Results 1 to 3 of 3

Math Help - create a square

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    2

    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............
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    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!]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Here is a sketch of Ticbol's solution:
    Attached Thumbnails Attached Thumbnails create a square-patrat.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help to create a question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 10th 2011, 04:22 AM
  2. How to create a formula
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 28th 2011, 12:57 PM
  3. create graphs
    Posted in the Math Software Forum
    Replies: 3
    Last Post: April 24th 2011, 08:46 AM
  4. how to create a sequence s1 s2 s3 ..s11 s12....
    Posted in the Math Software Forum
    Replies: 6
    Last Post: June 5th 2010, 12:31 AM
  5. How To - Create an Index
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 25th 2009, 04:34 PM

Search Tags


/mathhelpforum @mathhelpforum