What's more annoying is that it has two identical L pieces, instead of having one that is a mirror-image of the other, as they appear in Tetris.
The Simple Proof of the Tetris Lamp
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Re: The Simple Proof of the Tetris Lamp
#12What's more annoying is that it has two identical L pieces, instead of having one that is a mirror-image of the other, as they appear in Tetris.
Looks like the pieces are reversible, so the two L's and two S's are actually L, J, S, and Z.
Re: The Simple Proof of the Tetris Lamp
#13What's more annoying is that it has two identical L pieces, instead of having one that is a mirror-image of the other, as they appear in Tetris.
Well it looks like you can rotate them (I mean in the 3rd dimension not present in actual Tetris)
Re: The Simple Proof of the Tetris Lamp
#14A 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…
> Pedantry aside, you'd have to ask Alexey Pajitnov if there was any devilry involved in choosing the shapes since the makers of the lamp have faithfully included a full set.
No devilry, there's just only so many ways you can connect four squares together to make a shape.
Re: The Simple Proof of the Tetris Lamp
#15What's more annoying is that it has two identical L pieces, instead of having one that is a mirror-image of the other, as they appear in Tetris.
There's also two S pieces instead of an S and a Z. Irritating indeed. There must be order!
Re: The Simple Proof of the Tetris Lamp
#16So if you ignore piece number 7, can you form a rectangle with the remaining pieces?
Re: The Simple Proof of the Tetris Lamp
#17A 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…
Btw, the Tetris field is always exactly 10x20.
Re: The Simple Proof of the Tetris Lamp
#18A 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…
This is not an exercise in "valid" tetris configurations, per se. It's a matter of arranging these blocks to make a clean square - plain and simple. The "malicious design" is tongue-in-cheek.
Every engineer who has this lamp on their desk has thought of this.
Re: The Simple Proof of the Tetris Lamp
#19Terrific reasoning! That same "checkerboard coloring" strategy is used a lot for figuring out tiling problems.
It is too bad the lamp wasn't made of pentominoes (the 12 Tetris-like pieces with 5 squares vs. your tetrominoes with 4 squares.). See http://en.wikipedia.org/wiki/Pentomino. There are 2339 ways to form these into a perfect 6x10 rectangle (more if you include rotations and reflections).
FYI: The creator of Tetris actually got the idea for his game pieces from Solomon W. Golomb's book "Polyominoes" that introduced all kinds of variations on tiling puzzles and proofs. Chapter one starts using checkerboard reasoning right off the bat. So, you are in good company.
Re: The Simple Proof of the Tetris Lamp
#20Similar 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 get one extra square of one of the colors.