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Math Help - Covering board with dominoes

  1. #1
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    Covering board with dominoes

    A 6x6 board is covered with 2x1 dominoes. Show that we can find a line (which seperate the squares) that does not divide any dominoes.

    Any help would be appreciated.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by doug View Post
    A 6x6 board is covered with 2x1 dominoes. Show that we can find a line (which seperate the squares) that does not divide any dominoes.

    Any help would be appreciated.
    I think you need to be clearer about what properties this line is to posses (is it a straight line, and what does separate the squares mean?)

    CB
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  3. #3
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    Hello, doug!

    A 6x6 board is covered with 2x1 dominoes.
    Show that we can find a line which seperate the squares
    that does not divide any dominoes.

    Go a Goodle seartch on "fault-free rectangles".

    The statement says: If we tile a 6x6 board with 2x1 dominoes,
    there will always be a straight line formed by the sides of the dominoes
    that goes from one side of the board to the opposite side.
    (If it were a matzo, it can be broken along a straight line.)


    Here is one such tiling:


    Code:
    
          *---*-------*-------*---*
          |   |       |       |   |
          |   *---*---*---*---*   |
          |   |   |       |   |   |
          *---*   *-------*   *---*
          |   |   |       |   |   |
          |   *---*---*---*---*   |
          |   |       |       |   |
          *---*---*---*---*---*---*  ←  fault
          |       |   |   |       |
          *-------*   |   *-------*
          |       |   |   |       |
          *-------*---*---*-------*
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