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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 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
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Message has 8 Replies:
 | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Ahh, but that isn't true -- rotate one of the pieces. There are, in fact, an infinite number of ways to connect those two 1 x 1 bricks. (Of course, you probably can't tell the difference between two 1x1 bricks connected at 22 degrees and (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) 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*9...0309456440 (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) ... (...) Two 1x1 bricks can be connected together in an infinite number of ways. The top brick can be rotated freely to any angle and still connect, and the angles are countless. Given a 10 piece collection of different parts, the number of (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) I received a little LEGO brochure years ago that said something like 8 standard 2x4 bricks can be joined together (standard LEGO building techiques--not these 'rotate on a stud, therefore infinite) over a million different ways. That's 8 (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) The permutations when making only right angle stud connections with less than 1000 2x4s far exceeds the number of atoms in the universe or nanoseconds in the age of the universe (heck, probabably ALL the universes in Heinlen's Number of the (...) (20 years ago, 8-Dec-04, to lugnet.general, FTX)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Of course the number of combinations isn't 'unlimited', but if it takes more time than the life of the universe to check them out, it's 'practically unlimited'. (...) Not counting the endles possibilities of rotating one part :-) Take a look (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Well, 1st off, there's probably on the order of several hundred billion pieces on the planet. I remember reading in some FAQ the estimated number of pieces in the world, but I can't seem to find it at the moment. I know they make about 20 (...) (20 years ago, 8-Dec-04, to lugnet.general)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) From Hitchhiker's guide: "Forty-two!" yelled Loonquawl. "Is that all you've got to show for seven and a half million years' work?" "I checked it very thoroughly," said the computer, "and that quite definitely is the answer. I think the (...) (20 years ago, 8-Dec-04, to lugnet.general)
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