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Author Topic: How would you solve this math problem?  (Read 6355 times)

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Offline blue_bear_94

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How would you solve this math problem?
« on: May 10, 2012, 04:30:10 pm »
How would you solve this math problem?

Find the sum of the digits of the base-5 representation of 20122012.

By the way, I came up with this problem.
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Offline Juju

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Re: How would you solve this math problem?
« Reply #1 on: May 10, 2012, 04:37:49 pm »
Hm, 20122012 is a huge number, not sure every programming language would handle it.

Challenge accepted.
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Offline lkj

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Re: How would you solve this math problem?
« Reply #2 on: May 10, 2012, 04:43:50 pm »
It would be very easy in Python, but unfortunately I have to go to sleep now.
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Offline AngelFish

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Re: How would you solve this math problem?
« Reply #3 on: May 10, 2012, 04:54:56 pm »
19,112

EDIT: When in doubt, brute force with Mathematica.

Code: [Select]
Total[IntegerDigits[2012^2012, 5]]
I'm sure there's a nicer mathematical solution to this. I'm going to go find it.
« Last Edit: May 10, 2012, 05:01:07 pm by Qwerty.55 »
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Offline Juju

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Re: How would you solve this math problem?
« Reply #4 on: May 10, 2012, 04:58:46 pm »
I get to 19112 with C# and bc.

Dammit, ninja'd.

