442724252261
    step 105: 6848865996871408334989817180984428140686995688486
    + 6848865996860418244890817189894338041786995688486
    step 106: 13697731993731826579880634370878766182473991376972
    + 27967319937428166787807343608897562813739913779631
    step 107: 41665051931159993367687977979776328996213905156603
    + 30665150931269982367797977978676339995113915056614
    step 108: 72330202862429975735485955958452668991327820213217
    + 71231202872319986625485955958453757992426820203327
    step 109: 143561405734749962360971911916906426983754640416544
    + 445614046457389624609619119179063269947437504165341
    step 110: 589175452192139586970591031095969696931192144581885
    + 588185441291139696969590130195079685931291254571985
    step 111: 1177360893483279283940181161291049382862483399153870
    + 0783519933842682839401921611810493829723843980637711
    step 112: 1960880827325962123342102773101543212586327379791581
    + 1851979737236852123451013772012433212695237280880691
    step 113: 3812860564562814246793116545113976425281564660672272
    + 2722760664651825246793115456113976424182654650682183
    step 114: 6535621229214639493586232001227952849464219311354455
    + 5544531139124649482597221002326853949364129221265356
    step 115: 12080152368339288976183453003554806798828348532619811
    + 11891623584382889760845530035438167988293386325108021
    step 116: 23971775952722178737028983038992974787121734857727832
    + 23872775843712178747929983038982073787122725957717932
    step 117: 47844551796434357484958966077975048574244460815445764
    + 46754451806444247584057977066985948475343469715544874
    step 118: 94599003602878605069016943144960997049587930530990638
    + 83609903503978594079906944134961096050687820630099549
    step 119: 178208907106857199148923887279922093100275751161090187
    + 781090161157572001390229972788329841991758601709802871
    step 120: 959299068264429200539153860068251935092034352870893058
    + 850398078253430290539152860068351935002924462860992959
    step 121: 1809697146517859491078306720136603870094958815731886017
    + 7106881375188594900783066310276038701949587156417969081
    step 122: 8916578521706454391861373030412642572044545972149855098
    + 8905589412795454402752462140303731681934546071258756198
    step 123: 17822167934501908794613835170716374253979092043408611296
    + 69211680434029097935247361707153831649780910543976122871
    step 124: 87033848368531006729861196877870205903760002587384734167
    + 76143748378520006730950207877869116892760013586384833078
    step 125: 163177596747051013460811404755739322796520016173769567245
    + 542765967371610025697223937557404118064310150747695771361
    step 126: 705943564118661039158035342313143440860830166921465338606
    + 606833564129661038068044341313243530851930166811465349507
    step 127: 1312777128248322077226079683626386971712760333732930688113
    + 3118860392373330672171796836263869706227702238428217772131
    step 128: 4431637520621652749397876519890256677940462572161148460244
    + 4420648411612752640497766520989156787939472561260257361344
    step 129: 8852285932234405389895643040879413465879935133421405821588
    + 8851285041243315399785643149780403465989835044322395822588
    step 130: 17703570973477720789681286190659816931869770177743801644176
    + 67144610834777107796813961895609168218698702777437907530771
    step 131: 84848181808254828586495248086268985150568472955181709174947
    + 74947190718155927486505158986268084259468582845280818184848
    step 132: 159795372526410756073000407072537069410037055800462527359795
    + 597953725264008550730014960735270704000370657014625273597951
    step 133: 757749097790419306803015367807807773410407712815087800957746
    + 647759008780518217704014377708708763510308603914097790947757
    step 134: 1405508106570937524507029745516516536920716316729185591905503
    + 3055091955819276136170296356156155479207054257390756018055041
    step 135: 4460600062390213660677326101672672016127770574119941609960544
    + 4450699061499114750777216102762761016237760663120932600060644
    step 136: 8911299123889328411454542204435433032365531237240874210021188
    + 8811200124780427321355632303345344022454541148239883219921198
    step 137: 17722499248669755732810174507780777054820072385480757429942386
    + 68324992475708458327002845077708770547101823755796684299422771
    step 138: 86047491724378214059813019585489547601921896141277441729365157
    + 75156392714477214169812910674598458591031895041287342719474068
    step 139: 161203884438855428229625930260088006192953791182564784448839225
    + 522938844487465281197359291600880062039526922824558834488302161
    step 140: 684142728926320709426985221860968068232480714007123618937141386
    + 683141739816321700417084232860869068122589624907023629827241486
    step 141: 1367284468742642409844069454721837136355070338914147248764382872
    + 2782834678427414198330705536317381274549604489042462478644827631
    step 142: 4150119147170056608174774991039218410904674827956609727409210503
