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3x3 magic squares

  1. Oct 3, 2008 #1
    3x3 magic squares * updated

    http://en.wikipedia.org/wiki/Magic_square#Types_of_magic_squares_and_their_construction

    given a 3x3 block with 3 numbers inserted

    e.g.

    |2|_|_|
    |_|_|6|
    |_|3|_|

    How would I solve this magic square? Is there a pattern for this?

    The method in wikipedia only applies when it starts with the 1. What if it's something like the above?

    I have something that I cannot figure out in my notes. My instructor labeled some possible magic squares below...

    she labeled these four as 4 folder reflection

    |6|1|8|
    |7|5|3|
    |2|9|4|

    |4|9|2|
    |3|5|7|
    |8|1|6|

    |2|7|6|
    |9|5|1|
    |4|3|8|

    |8|3|4|
    |1|5|9|
    |6|7|2|

    then labeled this one below a two step found(i think it's called found can't make out the words)
    |6|1|8|
    |7|5|3|
    |2|9|4|

    then label this one below a 4 step found
    |4|9|2|
    |3|5|7|
    |8|1|6|

    and labeled this one below a 6 step found
    |6|7|2|
    |1|5|9|
    |8|3|4|
     
    Last edited: Oct 4, 2008
  2. jcsd
  3. Oct 3, 2008 #2

    statdad

    User Avatar
    Homework Helper

    I don't know whether you got the value for the common sum in your magic square, but for the 3 by 3 square the sum is 15.
    Look at your first column, decide how to finish that to get a column sum of 15. With that done you should be able to finish the rest of the square.

    There are algorithms for creating a magic square - the easiest ones i know of are for "odd" magic squares (3 by 3, 5 by 5, etc). The are easy to find if you look around.
     
  4. Oct 3, 2008 #3
    I understand this, however, in my notes it mentioned 4 steps, 6 steps, and stuff likr 4 folder reflexive... anyone got any idea what's all about?
     
  5. Oct 5, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Then, what, exactly, is your question? If you are given some of the numbers, like in your original post, then the simplest way to find the others is to set up the equations they must satisfy to add up to 15.

    What your teacher is giving is how, given one magic square, to create others by reflection, etc.
     
  6. Nov 13, 2009 #5
    I don't wish to bust your bubble, but there's only one 3 x 3 normal magic square, 880 distinct 4 x 4 normal MS; 275,305,224 distinct normal 5 x 5 MS (no one knows exactly how many above a 5 x 5 normal MS).

    MS formed by reflection, rotation and transposition are trivial since each member keeps the other members as the same neighbors. [MS = magic square(s)]
     
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