Seeking Help

[heavykevie]

Hello, apparently there is 7 unique tetris pieces - O I T L & J S & Z. In total they have 28 squares (4 each) - I am trying to fit all seven into a rectangle of 4 x 7. Can anyone assist. Thank you

[colour_thief]

Hi heavykevie! Welcome to the forum.

I'm assuming you mean a solution that could be assembled with physical pieces (so no line clears)? If that's what you're after it is easily proven to be impossible.

http://en.wikipedia.org/wiki/Tetromino#Tiling_the_rectangle_and_filling_the_box _with_2D_pieces

Although a complete set of free tetrominoes has a total of 20 squares, and a complete set of one-sided tetrominoes has 28 squares, it is not possible to pack them into a rectangle, like hexominoes and unlike pentominoes. The proof is that a rectangle covered with a checkerboard pattern will have 10 or 14 each of light and dark squares, while a complete set of free tetrominoes (pictured) has 11 light squares and 9 dark squares, and a complete set of one-sided tetrominoes has 15 light squares and 13 dark squares.

http://upload.wikimedia.org/wikipedia/commons/a/ad/Tetramino.png

To better understand the proof, imagine a checkerboard over your 4x7 rectangle. Now look at all the pieces. They have 2 of each checker colour right? Except for the T piece, which is imbalanced with 3 of one colour and 1 of another. So no matter how you place things, things will stay imbalanced and you can't evenly fill a rectangle.

I'm not sure what your purpose is, but you should be able to find something that works in a larger rectangle using 2 of every piece. Just be careful to place your T pieces in a balanced fashion.

(Or if you allow line clears it becomes possible with 7 pieces.)

[Zaphod77]

line clears are only possibl ewhen playing shimizu's tetris, or nds-tgd, as those are the only tetris games that alow a well width of four. :)

NO game has a well width of seven.

[Anonymous]

Thank you,

My purpose is to build a book case (read DVDs etc) which is 4 units wide and 7 units high, Rather than have horizontal shelves I intended to have the seven tetras outlines (no internals) constructed as irregular sub shapes. Then fit the irregular shapes within so as to have tall and shallow shelves stacked to neatly fill the bounding external (shelf-less) book case. Savvy? Impossible? So I think I'll need to introduce a non tetris outline and eliminate a genuine outline.

Thank you

[colour_thief]

Well, if you're really stuck with 4x7, you could either use two T pieces and drop one other, or use zero T pieces and double one other. Pretty sure that would work.

Good luck with your project. You should post some pictures later if you're proud of your work.

[xyz]

Thanks again for your help.

My next thought is a 5 x 8 tessellation using two sets of free tetris-onimos. The difference being that rather than have two (qty) L and Z - have an L, J, Z and S. Then when placing the Ts ensure that the placement is negating itself. The bookcase is for my grandson. I'm just the builder. Notionally the bookcase would now be 1.5m wide x 2m tall.

[Zircean]

NO game has a well width of seven.

Actually Shimizu can use any well width from 4 to 36, so technically, yes, it can have a well width of seven.

[muf]

I just love how people always have to set Zaphod's wild claims straight.

[Zaphod77]

I have nothing against being corrected when the corrections are correct. :)

(and this one does happen to be correct)

Revised claim. No official tetris game has a well width of seven available without modification of game files. :) (Tetris Worlds, i'm looking at you)

And a fair amount of my wild claims are correct. :) (Would you believe that SRS allows rotating both left and right in the same frame?)

Wow, looks like I'm special. I have a subtitle now. :)

[Hsanrb]

If you expand the bookcase to 4x8, you could make 2 sets of 4x4 out of squares (L,J,O... 4 T's... lots of combinations)

[Zaphod77]

and seems my revised claim is wrong! there is an authentic tetris game that has well width of seven in multiplayer. (!) It' s Japan only on ps1, though.

I'm beginning to think the universe is trying to spite me. :)

[Rosti LFC]

Stop emphasising things in capitals, and they won't be wrong the vast majority of the time. :P

[Zaphod77]

Okay,i need to try doing that with stuff i wish wasn't true. :) OF COURSE IT WOULD NEVER WORK.

[colour_thief]

and seems my revised claim is wrong! there is an authentic tetris game that has well width of seven in multiplayer. (!) It' s Japan only on ps1, though.

Which game?

[Caithness]

Tetris X

[Ai]

Tetris Dekaris has a well width of 12 in co-op, but each player can only use 7 of the playfield. 5 for each player and the 2 middle colums are shared by the 2 players if I remember correctly. There was a video somewhere, but I can't find it at the moment.