    + 3050129047279066597284764090148129301994774718066500717419110514
    step 143: 7200248194449123205459539081187347712899449546023110444828321017
    + 7101238284440113206459449982177437811809359545023219444918420027
    step 144: 14301486478889236411918989063364785524708809091046329889746741044
    + 44014764798892364019090880742558746336098981911463298887468410341
    step 145: 58316251277781600431009869805923531860807791002509628777215151385
    + 58315151277782690520019770806813532950896890013400618777215261385
    step 146: 116631402555564290951029640612737064811704681015910247554430412770
    + 077214034455742019510186407118460737216046920159092465555204136611
    step 147: 193845437011306310461216047731197802027751601175002713109634549381
    + 183945436901317200571106157720208791137740612164013603110734548391
    step 148: 377790873912623511032322205451406593165492213339016316220369097772
    + 277790963022613610933312294561395604154502223230115326219378097773
    step 149: 655581836935237121965634500012802197319994436569131642439747195545
    + 545591747934246131965634499913791208210005436569121732539638185556
    step 150: 1201173584869483253931268999926593405529999873138253374979385381101
    + 1011835839794733528313789999255043956299998621393523849684853711021
    step 151: 2213009424664216782245058999181637361829998494531777224664239092122
    + 2212909324664227771354948999281637361819998505422876124664249003122
    step 152: 4425918749328444553600007998463274723649996999954653349328488095244
    + 4425908848239433564599996999463274723648997000063554448239478195244
    step 153: 8851827597567878118200004997926549447298994000018207797567966290488
    + 8840926697657977028100004998927449456297994000028118787657957281588
    step 154: 17692754295225855146300009996853998903596988000046326585225923572076
    + 67027532952258562364000088969530989935869990000364155852259245729671
    step 155: 84720287247484417510300098966384988839466978000410482437485169301747
    + 74710396158473428401400087966493888948366989000301571448474278202748
    step 156: 159430683405957845911700186932878877787833967000712053885959447504495
    + 594405744959588350217000769338787778878239681007119548759504386034951
    step 157: 753836428365546196128700956271666656666073648007831602645463833539446
    + 644935338364546206138700846370666656666172659007821691645563824638357
    step 158: 1398771766730092402267401802642333313332246307015653294291027658177803
    + 3087718567201924923565107036422333133332462081047622042900376671778931
    step 159: 4486490333932017325832508839064666446664708388063275337191404329956734
    + 4376599234041917335723608838074666446664609388052385237102393330946844
    step 160: 8863089567973934661556117677139332893329317776115660574293797660903578
    + 8753090667973924750665116777139233982339317767116551664393797659803688
    step 161: 17616180235947859412221234454278566875668635543232212238687595320707266
    + 66270702359578683221223234553686657866587245443212221495874953208161671
    step 162: 83886882595526542633444469007965224742255880986444433734562548528868937
    + 73986882584526543733444468908855224742256970096444433624562559528868838
    step 163: 157873765180053086366888937916820449484512851082888867359125108057737775
    + 577737750801521953768888280158215484944028619739888663680350081567378751
    step 164: 735611515981575040135777218075035934428541470822777531039475189625116526
    + 625611526981574930135777228074145824439530570812777531040575189515116537
    step 165: 1361223042963149970271554446149181758868072041635555062080050379140233063
    + 3603320419730500802605555361402708688571819416444551720799413692403221631
    step 166: 4964543462693650772877109807551890447439891458080106782879464071543454694
    + 4964543451704649782876010808541989347440981557089017782770563962643454694
    step 167: 9929086914398300555753120616093879794880873015169124565650028034186909388
    + 8839096814308200565654219615103780884979783906160213575550038934196809299
    step 168: 18768183728706501121407340231197660679860656921329338141200066968383718687
    + 78681738386966000214183392312965606897606679113204370412110560782738186781
    step 169: 97449922115672501335590732544163267577467336034533708553310627751121905468
    + 86450912115772601335580733543063376477576236144523709553310527651122994479
    step 170: 183900834231445102671171466087226644055043572179057418106621155402244899947
    + 749998442204551126601814750971275340550446622780664171176201544132438009381
    step 171: 933899276435996229272986217058501984605490194959721589282822699534682909328
    + 823909286435996228282985127959491094506489105850712689272922699534672998339
    step 172: 1757808562871992457555971345017993079111979300810434278555745399069355907667
    + 7667095539609935475558724340180039791119703997105431795557542991782658087571
    step 173: 9424904102481927933114695685198032870231683297915866074113288390852013995238
