All Combinations of Six 2x4 Lego Bricks (opens in new tab)

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42 pointsmattmalin10y ago19 comments

19 comments

16 comments · 6 top-level

jgrahamc10y ago· 7 in thread

Well that makes my "how many ways can I arrange an Ikea train set" look pretty lame.

http://blog.jgc.org/2010/01/more-fun-with-toys-ikea-lillabo-...

Nonsense! Your post was great fun. The code was fun, too. I particularly enjoyed your comment about to how Pi was referenced in the bible, along with the ensuing rabbit trail of research that took me down.[1]

[1] http://www.tektonics.org/lp/piwrong.php

ggus10y ago

and how many combinations if I buy two sets?

fogleman10y ago

The Ikea one seems more practical.

OneOneOneOne10y ago

Thanks for your post. You've inspired me to write some code for similar problems!

dublinben10y ago

You can create more arrangements if you treat the bridge like two pieces, which it is.

pavel_lishin10y ago

How so? If your goal is to create a loop, the two pieces must be joined together.

lfowles10y ago

You could lengthen the bridge (theoretically, the pieces might not fit that snug) with any combination of the pieces all the way down to the case of a reverse bridge connected at the bottom.

1 more reply

tgb10y ago· 2 in thread

Won't their definition conflict with the rectilinear definition? Specifically, there are distinct rectilinear configurations which are homotopic. With two bricks connected by at corner, there are two rectilinear configurations but both are homotopic. So their method used to count "homotopy equivalence classes which contain at least one rectilinear configuration" would yield a lower number than the previous result. This seems to contradict when the paper says that their definition extends the previous one.

teraflop10y ago

Where are you getting two from? By the definitions on this page, it seems to me like there are four corner-connected rectilinear configurations of two bricks, and also four homotopy equivalence classes, so there's no inconsistency.

    +--+       +--+
    |  |       |  |
    |  |       |  |
    |  |-+   +-|  |
    +--+ |   | +--+
      |  |   |  |
      |  |   |  |
      +--+   +--+
    
    +-----+       +-----+
    |     |-+   +-|     |
    +-----+ |   | +-----+
         |  |   |  |
         |  |   |  |
      	 +--+   +--+

tgb10y ago

Your ascii art has convinced me! I imagined you could rotate the left two into each other but that makes no sense.

fit2rule10y ago· 1 in thread

I've always wanted to make a sorting box that, given any quantity of random Lego Mindstorms parts, sorts the parts into shape/size/purpose bins. A static box, no moving parts but the raw feed.

I suppose it will have to be a big box, mathematically.

DanBC10y ago

http://thetechnicgear.com/2014/02/best-lego-sorting-machines...

Some of these are interesting.

I'd be interested to see how good something that sorted purely by weight could be. And then with a vision stage?

DiThi10y ago

It bugged me that the 2-brick possibilities pic in [1] wasn't ordered so I made this http://i.imgur.com/ShWZnwl.png

[1] http://www.math.ku.dk/~eilers/lego.html

mattmalinOP10y ago

Note: this is not my work, just something I stumbled across.

GitHub project is here, including examples of all angles considered: https://github.com/LasseD/BrickCounting

randomanybody10y ago

A minor typo in this paper yields the quote "Our result is that using sic [sic] bricks, one can combine them into different models."

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