﻿ How would you solve this math problem?
21 May, 2013, 14:25:50
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 « on: 10 May, 2012, 22:30:10 » 0

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 » 0

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 » 0

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 » 0

19,112

EDIT: When in doubt, brute force with Mathematica.

 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

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 « Reply #4 on: 10 May, 2012, 22:58:46 » 0

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 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Spoiler for That in base 5:
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Spoiler for Code:
 12345678910 System.Numerics.BigInteger hugenumber = System.Numerics.BigInteger.Pow(2012, 2012);// now type iconv=10;oconv=5 then the result of hugenumber in bcstring 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 » 0

How would you do it without using a computer program, though?
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 « Reply #6 on: 11 May, 2012, 04:30:40 » 0

long hand
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 « Reply #7 on: 11 May, 2012, 04:38:25 » 0

There's got to be a shorter way...
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 « Reply #8 on: 11 May, 2012, 06:11:38 » 0

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 » 0

Does it have to do with ISEF? and CERN?
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 « Reply #10 on: 11 May, 2012, 06:14:50 » 0

What do ISEF and CERN have to do with anything?
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 « Reply #11 on: 11 May, 2012, 06:16:21 » 0

Anyway, that would be a total pain doing it by hand.
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Support Casio-Scene against the attacks of matt @ matpac.co.uk ! For more information: Casio-Scene shuts down & Matt actions threads
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Keytar Hero [|||||_____] 50% Engine done, wackiness left to do (Halted)
OmniOS
VVVVVV [||||______] 40% (Made most of the engine, extremely glitchy) (Gave it to Leafy)
░█▀█░█░█░█▀▀░█▀█░█▀█░█▀█░▀█▀░█▀▄
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I hate TI right now
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You make me lose the game
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<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:
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 « Reply #12 on: 11 May, 2012, 06:19:13 » 0

it's much easier if you choose bases that are powers of each other.
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