    + 8325993102580938823114706685197923861320782308915865964113397291842014094249
    step 174: 17750897205062866756229402370395956731552465606831732038226685682694028089487
    + 78498082049628658662283023713860656425513765959307320492265766826050279805771
    step 175: 96248979254691525418512426084256613157066231566139052530492452508744307895258
    + 85259870344780525429403525093166513266075131665248062421581452519645297984269
    step 176: 181508849599472050847915951177423126423141363231387114952073905028389605879527
    + 725978506983820509370259411783132363141324621324771159519748050274995948805181
    step 177: 907487356583292560218175362960555489564465984556158274471821955303385554684708
    + 807486455583303559128174472851655489564465984555069263571812065292385653784709
    step 178: 1714973812166596119346349835812210979128931969111227538043634020595771208469417
    + 7149648021775950204363408357221119691398219790122185389436439116956612183794171
    step 179: 8864621833942546323709758193033330670527151759233412927480073137552383392263588
    + 8853622933832557313700847292143329571517250760333303918579073236452493381264688
    step 180: 17718244767775103637410605485176660242044402519566716846059146374004876773528276
    + 67282537767840047364195064861766591520444024206667158450601473630157776744281771
    step 181: 85000782535615151001605670346943251762488426726233875296660620004162653517810047
    + 74001871535626140002606669257833262762488426715234964307650610015151653528700058
    step 182: 159002654071241291004212339604776514524976853441468839604311230019314307046510105
    + 501015640703413910032113406938864144358679425415677406933212400192142170456200951
    step 183: 660018294774655201036325746543640658883656278857146246537523630211456477502711056
    + 650117205774654112036325735642641758872656388856046345647523630102556477492810066
    step 184: 1310135500549309313072651482186282417756312667713192592185047260314012954995521122
    + 2211255994592104130627405812952913177662136577142826812841562703139039450055310131
    step 185: 3521391495141413443700057295139195595418449244856019405026609963453052405050831253
    + 3521380505042503543699066205049106584429448145955919315927500073443141415941931253
    step 186: 7042772000183916987399123500188302179847897390811938720954110036896193820992762506
    + 6052672990283916986300114590278391180937987489712038810053219937896193810002772407
    step 187: 13095444990467833973699238090466693360785884880523977531007329974792387630995534913
    + 31943559903678329747992370013577932508848858706339666409083299637933876409944459031
    step 188: 45039004894146163721691608104044625869634743586863643940090629612726264040939993944
    + 44939993904046262721692609004934636868534743696852644040180619612736164149840093054
    step 189: 89978998798192426443384217108979262738169487283716287980271249225462428190780086998
    + 89968008709182426452294217208978261738278496183726297980171248334462429189789987998
    step 190: 179947007507374852895678434317957524476447983467442585960442497559924857380570074996
    + 699470075083758429955794244069585244764389744674425759713434876598258473705700749971
    step 191: 879417082591133282851472678387542769240837728141868345673877374158183331086270824967
    + 769428072680133381851473778376543868141827738042967245783876274158282331195280714978
    step 192: 1648845155271266664702946456764086637382665466184835591457753648316465662281551539945
    + 5499351551822665646138463577541955384816645662837366804676546492074666621725515488461
    step 193: 7148196707093932310841410034306042022199311129022202396134300140391132284007067028406
    + 6048207607004822311930410034316932022209211139912202406034300141480132393907076918417
    step 194: 13196404314098754622771820068622974044408522268934404802168600281871264677914143946823
    + 32864934141977646217818200686120840443986222580444047922686002817722645789041340469131
    step 195: 46061338456076400840590020754743814488394744849378452724854603099593910466955484415954
    + 45951448455966401939599030645842725487394844749388441834745702009504800467065483316064
    step 196: 92012786912042802780189051400586539975789589598766894559600305109098710934020967732018
    + 81023776902043901789090150300695549866789598598757993568500415098108720824021968721029
    step 197: 173036563814086704569279201701282089842579188197524888128100720207207431758042936453047
    + 740354639240857134702702027001821888425791881975248980282107102972965407680418365630371
    step 198: 913391203054943839271981228703103978268371070172773868410207823180172839438461302083418
    + 814380203164834938271081328702014868377271070173862879301307822189172938349450302193319
    step 199: 1727771406219778777543062557405118846645642140346636747711515645369345777787911604276737
    + 7376724061197877775439635465151177476366430412465466488115047552603457778779126041777271
    step 200: 9104495467417656552982698022556296323012072552812103235826563197972803556567037646054008
    (unsolved after 200 iterations)

