Subject:
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Re: Is lego *truly* unlimited? (some thoughts)
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Newsgroups:
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lugnet.general
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Date:
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Wed, 8 Dec 2004 13:18:48 GMT
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Viewed:
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1048 times
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In lugnet.general, Samarth Moray wrote:
> I was just wondering today about how much lego is trumpeted as having an
> 'unlimited' number of possibilites. Now I'm no math whiz, but it seemed
> logically impossible to me. So here's some food for thought for the gurus out
> there to digest and make sense of:
>
> Each lego brick has a limited number of uses. A *very* small example of this
> would be two 1 x 1 bricks, can only be connected together in one way, or two if
> theyre of a different colour. (a red on top of a blue, or blue on a red)
> Obviously, the possibilites for each individual brick increase, a 1 x 2 - 1 x 4
> bracket has A LOT more possibilites than a 1 x 1. The point I'm getting at here
> is that it should be possible to hence calculate the exact number of
> possibilites that YOUR collection is capable of achieving. For example, if you
> had a hundered various pieces, the things you could do with them would be the
> sum of all possibilites each one has in relation to the others. (this is
> counting the various SNOT, AZMEP, and whatever else included). Now this is still
> a very small number, I'd expect the average 5-digit collection to generate a
> 10000000000(?) digit possibility, or even more.
>
> Some thoughts/comments from the Mathematicians out there?
>
> Samarth
Hello.
Very interesting question.
Just the selection of pieces from a collection generates a very large amount of
possibilities; Selecting 10 pieces from a collection of 100 (different) pieces
generates
100!/(90!*10!)=100*99*...3*2*1/(90*98*..*3*2*1*10*9*8...*3*2*1)=17310309456440
possible model kits.
Just putting these in a line, for instance a column of bricks (assuming they all
are brick-configured in some way) of different shapes and colours, gives
62815650955529472000 different models, without rotating the pieces or
considering alternate placements of one brick on top of the other.
My collection contains about 46000 LEGO pieces of approximately 4000 different
varieties.
If I were to build a 46000-piece MOC and all pieces are assumed to be
individually unique, the 46000! ways to order the pieces could serve as a base
figure for how many MOCs I can choose to build, considering that not all pieces
can be connected to all others, but most pieces can be put together in several
different ways. (A Technic Bush and a Technic Pin, can´t be together, for
example, but two different 2x4 bricks can be put together in more than 90 ways)
This number is about 1.1*10^194512. Large, but not infinite.
The possibilities are well beyond what I have time to explore in my lifetime,
though, I´m sure!
Olof
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Message has 1 Reply:
 | | Re: Is lego *truly* unlimited? (some thoughts)
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| SNIPPY (...) Hi All, This is exactly the answer I was looking for. Thanks, Olof! Now to the others, (I'll write one reply, cause it's easier when youre not a member :-l) although you could combine 2 1 x 1 bricks in infinite number of ways by (...) (20 years ago, 8-Dec-04, to lugnet.general, FTX)
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Message is in Reply To:
| | Is lego *truly* unlimited? (some thoughts)
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| I was just wondering today about how much lego is trumpeted as having an 'unlimited' number of possibilites. Now I'm no math whiz, but it seemed logically impossible to me. So here's some food for thought for the gurus out there to digest and make (...) (20 years ago, 8-Dec-04, to lugnet.general, lugnet.build)
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