Question

Python:

Lo Shu Magic Square

The Lo Shu Magic Square is a grid with 3 rows and 3 columns, shown in figures below. The Lo Shu Magic Square has the following properties:

The grid contains the numbers 1 through 9 exactly.

The sum of each row, each column, and each diagonal all add up to the same number. This is shown in Figure B.

In a program you can stimulate a magic square using a two-dimensional list. Write a function that accepts a two-dimensional list as an argument and determines whether the list is a Lo Shu Magic Square. Test the function in a program.

Figure A

4	9	2
3	5	7
8	1	6

Figure B

4	9	2
3	5	7
8	1	6

Answer 1

PYTHON CODE

# function to add a row for the given index

def sumRow(m,index):

    # decrement by 1 , since index starts at zero
    index=index-1

    # variable to hold the sum of values in a row
    total=0
    try:

        # loop through the list
        for i in range(len(m)):

            # adding every value in the inner list
            for j in range(len(m[i])):

                if i==index:
                    total+=m[i][j]
    except:
        print('Index Error')

    # returning the total
    return total

def sumCol(m,col):

    # decrement by 1 , since index starts at zero
    column=col-1

    # variable to hold the sum of values in a row
    total=0
    try:

        # loop through the list
        for i in range(len(m)):

            # adding every value in the inner list
            for j,v in enumerate(m[i]):

                if j==column:
                    total+=v
    except:
        print('Index Error')

    # returning the total
    return total

def sumdiagonal(m):

    d1=m[0][0]+m[1][1]+m[2][2]
    d2=m[0][2]+m[1][1]+m[2][0]

    return (d1,d2)

def main(m):

    # calling the sumRow() for row 1
    s=sumRow(m,1)  

    # calling the sumRow() for row 1
    r=sumRow(m,2)
  
    # calling the sumRow() for row 1
    t=sumRow(m,3)
      
    c1=sumCol(m,1)
    c2=sumCol(m,2)
    c3=sumCol(m,3)

    d1,d2=sumdiagonal(m)

    if s == r == t == c1 == c2 == c3 == d1 ==d2:
        print('The given list is Lo Shu Magic Square')
    else:
        print('The given list is not a Lo Shu Magic Square')  

# testing
if __name__=="__main__":

    m=[[4,9,2],[3,5,7],[8,1,6]]
    main(m)
    m=[[1,2,3],[4,5,6],[7,8,9]]
    main(m)
  

  

SCREENSHOT FOR OUTPUT