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Math Help - I've got 4 balls and 4 boxes - explain how I work out the number of arrangements

  1. #1
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    Question I've got 4 balls and 4 boxes - explain how I work out the number of arrangements

    I have 4 balls, numbered 1-4 or different colours - basically 4 balls all different.

    I have a box - I'll call it my universe.

    In this box I can arrange the balls

    12
    34

    23
    14

    and so on. NO REPEATS are allowed.

    How do I calculate - with an explanation - how many different arrangements I have.

    I think the answer should be 16.

    Can anyone explain?
    Last edited by rintelen; May 15th 2011 at 08:08 AM. Reason: slight modification to make clearer
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  2. #2
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    Hello, rintelen!

    \text{I have 4 distinct balls, and I have a box.}

    \text{In this box I can arrange the balls: }\;\boxed{\begin{array}{c}12\\34 \end{array}} \qquad \boxed{\begin{array}{c}23\\14\end{array}} \quad \text{ and so on.}

    \text{How do I calculate how many different arrangements I can have.?}

    \text{I think the answer should be 16.} . . . . no

    For ball #1, there are 4 choices for its position.
    For ball #2, there are 3 choices for its position.
    For ball #3, there are 2 choices for its position.
    For ball #4, there is 1 choice for its position.

    Therefore, there are: . 4 \times 3 \times 2 \times 1 \:=\:24 arrangements.

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  3. #3
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    Not according to Max Tegmark

    THe reason why I asked this is that I saw this article by Max Tegmark. According to him 16 is the answer. I cannot imagine a physicist getting it wrong. I've copied below what he wrote. He also draws a diagram...not shown here. What am I missing from this description - in understanding - that gives him 16 arrangements? I don't get it.

    EXAMPLE UNIVERSE

    Imagine a two-dimensional universe with space for four particles.


    Such a universe has 2^4, or 16, possible arrangements of matter.
    If more than 16 of these universes exist, they must begin to

    repeat. In this example, the distance to the nearest duplicate is

    roughly four times the diameter of each universe.
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    Quote Originally Posted by rintelen View Post
    THe reason why I asked this is that I saw this article by Max Tegmark. According to him 16 is the answer. I cannot imagine a physicist getting it wrong. I've copied below what he wrote. He also draws a diagram...not shown here. What am I missing from this description - in understanding - that gives him 16 arrangements? I don't get it.

    EXAMPLE UNIVERSE

    Imagine a two-dimensional universe with space for four particles.


    Such a universe has 2^4, or 16, possible arrangements of matter.
    If more than 16 of these universes exist, they must begin to

    repeat. In this example, the distance to the nearest duplicate is

    roughly four times the diameter of each universe.
    A Physicist wrong about a Math problem? Never!

    Anyway, I suspect the diagram is limiting some of the possibilities that Soroban is counting. I don't suppose you could describe it?

    -Dan
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    Quote Originally Posted by rintelen View Post
    Max Tegmark EXAMPLE UNIVERSE
    Imagine a two-dimensional universe with space for four particles.
    Such a universe has 2^4, or 16, possible arrangements of matter.
    If more than 16 of these universes exist, they must begin to
    repeat. In this example, the distance to the nearest duplicate is
    roughly four times the diameter of each universe.
    I have absolutely no knowledge of physics.
    However, if he means that there are four particles that have binary states, on or off, then 2^4=16 makes sense.
    (Physicist Edward Fredkin, has a metaphysics/ontology built on that model.)

    On the other hand, if each of the four must be in one of four positions then the answwer is 4!=24.
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    Looking at the diagram it shows this

    It looks as if what he's describing is being able to put 4 particles in any combination within 4 boxes

    so for example: white and grey particles - are shown in the diagram. So perhaps he's saying 4 particles but two one kind and two of another?



    white, white
    grey, white

    grey, white
    grey, grey

    and so on.

    So perhaps I misread it. He didn't say that though!
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  7. #7
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    Quote Originally Posted by rintelen View Post
    It looks as if what he's describing is being able to put 4 particles in any combination within 4 boxes
    so for example: white and grey particles - are shown in the diagram. So perhaps he's saying 4 particles but two one kind and two of another?
    white, white
    grey, white

    grey, white
    grey, grey

    and so on.
    In this model the data points are binary: gray or white.
    So 2^4=16 is correct.
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  8. #8
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    Are you able to explain how this is worked out then please?

    Hi Okay, are you able to tell me how one gets to the 2 to the power of 16 with this particular situation please?

    THe formula used, why and how please?
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  9. #9
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    Quote Originally Posted by rintelen View Post
    Hi Okay, are you able to tell me how one gets to the 2 to the power of 16 with this particular situation please? THe formula used, why and how please?
    Where in the "H__" did you get 2^{16}~?
    Where is that ever mentioned in any reply?
    Are you trolling this site?
    If so, why?
    We are really trying to provide a service.
    Are you mocking us?
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  10. #10
    Forum Admin topsquark's Avatar
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    Question answered. Thread closed.

    -Dan
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