HN Explorer

19 comments

[ 4.9 ms ] story [ 43.7 ms ] thread
tgb
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.
teraflop
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.

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

fogleman
The Ikea one seems more practical.
dublinben
You can create more arrangements if you treat the bridge like two pieces, which it is.
pavel_lishin
How so? If your goal is to create a loop, the two pieces must be joined together.
lfowles
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.
JoshTriplett
Unless they fit very snugly, I don't think anything would hold up the extra pieces in the middle, especially not well enough to support a train.
ggus
and how many combinations if I buy two sets?
OneOneOneOne
Thanks for your post. You've inspired me to write some code for similar problems!
unoti
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

fit2rule
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.

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