31–40 of 90 posts
https://3dwarehouse.sketchup.com/model.html?id=u2d94f70c-682... (there's a webgl viewer)
Here's one nice-looking configuration I found. You seem to be implicitly assuming you can only have a depth of one unit but that's possibly an unnecessary limitation. I'm working on seeing if some kind of perfect cuboid can be made. https://3dwarehouse.sketchup.com/model.html?id=u2d94f70c-682... (there's a webgl viewer)
You can make a rectangle as long as you don't use all of the pieces (maybe that is part of the puzzle?). For example, from http://www.amazon.co.uk/Lychee-Tetris-Constructible-Three-di... , remove the purple piece, shift the red piece to the left one space and flip it, then place the blue piece vertically on the right hand side.
So if you ignore piece number 7, can you form a rectangle with the remaining pieces?
Well, this proof doesn't mean you can't. It's not sufficient to prove that you can.
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6664Earlier quoted context omitted.
Well, this proof doesn't mean you can't. It's not sufficient to prove that you can.
It can be done, at least if you're allowed to flip one of the 'L' pieces into a 'J'. 1112 1322 3324 3554 6554 6664
(on second thoughts, you could probably get away with rotating your solution if you're willing to forfeit the '4 width' condition)
You can make a rectangle as long as you don't use all of the pieces (maybe that is part of the puzzle?). For example, from http://www.amazon.co.uk/Lychee-Tetris-Constructible-Three-di... , remove the purple piece, shift the red piece to the left one space and flip it, then place the blue piece vertically on the right hand side.
The argument in the article was that it's the purple piece (the "T") that is the problem (or least that makes the proof trivial). Can you make a rectangle with a subset that includes the T?
Proof: Any rectangle made of Tetris pieces must have an even number of squares (in fact, a multiple of 4) and hence the same number of black/white squares. Every Tetris piece except the T has the same number of black/white squares, hence the T cannot be used in any arrangement of a subset of Tetris pieces into a rectangle.
Here's one nice-looking configuration I found. You seem to be implicitly assuming you can only have a depth of one unit but that's possibly an unnecessary limitation. I'm working on seeing if some kind of perfect cuboid can be made. https://3dwarehouse.sketchup.com/model.html?id=u2d94f70c-682... (there's a webgl viewer)
I'm not sure, but i think the lamp wouldn't work anymore - it seems like the front and back metal strips might have different polarity.
I came here looking for a link to someplace where I can buy this lamp. Since no one has posted such a link yet, here it is: http://www.thinkgeek.com/product/f034/ (I realize we all have access to Google, but if I save 100 people 10 seconds, then I just saved 1000 seconds!)