7 ms·
All Combinations of Six 2x4 Lego Bricks
- mattmalin 11y agoNote: 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 https://github.com/LasseD/BrickCounting
- DiThi 11y agoIt bugged me that the 2-brick possibilities pic in [1] wasn't ordered so I made this http://i.imgur.com/ShWZnwl.png http://i.imgur.com/ShWZnwl.png [1] http://www.math.ku.dk/~eilers/lego.html http://www.math.ku.dk/~eilers/lego.html
- tgb 11y agoWon'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 11y agoWhere 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 11y agoYour ascii art has convinced me! I imagined you could rotate the left two into each other but that makes no sense.
- jgrahamc 11y agoWell 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-train.html http://blog.jgc.org/2010/01/more-fun-with-toys-ikea-lillabo-...
- fogleman 11y agoThe Ikea one seems more practical.
- dublinben 11y agoYou can create more arrangements if you treat the bridge like two pieces, which it is.
- pavel_lishin 11y agoHow so? If your goal is to create a loop, the two pieces must be joined together.
- lfowles 11y agoYou 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 11y agoUnless 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.
- dublinben 11y agoThe original creator of this type of train track offers just such a support piece.[0] You can also 3D print your own supports![1] [0] http://i.ebayimg.com/00/s/MTIwMFgxNjAw/z/DAUAAOSwGvhT3ny3/$_35.JPG http://i.ebayimg.com/00/s/MTIwMFgxNjAw/z/DAUAAOSwGvhT3ny3/$_... [1] http://www.thingiverse.com/thing:110221 http://www.thingiverse.com/thing:110221
- fit2rule 11y agoI'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.
- DanBC 11y agohttp://thetechnicgear.com/2014/02/best-lego-sorting-machines-will-see/ 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?
- randomanybody 11y agoA minor typo in this paper yields the quote "Our result is that using sic [sic] bricks, one can combine them into different models."