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Author Topic: How would you solve this math problem? -  (Read 649 times) Bookmark and Share
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blue_bear_94
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« on: 10 May, 2012, 22:30:10 »
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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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« Reply #1 on: 10 May, 2012, 22:37:49 »
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Hm, 20122012 is a huge number, not sure every programming language would handle it.

Challenge accepted.
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« Reply #2 on: 10 May, 2012, 22:43:50 »
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It would be very easy in Python, but unfortunately I have to go to sleep now.
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« Reply #3 on: 10 May, 2012, 22:54:56 »
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19,112

EDIT: When in doubt, brute force with Mathematica.

Code: Select All | Copy To Clipboard

1
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: 10 May, 2012, 23:01:07 by Qwerty.55 » Logged
∂²Ψ    -(2m(V(x)-E)Ψ
---  = -------------
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« Reply #4 on: 10 May, 2012, 22:58:46 »
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I get to 19112 with C# and bc.

Dammit, ninja'd.

Spoiler for 2012^2012:
793393219137062013449185422535299787263842670011150329002477655290888344267512924193397195937010420 304887068625876429394545694904022216295355600037521010337359307814096351900626525184791837457960435 609758652761037949130652596493540700880665674833332242862673337419737848511929159985515679614517527 970395436244178358207196762083114126730635214165367160754982612239998595608030406057373395181871541 269891561239758143088454479143155154936720448504914882008137909356758846435691345843509292652895085 423653460505819363899229075587424610470878125913455863186031229574292742842484952098358272926672582 801294061583443037130216313753526285155703112076090117976384237076915419816589292474140938513855585 671888486607967992527617281039841007114174034464300787310032348933639229394596221518479393806694200 381851717929281767255365154245758868545878326434782114798458787296907319635418687616203762155850544 669228632312518016016393780054385138519950935845500374691115673011121903451751464703439772081562263 525672200510958648661621532658401113703441585362323327167445710778131296677205983882079969701704170 698392985985437210708470931316971719300090799230285250652299352914760892040179358181184338874879305 092070085290163367155727713439334274706743444459594636865384601183317031393539910605683448880285722 084487635225100735606684867864295500728992394828217562342429735604953478961286744780121673693109552 930563182840642804302157110289893843103888361138827587141693575724523192951498416292705546250202623 440764981641042569036331496300611118701823072821380088585122114044151331569585715342553030816796088 120737470155116922660964953804063801575540502230847984160219928395557446980804217415632794030114489 181607641235583436648475712875653307143360527880891684441460121430202267745109324321137346364137599 317676380287398037061366971068788347324243364605414106176308764114957408953168959130112236661615461 077539343755877718127310027277378893715092148736121307139826231583052399569284282987742539397885788 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642298291347178244973555094287473528371561184542236571249223505825580864023795357427038506465833324 052902805483464121638458429664332002439498717116244091641603408446175025460209595505797765036736881 171381616627906254783750410120223392599774600044192233596744842658069345219841159863972923286245321 655053161378090131060931862864149484083468785471175621743651550777194075836962336782381650761170241 836431840238695871232743665852111839560772489710894915860414811302950999831052008613478486294465172 083296214230381412129132007015940724677756316149915560875316914310720017391207747386258704266842704 705261020980263375086728973380463068050330122801641542786791257448360352834451055656132462834067951 48933260640256
Spoiler for That in base 5:
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014304042130141142434302200011222243123032010200413314402402134311320232214411002303043232122130421 140133042033323434233240003411302314211404401042313001300031122410410414040031333002121304403131130 142134333240314003102014412430313144130021420211413323341124333130034102444304442003131243330100030 212002412313241404034301221014232112223301233143242043114004044242004000114110213423131033434323122 341403014342044210302322124423412242212214204233213402040321203033043414401104242010220233340214312 013330103234004403302401113313023402224132440340302240221342022133343244432423123002112230110304210 442011
Spoiler for Code:
Code: Select All | Copy To Clipboard

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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: 10 May, 2012, 23:04:10 by Juju » Logged
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« Reply #5 on: 11 May, 2012, 04:16:07 »
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How would you do it without using a computer program, though?
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« Reply #6 on: 11 May, 2012, 04:30:40 »
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long hand Cheesy
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« Reply #7 on: 11 May, 2012, 04:38:25 »
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There's got to be a shorter way...
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<< stdradiation

