6 ms·

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

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
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