    Calculation Overload?

    It would take a human over an hour to perform the above calculations at a rate of three single digit additions per second, assuming it was done flawlessly.

    A program I created (running on my 200 MHz AMD-K6 desktop PC) can perform the above calculations in 0.0006 seconds (0.6 thousandths of a second). It was programming in assembly language - hand coded and optimized in pure computer language - this is almost as fast as it gets without upgrading hardware (I have untested theories on how to improve the algorithm, such as look up tables, multiple digits stored per byte, etc. There's always a way to make it go faster . . .).

    This program has continued the above sequence to 32,000,000 iterations. This resulted in a number over 13,000,000 digits long, which has yet to produce a palindrome. It took just over 283 days of calculations on a 266 MHz and a 400 MHz desktop machine, running at separate times. The nature of the algorithm eliminates the option of using multiple machines to improve its calculation speed as each iteration depends on the full answer of the last iteration. (To perform the calculations on multiple machines, you would need a very reliable high speed connection with minimal latency between the machines, and a completely new algorithm that allows partial processing of the huge number. I will not get into it here, but I have some very good ideas regarding this. If anyone is thinking about moving the 196 Palindrome Quest to a parallel network, please take a look at the Processing Across a Network thread, on the 196 Discussion Board. You can see my thoughts there. [Note: This message board is offline. If anyone is willing to host this message board, so it can continue to exist, please contact me. Internet Archive of Processing Across a Network thread.]) To give an indication of how many calculations this actually is, it would take a human being, at the rate of 3 additions per second, 3,300,000 years to accomplish this working 24 hours a day, 7 days a week, without any breaks, and assuming the calculations are done flawlessly.

    The next goal was 40,000,000 iterations, which would have resulted in a 16,000,000 digit number taking a little over a year. But, I stopped the quest at this time, since I no longer had access to a computer to continue the calculations. I have passed on my work to Wade VanLandingham. On his web site, 196 and Other Lychrel Numbers, he has continued the quest to over 300,000,000 digits (almost 725,000,000 iterations).

    Please take a look at my World's Record page for more information on my involvement in this quest, as well as other palindrome records.

    Back to World Records page

     
    22,778 visitors since August 18th, 1999
    2,037,676 total page views since May 13th, 1999
    Jason Allen Doucette / Xona Games
  • 梦之城|登录

    梦之城登录注册平台

    龙8国际娱乐long88.com

    mg电子游戏最佳平台

    qy8千亿国际娱乐网址

    吉利i的彩的网的登陆网址

    ca888亚洲城娱乐

    凤凰彩票平台网站

    新金百利国际首页