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Math Help - Trominoes Induction Pf?

  1. #1
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    Trominoes Induction Pf?

    Hi guys,

    Help...!!!

    Prove by induction why a "3 by odd" tiling of trominoes won't work.
    Also, prove by induction why a 2^k by 2^k tiling of trominoes WOULD work.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by harold View Post
    Hi guys,

    Help...!!!

    Prove by induction why a "3 by odd" tiling of trominoes won't work.
    Also, prove by induction why a 2^k by 2^k tiling of trominoes WOULD work.
    You had better tell us what you mean by trominoes, and what
    restrictions there are on how you do the tillings.

    RonL
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  3. #3
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    Hello, harold!

    Prove by induction why a "3 by odd" tiling of trominoes won't work.
    Also, prove by induction why a 2^k by 2^k tiling of trominoes WOULD work.

    If a tromino is a three-unit polyomino (as defined by Solomon W. Golomb),
    . . there are two possible shapes.
    Code:
          *---*
          |   |
          * - *---*       *---*---*---*
          |   :   |       |   :   :   |
          *---*---*       *---*---*---*
             "L"               "I"

    I must be missing something . . . I don't understand the questions.

    A "3 by odd" can be tiled with a number of I-trominos.

    And a "2^k by 2^k" region has 4^k square units
    . . which can not be a multiple of 3.

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  4. #4
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    I'm not sure either...this is a page that talks about trominoes and gives some induction but I still don't get it...

    A Geometric Induction Example: the Tromino Puzzle
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  5. #5
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    Hello again, Harold!

    It would have helped if you had explained the problems clearly.

    First of all, we're limited to the L-shaped tromino.

    Secondly, for the tiling of a "2^n by 2^n" square, you neglected to tell us
    . . that one unit square is already covered.

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  6. #6
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    Sorry bout that Soroban...I didn't know myself--new territory for me. I see what they're getting at with the discussion about the induction but how do I formally write it out for both cases??
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