Subject:
|
Re: Is lego *truly* unlimited? (some thoughts)
|
Newsgroups:
|
lugnet.general
|
Date:
|
Wed, 8 Dec 2004 17:02:50 GMT
|
Viewed:
|
1094 times
|
| |
|
|
SNIPPY
| |
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
|
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 rotating them
(smart answer, you guys, I didn’t see that coming :-D) it wouldn’t be in a way
that was GEOMETRICALLY compatible with other parts. What I mean is that you
couldn’t make a sensible MOC with just an infinity of rotations, since you’d be
breaking out of lego geometry anyway, making those two bricks in that
combination unusable (for the most part) with other elements in a side-by-side
type configuration. Now I’ve seen this used in Ben Beneke’s SNIR fisherman’s
house: http://www.brickshelf.com/cgi-bin/gallery.cgi?f=69760 But whatever’s
possible in this case is mostly because of the jumper plates, and hence keeps
the 1 x 1s within the boundries of legometry.
Now as for James, I thought I mentioned INCLUDING AFOL building techniques,
including TOPLESS. And Juergen, I find the empty MOC a very interesting concept
:-d. I could make many of those ;-P The whole goal of this post was whether some
mathematical formula could be made in order to calculate the number of ways we
could combine the bricks in our collection, and still have them geometrically
compatible with the other pieces, which is not possible with the 1 x 1 with
infinite angles. Now even though I’m NOT a mathematician (heck, I’m 16, no one’s
a mathematician at that age), I think I’ll take the first plunge:
(Possibilites of your collection)=(the sum of all the possibilites of each
individual brick, and then 2,3 and so on in relation to every other brick in
your collection) x (itself)
Am I right guys?
Samarth
http://www.mocpages.com/home.php/604
|
|
Message is in Reply To:
 | | Re: Is lego *truly* unlimited? (some thoughts)
|
| (...) 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)
|
18 Messages in This Thread:
  
- Entire Thread on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
|
|
|
|
