You could rotate some pieces such that they're partially jutting out of the back of the lamp, which might make it possible.
The Simple Proof of the Tetris Lamp
21–30 of 90 posts
Re: The Simple Proof of the Tetris Lamp
#22A few things: 1) Why limit yourself to 4x7? The 1988 NES version of Tetris is 10 units wide. 2) There isn't any malicious design, you simply get 1 of each shape (one of the L pieces in the author's photo is reflected, should be turned the other way). 3) In Tetris, a full row is removed immediately so having a complete rectangular shape that occupies the full available width is unrealistic. Pedantry aside, you'd have…
> 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 removed.
Re: The Simple Proof of the Tetris Lamp
#23So 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.
Re: The Simple Proof of the Tetris Lamp
#24Speaking of Tetris proofs, I've had the following problem on the back-burner for a while: is there a way to check whether an arbitrary contiguous space comprised of squares can be filled in by tetrominoes? I don't have a math background so reasoning about it is difficult. Here's the question on StackOverflow: http://stackoverflow.com/questions/20083552/tetromino-space-...
Re: The Simple Proof of the Tetris Lamp
#25That's exactly how they get you to buy TWO lamps! :)
Is that really obvious? I think the checkerboard pattern only says something about the neighborhoods of the pieces and the amounts of tiles of each color used, not whether there exists is a rectangle configuration.
If you buy 2 lamps, you've got 2 of all the 7 pieces. Piece 7 (the T-shaped piece) is doubled and you can switch the pattern for the second set. You'll have 15x color A and 13x color B in the first set and 13x color A and 15x color B in the second set. I'm pretty sure this would enable you to create a rectangular lamp.
Re: The Simple Proof of the Tetris Lamp
#26Earlier quoted context omitted.
Is that really obvious? I think the checkerboard pattern only says something about the neighborhoods of the pieces and the amounts of tiles of each color used, not whether there exists is a rectangle configuration.
If you buy 2 lamps, you've got 2 of all the 7 pieces. Piece 7 (the T-shaped piece) is doubled and you can switch the pattern for the second set. You'll have 15x color A and 13x color B in the first set and 13x color A and 15x color B in the second set. I'm pretty sure this would enable you to create a rectangular lamp.
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.
Re: The Simple Proof of the Tetris Lamp
#27you should turn that link into an affiliate link. i would love to know how many (other) people also bought that tetris lamp after reading the article.
Re: The Simple Proof of the Tetris Lamp
#28>"Maybe now I can shift my irritation from the lamp itself to whoever designed it to possess such a property. "
I wouldn't be mad at the designer. That person designed a lamp and proposed an impossible puzzle that at first glance looked plausible.
It is the best way to troll people... ever!
Re: The Simple Proof of the Tetris Lamp
#29I 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!)
Re: The Simple Proof of the Tetris Lamp
#30Similar to: https://en.wikipedia.org/wiki/Mutilated_chessboard_problem
Yes. Every time you get a problem with a rectangle table, you must paint it like a chessboard. If that is not enough to find the solution, you must try to think. A small technical detail, dew to professional deformation. The article says that the numbers of squares of each color must be the same, but that only happens if the total number is even, like in this case 13+15=28. If the total number of squares is odd, then…
You must paint it, but it is sometimes better to choose a pattern specific to the problem you're trying to solve.