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Thread: create a square

  1. #1
    Aug 2007

    create a square

    This is making me crazy..............

    Question: There are two squares a 6 x 6 and a 8 x8. Cut each square only once and arrange the pieces to make a 10 x 10. ( You should have 4 pieces)

    Thank you in advance if anyone can figure this out............
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  2. #2
    MHF Contributor
    Apr 2005
    This is by trial and error. By chance only. Hit or miss. Yes, even a 5th grader can solve this puzzle. I don't know how logic is used here. It's more of doodling, or "drawing-drawing", than "2+2"or reasoning.

    There could be some other ways but here is one way that I found by doodling.

    I sketched 3 squares. One 6x6, one 8x8, and one 10x10. Done oblique or skewed cuttings, used the 6-8-10 right triangle, etc. Finally I stumbled onto a correct way of doing it. I doodled it on the 10x10 square.

    I subdivided all the 3 squares into stacks or mosaics of 2x2 squares. So the 6x6 has nine 2x2's, the 8x8 has sixteen 2x2's, the 10x10 has twenty five 2x2's.

    [6x6 reads "six by six". 2x2 is "two by two". Etc.]

    The 6x6 square:
    At its upper lefthand corner, cut away a 4x4 square
    Then place this 4x4 piece on top of the other piece, which is an "L" facing to the left, whose equal legs are three 2x2's each. [How hard it is to explain. If I could only draw on this board....]
    Now the resulting figure is the left side of the 10x10 square. Its height is five 2x2's. Its top is a row of two 2x2's. Its bottom or base is a row of three 2x2's. [If you could understand or follow so far, congratulations.]

    The 8x8 square:
    At its upper righthand corner, cut away a column (vertical) of two 2x2's.
    Then place the other (bigger) piece snugly, like jigsaw puzzle, to the existing or earlier-formed figure.
    Then place the smaller piece of two 2x2's horizontally below the bottom of the said bigger piece.

    Voila! You have your 10x10 square.

    [If you are still reading this, and you understood what I just described, gimme your five, Up Here!]
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  3. #3
    MHF Contributor red_dog's Avatar
    Jun 2007
    Medgidia, Romania
    Here is a sketch of Ticbol's solution:
    Attached Thumbnails Attached Thumbnails create a square-patrat.jpg  
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