We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies.
  1. Prepare
  2. Algorithms
  3. Implementation
  4. Forming a Magic Square
  5. Discussions

Forming a Magic Square

  • christopher_par2
     + 5 comments

    It helps to know (from wiki [1] and YouTube video [2]) there are 8 possible 3x3 magic squares. Each can be obtained by a rotation or reflection (or combination of) of each other.

    If you define a starting magic square, you can perform the following relatively simple transormations to obtain all 8 squares:

    M # Starting square
rotate(M) # rotate clockwise 90 degrees
rotate(rotate(M)) # rotate clockwise 180 degrees
rotate(rotate(rotate(M))) # rotate clockwise 270 degrees
refect(M,dim=rows) # reflect along row dimension
reflect(M,dim=cols) # reflect along column dimension
reflect(M,dim=diag) # reflection along main diagonal
transpose(M) # reflect along off-diagonal

    You have to define these functions, but atleast they're quite simple and you don't have to search all possible permutations.

    A useful YouTube video is 'SOLVE The 3x3 Magic Square Completely - There Can Only Be One!'

    [1] https://en.wikipedia.org/wiki/Magic_square

    [2] https://www.youtube.com/watch?v=zPnN046OM34