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Brain Teaser 5 ?

  1. Jul 3, 2003 #1

    drag

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    Greetings !

    What's all that stuff about (0! + 0! + 0! + 0!)! = 24 !?

    Thanks ! :smile:

    Live long and prosper.
     
  2. jcsd
  3. Jul 3, 2003 #2
    (0)! (pronounced as Zero -Factorial), is equal to 1. The factorial of the sum of the factorials of four zeros, each taken separately, giving 4!, which is equal to 24.
     
  4. Jul 3, 2003 #3

    drag

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    Eeh... factorial ?
     
  5. Jul 3, 2003 #4

    FZ+

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    Consider this:

    4! = 4 * 3 * 2 * 1

    So n!, where n is a natural number =

    n * (n-1) * ... * 1

    It can be mathematically proven that 0! = 1

    Don't ask me how, because I forgot.
     
  6. Jul 3, 2003 #5
    there is no 0! proof

    actually there is no proof that 0! = 1. look at it from this perspective:


    disregarding the order in which we choose, how many ways we can choose k objects from a set of n objects? when finding ways to choose we use the following: nCk = n!/(k!(n-k)!). since there is only one way that one can choose 0 objects, we define 0! = 1 so that n!/(0!(n-0)!) = n!/0!n! = 1/0! = 1.


    bascially 0! = 1 is defined as such because we simply need it to be. try to choose k = 0 objects from a set of n objects if 0! = 0. now that's chaos.

    i hope that helps.
     
  7. Jul 4, 2003 #6

    drag

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    Re: there is no 0! proof

    Aah...so 0! = 1 , in that case I knew what a factorial is but
    I never heard of this equality so I thought this may be something else.

    Thanks ! :smile:

    Live long and prosper.
     
  8. Jul 4, 2003 #7
    4*3*2*1=24 how does that work?
     
  9. Jul 5, 2003 #8

    dav2008

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    What do you mean? By definition 4!=4*3*2*1 which is 24. THats not the answer to the brain teaser, its just an example
     
  10. Jul 5, 2003 #9
    Sarcasm gets lost online.
     
  11. Jul 5, 2003 #10

    dav2008

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    What are you talking about?!?!?!...I was not being sarcastic. I was answering your question. If I didnt understand your question, that isnt my fault.
     
  12. Jul 5, 2003 #11
    I was trying to be sarcastic, most probably just a piss poor attempt at sarcasm, but i was trying.
     
  13. Jul 7, 2003 #12
    Basically, (0! + 0! + 0! + 0!)! = (1 + 1 + 1 + 1)!, which equals 4! which evaluates to 24. That is all there is to it!
     
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