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Progressions of polyominoes

  1. Aug 18, 2010 #1
    Let us define a progression of polyominoes with n terms as a sequence of n polyominoes, starting with the single square (the monomino), such that every shape is obtained by adding a square to the previous polyomino in the sequence.

    Conjecture: Every progression of polyominoes with 6 terms can be extended to a progression of polyominoes with 8 terms so that the set of shapes thus obtained can fill a 6x6 square.

    Please post any particularly nasty-looking cases and perhaps someone will be able to help. Good luck!
     
  2. jcsd
  3. Aug 18, 2010 #2

    loseyourname

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    I'm not sure I'm understanding this. How would you extend a linear coupling of 6 squares into a 6 x 1 rectangle to fit into a 6 x 6 square? At least some of the obtainable shapes would have a linear dimension greater than 6, so they wouldn't fit inside that square.
     
  4. Aug 18, 2010 #3
    And we would not try to use those extensions containing polyominoes that don´t fit in a 6x6. The conjecture is that given any progression with 6 terms, we can find SOME extension thereof with 8 terms that can fit in a 6x6.
     
  5. Aug 18, 2010 #4

    loseyourname

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    Okay, I get it. I thought you were saying all obtainable shapes from the 6-term forms would fit.
     
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