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Hi everybody!
I was idly flipping through my copy of The Ultimate LEGO book the other day
and I noticed a little bit of trivia on page 8. It says that two 2x4 bricks can
be combined in 24 ways, three bricks: 1060 ways, and six bricks: 102,981,500
ways. ( assuming both bricks are the same color ).
I don't know if this has already been done and posted about but… I decided to
see if this were true. I took out 48 2x4 bricks to build all the combinations.
To be honest however, I used two separate colors so I could see the difference
between each construction. Despite the simplicity of studs-up and 90-degree
angles only, it actually turned out to be a little challenging to work out all
the different forms! If you're interested, I've posted a set of all 24 to
demonstrate the definitive set of different combinations.
It may appear that I have a lot of duplicates, but they are actually mirror
images that would not be able to overlap. Please let me know if I did slip up
though…
They can be viewed at http://www.brickshelf.com/cgi-bin/gallery.cgi?f=3862
When I have the time, I am going to attempt the 1060 ways for three bricks. At
the same speed I found the 24, I'm going to need 22 hours!! Plus, I'll need a
ton of new bricks :-)
Now, since it would take over 400 years to put together the six bricks, I am
wondering if TLC has some mathematical formula they used. Anyone know what it
might be? I'd personally like to figure out the combinations for 4 or 5 bricks.
For the very curious: I built them with real LEGO first, then created them in
BlockCAD.
--- mrgraff
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Message has 1 Reply:
 | | Re: Combining 2x4 bricks
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| Very interesting! One of my co-workers is a math geek - the next time I see him I'll ask him about this problem. I think it falls under the category of math known as combinational topology. Brickshelf's thumbnail script produced an interesting (...) (23 years ago, 24-Mar-01, to lugnet.general, lugnet.build)
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