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Thread: odd math problem

  1. #1
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    Lightbulb odd math problem

    hello everybody, i love math and do it in competitions at my highschool and am relatively new here, and theres this problem that stumped me. hoping some of you guys can help.

    its simply this.

    "simplify 1994^1994" (1994 raised to the 1994 power)

    cant do it on a calculator

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    "x^x" ?
    There used to be something meaningful here.

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    I'm not sure what exactly you mean by simplifying it? Anyway you do it will still get you the same answer. You could split it up into something like this though..

    (Y^N) * (Y^N) = (Y^M).. In this case Y = 1994, M = 1994, and N = M/2. You could keep expanding it infinitely, but you'd still get (Y^M) in the end.

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    simplify as in 4.487x10^6579 (this is the answer)
    Last edited by martini0072; 05-08-2012 at 12:23 AM.

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    11111001010

    Shift Right 1

    1111001010
    S = Square, X = multiple by 1994.

    the binary above becomes
    S1994S1994S1994S1994SSS1994SS1994S
    1994^2 = ...
    Result * 1994 = ....
    That squared^2... and so on..


    The result of 1994 ^ 1994 is both of the below in two different forms.

    4.4870098966106959081161009800253e+6579

    OR

    4.4870098966106959081161009800253 * 10 ^ 6579
    I am Ggzz..
    Hackintosher

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    Quote Originally Posted by Brandon View Post
    11111001010

    Shift Right 1

    1111001010
    S = Square, X = multiple by 1994.

    the binary above becomes
    S8S8S8S8SSS8SS8S
    1994^2 = ...
    Result * 1994 = ....
    That squared^2... and so on..


    The result of 1994 ^ 1994 is both of the below in two different forms.

    5.7734320919198422404919208157297 e+1800

    OR

    5.7734320919198422404919208157297 * (10 ^ 1800)
    how does one do binary? how does one square such big numbers on a calculator? and also my answer sheet said the answer was 4.487x10^6579

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    Quote Originally Posted by martini0072 View Post
    how does one do binary? how does one square such big numbers on a calculator? and also my answer sheet said the answer was 4.487x10^6579

    Check my edit.. I accidentally missed an S. lol

    K it goes like this:

    Convert the powered number to binary.

    Example: 2 ^ 6.. Convert the 6 to binary.
    Example: 1994 ^ 1994.. Convert 1994 to binary.

    Now you got some binary crap.
    For every 0, replace it with S.
    For every 1 Replace it with S1994.

    S means square the previous value and 1994 means multiple the previous by that.

    thus starting out we'd do:

    1994 * 1994 = X;
    X * X = Y.. Finally we hit 1994

    Y * 1994 = Z
    Z * Z = Alpha.
    Alpha * 1994 = Beta
    Beta * Beta = Iunno.. keep going till u eliminated all the S's and the 1994's. Finally you get your answer.

    Also calculators can only do this in scientific notation.

    Code:
    C++:
    int main()
    {
              cout<<setprecision(15)<< pow(1994.0, 1994.0);   //these are doubles and hold the decimals no matter what.
    }
    The value in the end may be truncated.


    Ohh and if you like cool tricks like that, wait till you hear about the taylor series for calculating sine of an angle manually!

    sin x = x - x3/3! + x5/5! - x7/7! + ... y
    I am Ggzz..
    Hackintosher

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    Quote Originally Posted by Brandon View Post
    11111001010

    Shift Right 1

    1111001010
    S = Square, X = multiple by 1994.

    the binary above becomes
    S1994S1994S1994S1994SSS1994SS1994S
    1994^2 = ...
    Result * 1994 = ....
    That squared^2... and so on..


    The result of 1994 ^ 1994 is both of the below in two different forms.

    4.4870098966106959081161009800253e+6579

    OR

    4.4870098966106959081161009800253 * 10 ^ 6579
    I get a similar answer:

    44870098966106959081161009800253338947743890921828 97072419804639495785340115229062597024725485188410 65522025768823148251336080351104286244085663974373 46366730240998403312072561637865799536669837993265 72846284939532923893914939821949041684204912457663 81106227816211459260493473257659172259202210994483 36969005166200487822520499664369595012342967891371 75620023525053362202331608509414356328268368120252 25563106891916557494823975493638493728977800290703 23040732185754530557827398459801999780758598456175 98386829947516158091676830157801043763723937874124 46222450518638992828381232308263528018769249762081 63423480093293837163992400412067358479262062562272 27382387644620468049577319668456450030386494104581 09434748391014978255739764386187878352746747328587 91421602880320589889729888442755243038741791353473 51001205047158268466062226593702139083167158286501 23816819265793232733618450386993795604935327026006 49918162231848394292437376255673048943668522372411 08218592326051092492816691649174352298230041566298 34038375667729796018124395398920971729876900358965 94576186294788498775729800017545294761945109453643 92595497716756646388779701025786016641978243129691 83686468731588983088363858846189840892310461664495 88797548167619081358551455418897615243703952823112 69332846699066715407208829685536826764055745091764 16215580326870157535133624163090886167873711036729 74610027712469281027507053783885408922862011896725 18780762458970469648370035886778182667080557296939 80812067691927486190180283220225795242869177114094 31930362184982800315888426767171053827406981598176 95814757195628057014003775087820445880123120080987 30704772260031170957730942044451474208451744955534 87296078632332057243812211584249297935146824226612 21494228086683689839891244256531667585464145745391 60347478264789770710732419067543577624149853489641 76348799466311506216209953609638734561405201650978 39952972988780935814439701657092452388214546345434 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    or you could just say 2^(2*997) * 997^(2*997) but basically finding out what is it that they're looking for is probably best place to start... by the way what i wrote is factored version of your answer, and you can write it even nicer like this:

    2^(997*2) * 997^(2*997)

    and then it looks cool :P
    Perfect script? There is no such thing as "perfect", only "better than you expect".

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    use wolfram alpha or mathematica

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    1994^1994=10^x
    log(1994^1994)=x
    1994*log(1994)=x
    1994*log(1994)=~6579.651957

    1994^1994=~10^0.651957 * 10^6579 = 4.4870096*10^6579

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    Quote Originally Posted by doorsftw View Post
    use wolfram alpha or mathematica
    I used MAPLE and gave him an exact answer to his question, not sure why this is still being commented on.

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    Why would you guys do this via binary and such when it's easily solvable with a logarithm...

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