Spoiler For 2012^2012:
79339321913706201344918542253529978726384267001115032900247765529088834426751292419339719593701042030488706862587642939454569490402221629535560003752101033735930781409635190062652518479183745796043560975865276103794913065259649354070088066567483333224286267333741973784851192915998551567961451752797039543624417835820719676208311412673063521416536716075498261223999859560803040605737339518187154126989156123975814308845447914315515493672044850491488200813790935675884643569134584350929265289508542365346050581936389922907558742461047087812591345586318603122957429274284248495209835827292667258280129406158344303713021631375352628515570311207609011797638423707691541981658929247414093851385558567188848660796799252761728103984100711417403446430078731003234893363922939459622151847939380669420038185171792928176725536515424575886854587832643478211479845878729690731963541868761620376215585054466922863231251801601639378005438513851995093584550037469111567301112190345175146470343977208156226352567220051095864866162153265840111370344158536232332716744571077813129667720598388207996970170417069839298598543721070847093131697171930009079923028525065229935291476089204017935818118433887487930509207008529016336715572771343933427470674344445959463686538460118331703139353991060568344888028572208448763522510073560668486786429550072899239482821756234242973560495347896128674478012167369310955293056318284064280430215711028989384310388836113882758714169357572452319295149841629270554625020262344076498164104256903633149630061111870182307282138008858512211404415133156958571534255303081679608812073747015511692266096495380406380157554050223084798416021992839555744698080421741563279403011448918160764123558343664847571287565330714336052788089168444146012143020226774510932432113734636413759931767638028739803706136697106878834732424336460541410617630876411495740895316895913011223666161546107753934375587771812731002727737889371509214873612130713982623158305239956928428298774253939788578853990719148490096496562573251129234395611049295474888356725558895157741200114303549072971271172475485298345792473681604820915505836102275629089939257081109290984711112521936963990773722242756821776116677773860667586225662248030302263016212506250843211630994495009594676181059528498709149307940567652441567128909352765961975349207070199153471026910775605688998810358732219882241143182604282712474049047043226828150204590134945328462557418100041852238954570808107784069011054847472753562168812035279631417711425370575482422676765480492514612059274910487291202942405634664878870514865040023199858590278913509595327066160708955773934930054203813490972772353313230753406109300696023494166119818206700203884601965010061146289992068630636172312631900011885228191211658335594363338399255781840674692727920029974900960188406345068041289611912113790245324893701200154216536595776762893748851079969055167859693692293941003359411749073260880131228307623871936798467583878291725672009524432461552888656107115233815893737459266418489892406645765494241216293080059570245087759181616778457403505163350533370975967222853957722917626307917027790755969575213016548462332842493271431137990438941432547471046681557561161447320656959478643723405558609699475561436777688113211590028823476161487423699778327820589674804630232349760566883977012557741081201767293773004261191462696373541029413758521761989046675756193755462491664161737461089786469179392559840401676253791610104090525359066320711004121024332561738986929205634720905290720399538157150807141156682105805259902888585953396275530408341160690997530571710155619248324964581683062643532150623746471406681222506245091327597152712092519689659503933135734408479545738073300280355472718527199741456168312111293997219912021457148249276520916000852922018147166386207319857119002592230122992680269784060102169630201055639794641822132035541975738972084821285023037523458187653822867556634787514082277406798715437796893120583559741145321788007756428526829820428616107250195767171944189435501030298826967840727134903987944138054771172682945634518555008606501122319934333486248722832377352832141437320118225663053118708637833031952113222612100547083524187580603221908090082589473905984928875094902904215458786429475879312069152423718228880046628764975193642845099987210187541783648038320218626799829390519637997556654087206764293465494108442490933980739849516074405840101744723571606890967550596145468871100427216548536083568720817671632918109907991775819382961960600909825613664834326900376545255406855196308868114478219326336840341953931987695938602369013155310823602090412109514895799861816924192749926089959835555017282201930512686939938902859072025289347862751619870748510723457982109744027860330048769166408820686488344614557077890727082446803092362855451298281897209720832663503534713194398229196996944167743143273739209918961989228224648430119509291183310976005444800216949781514649597619672956881936234521818210961284046359772287166166443036716984063895823360494450665697219115813617754717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Spoiler For That in base 5:
22142142303324132434420424412343430121230214123441102123410221423243044233303312040334131313034042024203140442321343240312302001024433200200032140303113113414221223344420213340301423010043002241043134202141441310230032320102110403034332324421222404414021041302313234202202232334203141204420310142021322124010012322023303012122113124231300331141440013423332440341231101001133212304421304200034431423423400421200411111442203014342144012131300312430431224043242230022100411244431401030301044343133233341114144323044020023002121014431441223432240032414101244022140131242310233004111004140221433222144202440002140434143322212323042044144304024200044012012303120140241420041302023040222410421400004001221243023241142100031032143222400011022343300001004030013321144130003224031420010243241102103424021011032443143221402441020423034222133020123240402232232234043022330211122020021432002033240404104400014111413110412232413412212141222141324443010020222311224413012131143420111234221021132442223412412021432213220244130443240304013401021023443022411103132023204221144312310013114044120214234241332234434004101223433430122040304123030033414042124022331434224404314201041141020130134033304104432344142210020002100412321011011304144141304241220324130423013213200202223140210432310411341202002103331210111444320414000124324314422302123244441301431143241420010443322243210312133443312420303030140414103433112201230130404311222211244420032130401230124424122411434342041334313320032040000412001211322442234344144210124444001302321134330121201020430312430422032341100234202201410231203133324331431234304114340232101141001340322311400444212110323231220041243041001022342430042311202321432143032134123023310403224112312233212120031442400410434220430133313144242434204143323101423400011134124132231233224442121002414423332121012443413314411122030222033002123012203143230124320430041131124020024220301403124130413044422122203210144343123110211113321004424434142431322303140323141132143431230442223433120201013222134244424410333434031423223301032124302434430440214031244324041230043002043423142141204134112134411114341332133431223202130301234420414320221100330014201423120443442412120103011343402103234241313222310410331230230233343121122230423320340112201032211010320021132041401440324131410443041334124033342100130343431124214134232123010141214042124224140202423401114322431222000321130242033122144213240140331314210202032013440104232310113332340234302342214102011241041042130003240131144132014234403212243133332213441144030130103131141213343033111003224210440123323220033311013424110103333112434340014043200003333431334213402221401031304202223032033432043421432013111213034401132240344310241344134203202240430413401442301000044444023422134031202244020131042004311220301003010423404320234124122332302203410210421422332120121231000202031303304434344101301021320420323120133303240014314442304414231443420414101101313314420213430244102212340400422143034020001141032242104032430131011221021424310034232023033210320423140110130243142240213242424314030202000333430113113302010333433301234402443120301003213342134312341102321441102101024311342302430032202122421414244203313120100002034221104123231011120040441311410300003004230331142121444044200342311133241243442124344210302244122001301002122404224042311131144430020321441334043221432442021124302110124413312303401322102411422200344210423111110044032403142111024130101413313414203441141032210232112424122310114204213244434130123423110334422224323213011034011131101333431340202323030203044404412310344311304021304024400131033412203103440212303044102402013041320032321032114132023403423114322431010241210121121110424343123113322444212030101134224404030242304322242142120214021041332043134323200200144103014343200422344311240114443443122301320423224122033341340223101212101410124341130113010324013102112334400423310442244314404440204313000103211200140034101324011413123113210101212140431434211332301044140013324411442210233411010312302140421232111012344312432432201043042021214010441243020021121320041400203001033210302334101201210200332334030120311031122444200243141131342042330400440210244334101222022211311434014411403113431203323042341313202123012443311104044313133423043120030044023304112044010212334204203413032443230004341020234041022124304323102011202202013133240211402332434442013324233134300221102230231443434110132124101114441344041431243411114210310040133414213144410131211220403032431002220431020420423430401442024400222341310403310330302011100031144143003132030340402100130320101312202001304012212200142311313214421220231132104024434023303414141010013041402114011420211422033210324421312302330143001024343112010042033232204311441332141402212401020341210242203444414120224121221413114030122334331132242314434330342343324031032230020312331123343410434344131222313313302020304443011023030021122044411044402312321410300321331022204002142242131120031402233104042011103343034433242044041400424200100332011113311310041304141434013332033202142441341233211133120201432204211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Spoiler For Code:
Code: (C#) [Select]
System.Numerics.BigInteger hugenumber = System.Numerics.BigInteger.Pow(2012, 2012);
// now type iconv=10;oconv=5 then the result of hugenumber in bc
string lolbase5number = "whatever you got in bc";
int TheAnswer = 0;
for (int i = 0; i < lolbase5number.Length; i++)
{
    TheAnswer += lolbase5number[i]-48;
}
// now output it
« Last Edit: May 10, 2012, 05:04:10 pm by Juju »
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Offline blue_bear_94

