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64 Squares

  1. Nov 11, 2004 #1
    Everyone will appreciate that a Chess board consists of 64 squares.
    The board is eight squares by eight squares.
    A puzzle may be made by cutting the board into pieces , along the boundary of the squares, and then attempting to reassemble the pieces back into the original 8 x 8 square shape.
    One might for example cut the board into two, making 2 pieces 4 squares by 8 squares which would be quite simple to solve.
    Alternatively the board may be cut into 64 individual squares which would take longer to complete.
    Somewhere in between these two extremes an arrangement of pieces, comprising of complete individual squares, will exist which will involve the maximum amount of complexity to restore the board into its 8 x 8 square format.
    What arrangement of pieces would most satisfy this requirement.
  2. jcsd
  3. Nov 11, 2004 #2
    Highlight to see.

    If you made the chess board in to 4 even pieces. Cause of the alternate colours, it would be hard. I think. Either that, or cut it up in to 64 pieces and destroy 1 of them. Ha.
    Last edited: Nov 11, 2004
  4. Nov 11, 2004 #3


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    cut it into L shaped pieces with different square counts

  5. Nov 12, 2004 #4
    Oh, i thought you had to cut it in to actual squares, i didn't know you could make any shape you want. My bad.
  6. Nov 12, 2004 #5


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    I'm not sure I follow

    This seems like an interesting question, but I don't understand what you mean by 'most complex'.
  7. Nov 12, 2004 #6
    Neither do I, and as a chess player, I think putting a board cut up into L shapes together would be easy. I suppose asking "most complex" is a bit like asking "most tasty" or "most beautiful."
  8. Nov 13, 2004 #7
    Most complex. That which is most difficult to solve.
  9. Nov 13, 2004 #8
    I would say the twelve different pentominoes (60 squares in total) plus the 2x2 tetromino would form one of the most complex sets.
  10. Nov 16, 2004 #9
    Ceptimus,rather like your solution,can you form your twelve different pentominoes into rectangles.

    20 x 3 ;15 x 4 ;12 x 5 ;10 x 6 ;
  11. Dec 6, 2004 #10


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    Are all green and white squares considered equal or do they have to be back in their original places?
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