4 ms·

That's exactly how they get you to buy TWO lamps! :)

deleted 12y ago
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rndn 12y ago
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.
- rmetzler 12y ago
  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.
  - nemetroid 12y ago
    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.
    - eterm 12y ago
      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 http://nterm.co.uk/content/images/tetris.png
      - penguat 12y ago
        <nitpick>rectangle specifies 2d</nitpick> I believe you could form a hollow cuboid, but I don't think you could complete a solid cuboid.
    - dkersten 12y ago
      So the obvious next question is: how many sets do you need to create a perfect rectangle?
      - evanb 12y ago
        Two! (see my same-level comment)
        ecesena 12y ago
        So the next questions are: - how many 8x7 solutions exist? - does any 4x14 solution exist? - does any 2x4x7 solution exist? :)
        evanb 12y ago
        Let's stick to accept-reject questions for now :)
        dkersten 12y ago
        Awesome, thanks :)
    - evanb 12y ago
      That's true, but here's a construction: OOZZ OOSZZ LLSS ILTS ILTT IJT IJJJ That's built out of one full set of OZSLJTI. If you take two of those, one rotated by 180˚, you get a rectangle.
  - JoshTriplett 12y ago
    The proof in the article is a proof by contradiction. Having equal numbers of each colored square is a necessary but not sufficient condition to form a rectangle.
  - deleted 12y ago
    [deleted]
- ecesena 12y ago
  Here's an example. The trick I used was creating the extra block and the hole on the same side (so, not like the pic). With the pieces numbered as in the post: 2233ffff 72233ddd 7744eaad 7114eaag 5114eegg 555bbccg 6666bbcc Note that, as in the post, I'm not "respecting" Tetris in 2d: pieces 2 and 3 have been "3d rotated" and are "looking in the same direction".

deleted 12y ago

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rndn 12y ago

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.

rmetzler 12y ago
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.
- nemetroid 12y ago
  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.
  - eterm 12y ago
    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 http://nterm.co.uk/content/images/tetris.png
    - penguat 12y ago
      <nitpick>rectangle specifies 2d</nitpick> I believe you could form a hollow cuboid, but I don't think you could complete a solid cuboid.
  - dkersten 12y ago
    So the obvious next question is: how many sets do you need to create a perfect rectangle?
    - evanb 12y ago
      Two! (see my same-level comment)
      - ecesena 12y ago
        So the next questions are: - how many 8x7 solutions exist? - does any 4x14 solution exist? - does any 2x4x7 solution exist? :)
        evanb 12y ago
        Let's stick to accept-reject questions for now :)
      - dkersten 12y ago
        Awesome, thanks :)
  - evanb 12y ago
    That's true, but here's a construction: OOZZ OOSZZ LLSS ILTS ILTT IJT IJJJ That's built out of one full set of OZSLJTI. If you take two of those, one rotated by 180˚, you get a rectangle.
- JoshTriplett 12y ago
  The proof in the article is a proof by contradiction. Having equal numbers of each colored square is a necessary but not sufficient condition to form a rectangle.
- deleted 12y ago
  [deleted]
ecesena 12y ago
Here's an example. The trick I used was creating the extra block and the hole on the same side (so, not like the pic). With the pieces numbered as in the post: 2233ffff 72233ddd 7744eaad 7114eaag 5114eegg 555bbccg 6666bbcc Note that, as in the post, I'm not "respecting" Tetris in 2d: pieces 2 and 3 have been "3d rotated" and are "looking in the same direction".