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 Cheesy({ MadSmileySmileySadSmileySadSadSad, MadSmileySmileySadSadSmileySadSmiley,
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« Reply #8 on: 11 May, 2012, 06:11:38 »
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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: 11 May, 2012, 06:14:20 by Qwerty.55 » Logged
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« Reply #9 on: 11 May, 2012, 06:13:36 »
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Does it have to do with ISEF? and CERN?
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« Reply #10 on: 11 May, 2012, 06:14:50 »
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What do ISEF and CERN have to do with anything?
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« Reply #11 on: 11 May, 2012, 06:16:21 »
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Anyway, that would be a total pain doing it by hand.
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Reuben Quest HD: The PC Remake
Zarmina Project: Play Read
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Spoiler for Other stuff:
Also Yuki "ジュジュ" Kagayaki
Support Casio-Scene against the attacks of matt @ matpac.co.uk ! For more information: Casio-Scene shuts down & Matt actions threads
Find what P+4zJ means and you get free candy! cc4daa9c4645bd123ed22e385ed701fd
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Omnimaga Owner and Former Administrator
Fan of My Little Jim Bauwens: Losing the Game is Magic
Proud member of POLN - Ponys Oppositing Lol Names
Member of OBEL - Omnimaga Board of the EFnrgelnicshh Language - Office Omnimagois de la Langue FArnagnlçaaiiss
あなたはこのゲームを失った
Spoiler for Old spoileryception stuff:

Spoiler for Coming soon...:
Indefinitely halted [|.........] 10%
OmnomIRC Mobile [||||......] 40% (argh threads >_<)
Spoiler for Current/Past TI-related projects:
The Axe Parser Wiki / Founder and maintainer
Keytar Hero [|||||_____] 50% Engine done, wackiness left to do (Halted)
OmniOS
VVVVVV [||||______] 40% (Made most of the engine, extremely glitchy) (Gave it to Leafy)
░█▀█░█░█░█▀▀░█▀█░█▀█░█▀█░▀█▀░█▀▄
░█▀█░▄▀▄░█▀▀░█▀█░█░█░█░█░░█░░█░█v0.1.0
░▀░▀░▀░▀░▀▀▀░▀░▀░▀░▀░▀▀▀░▀▀▀░▀▀░[|||||||||¦] 95ish% (Completed)
tilibs-wii? [._________] 0% (Nope.)
Spoiler for Spoilers:
<!---->
wxWabbitemu Developer
Spoiler for Other Userbars:






<!--Everything done, got 90% Cheesy sudo apt-get install z80asm z80dasm-->
Spoiler for Quote:
We are in 2034. The situation on Earth is catastrophic. The ozone layer has been completely destroyed by the carbonic gas of automobiles, the chemical industries, and the poosh-poosh in little cans. In the end, the earth cooks under the rays of the sun. We must find a planet on which can live 6 billion idiots. The planetary federation turns to the strongest country in the world: Canada. It is Canadian knowledge that has allowed, on October 28, 2034, the launch of the spaceship Romano Fafard, which leaves earth to search the confines of the Universe. Where the hand of man has never set foot.
Quote from: ruler501 on 21 May, 2011, 02:47:48
I hate TI right now
Quote from: jimbauwens
You make me lose the game
Everytime I read your name
Spoiler for The real answer to life, the universe and everything:
Spoiler for Old HTML stuff:
<div style="margin:20px; margin-top:5px"><div class="smallfont" style="margin-bottom:2px">Spoiler for This is another spoiler: <input type="button" value="Show" style="width:60px;font-size:10px;margin:0px;padding:0px;" onclick="window.location.replace('http://goo.gl/QMET');"></div><div class="alt2" style="margin: 0px; padding: 6px; border: 1px inset;"><div style="display: none; ">HAHAHA SUCCESSFUL RICKROLL IS SUCCESSFUL</div></div></div><!-- old avatars:
http://fc00.deviantart.net/fs71/f/2011/120/d/f/nepeta_nyan_cat_by_supuru-d3f8tcx.gif
http://th01.deviantart.net/fs70/PRE/i/2011/099/5/b/rainbow_dash_derping_by_moongazeponies-d3dmg7l.png--><!---->
I may or may not be inactive during work hours (9AM to 5PM EST, Monday to Friday), so for any inquiries please leave a message after the beep and I'll answer you when I have time. Beep. Nevermind, I'm on vacation now. Cheesy
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« Reply #12 on: 11 May, 2012, 06:19:13 »
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it's much easier if you choose bases that are powers of each other.
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