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Re: How would you solve this math problem?
« Reply #5 on: May 10, 2012, 10:16:07 pm »
How would you do it without using a computer program, though?
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Offline ZippyDee

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Re: How would you solve this math problem?
« Reply #6 on: May 10, 2012, 10:30:40 pm »
long hand :D
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Re: How would you solve this math problem?
« Reply #7 on: May 10, 2012, 10:38:25 pm »
There's got to be a shorter way...
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Offline AngelFish

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Re: How would you solve this math problem?
« Reply #8 on: May 11, 2012, 12:11:38 am »
Huh, it turns out this problem is highly related to a problem Xeda and I were working on AND a problem I was working on by myself awhile ago. Interesting...

EDIT: Also, there is almost certainly a reasonable way to do this by hand.
« Last Edit: May 11, 2012, 12:14:20 am by Qwerty.55 »
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Offline willrandship

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Re: How would you solve this math problem?
« Reply #9 on: May 11, 2012, 12:13:36 am »
Does it have to do with ISEF? and CERN?
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Re: How would you solve this math problem?
« Reply #10 on: May 11, 2012, 12:14:50 am »
What do ISEF and CERN have to do with anything?
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Re: How would you solve this math problem?
« Reply #11 on: May 11, 2012, 12:16:21 am »
Anyway, that would be a total pain doing it by hand.
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Offline willrandship

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Re: How would you solve this math problem?
« Reply #12 on: May 11, 2012, 12:19:13 am »
it's much easier if you choose bases that are powers of each other.
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