If you remove the T piece, is it possible to assemble the other six into a rectangle? I suspect not, but the checkerboard proof does not suffice for this.
The Simple Proof of the Tetris Lamp
71–80 of 90 posts
Re: The Simple Proof of the Tetris Lamp
#72Author here - slightly overwhelmed by the response, but thanks for everyone's feedback! I never thought so many people would be as interested as I am in the lamp...
Re: The Simple Proof of the Tetris Lamp
#73If you remove the T piece, is it possible to assemble the other six into a rectangle? I suspect not, but the checkerboard proof does not suffice for this.
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rZIIIISLRe: The Simple Proof of the Tetris Lamp
#74Earlier 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
Re: The Simple Proof of the Tetris Lamp
#75Earlier quoted context omitted.
Having the same number of both colours is not sufficient. 14 Z pieces will give you 28 of each color, but you can't make a rectangular lamp (of any size) from only Z pieces.
Not in 2D, but you can in 3D! edit: Actually I'm not sure my previous statement was true. You can make it more pleasing such as this though: http://nterm.co.uk/content/images/tetris.png
rectangle specifies 2d
I believe you could form a hollow cuboid, but I don't think you could complete a solid cuboid.
Re: The Simple Proof of the Tetris Lamp
#76If you remove the T piece, is it possible to assemble the other six into a rectangle? I suspect not, but the checkerboard proof does not suffice for this.
rr Z [] S LL r ZZ [] SS L r Z IIII S L rr Z [] S LL r ZZ [] SS L r Z IIII S L rrZ[]SLL rZZ[]SSL rZIIIISL
Interesting! I just came here to say that I’ve found a 4x6 packing. I love the fact you can also do 3x8!
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SSJJRe: The Simple Proof of the Tetris Lamp
#77I 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!)
The article links to it in the first sentence also: http://www.amazon.co.uk/Lychee-Tetris-Constructible-Three-di...
According to this [1] comment on Amazon US, the Lychee product is a cheaper version of the official Tetris product [2].
[1] http://www.amazon.com/review/R10BVZ9OBT3IW3
[2] http://www.amazon.co.uk/Tetris-Version-2-Tetrimino-Light/dp/...
Re: The Simple Proof of the Tetris Lamp
#78Earlier quoted context omitted.
> 1) Why limit yourself to 4x7? The 1988 NES version of Tetris is 10 units wide. Presumably, the objective is to arrange the tetriminos into a pleasing rectangle shape. Unfortunately, the factors of 28 are 1, 2, 4, 7, 14 and 28, so 4x7 is the closest you can get to a square, and 2x14 has a similar problem of having the same number of 'white' squares as 'black' squares. The closest one can get is 5x6 with two holes re…
Why? A full row in tetris is removed. To someone who knows the game, leaving a hole in each row would be more pleasing. Aesthetically I'd also find it more interesting, but that's an aside.
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Re: The Simple Proof of the Tetris Lamp
#79Earlier quoted context omitted.
> 1) Why limit yourself to 4x7? The 1988 NES version of Tetris is 10 units wide. Presumably, the objective is to arrange the tetriminos into a pleasing rectangle shape. Unfortunately, the factors of 28 are 1, 2, 4, 7, 14 and 28, so 4x7 is the closest you can get to a square, and 2x14 has a similar problem of having the same number of 'white' squares as 'black' squares. The closest one can get is 5x6 with two holes re…
Why? A full row in tetris is removed. To someone who knows the game, leaving a hole in each row would be more pleasing. Aesthetically I'd also find it more interesting, but that's an aside.
If you must, pretend it's half scale and it's a 4x7 rectangle in a 5 block wide well. The author is waiting for a long piece.
Re: The Simple Proof of the Tetris Lamp
#80I 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!)
And for those in Europe: