How to perform Magic Square Operation in a Matrix using Python3

By Priyam Sur

In this Python tutorial, we are going to learn how to perform a magic square operation in a matrix in Python. Here we will show you an easy example so that you can understand this tutorial easily.

MAGIC SQUARE OPERATION IN PYTHON

A Magic Square is:

  • The square is itself having smaller squares (same as a matrix) each containing a number.
  • The numbers in each vertical, horizontal, and diagonal row add up to the same value.
  • The dimension of the square matrix is an (odd integer x odd integer) e.g., 3×3, 5×5, 7×7.

An example of this is given below in the image, where the sum is 15 for every column or row.

magic square in Python

magic square

To know about this interesting puzzle, Magic Square on Wikipedia

Now, let’s take a look at the code.

PROGRAM: Python program for magic square operation

#Function
def generateSquare(n): 
    # 2-D array with all  
    # slots set to 0 
    magicSquare = [[0 for x in range(n)] 
                      for y in range(n)] 
    # initialize position of 1 
    i = n / 2
    j = n - 1
    # Fill the square by placing values 
    num = 1
    while num <= (n * n): 
        if i == -1 and j == n: # 3rd condition 
            j = n - 2
            i = 0
        else:  
            # next number goes out of 
            # right side of square  
            if j == n: 
                j = 0    
            # next number goes  
            # out of upper side 
            if i < 0: 
                i = n - 1
        if magicSquare[int(i)][int(j)]: # 2nd condition 
            j = j - 2
            i = i + 1
            continue
        else: 
            magicSquare[int(i)][int(j)] = num 
            num = num + 1
        j = j + 1
        i = i - 1 # 1st condition 
    # Printing the square 
    print ("Magic Square for n =", n) 
    print ("Sum of each row or column",n * (n * n + 1) / 2, "\n") 
    for i in range(0, n): 
        for j in range(0, n): 
            print('%2d ' % (magicSquare[i][j]),end = '') 
            # To display output  
            # in matrix form 
            if j == n - 1:  
                print()
# Driver Code 
# Works only when n is odd 
n=int(input("Number of rows of the Magic Square:"))
generateSquare(n)

OUTPUT 1:

Number of rows of the Magic Square:7
Magic Square for n = 7
Sum of each row or column 175.0 

20 12  4 45 37 29 28 
11  3 44 36 35 27 19 
 2 43 42 34 26 18 10 
49 41 33 25 17  9  1 
40 32 24 16  8  7 48 
31 23 15 14  6 47 39 
22 21 13  5 46 38 30

OUTPUT 2:

Number of rows of the Magic Square:5
Magic Square for n = 5
Sum of each row or column 65.0 

 9  3 22 16 15 
 2 21 20 14  8 
25 19 13  7  1 
18 12  6  5 24 
11 10  4 23 17

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2 responses to “How to perform Magic Square Operation in a Matrix using Python3”

  1. Steve Shambles says:
    January 12, 2019 at 7:40 am

    Hey, nice idea, I have shared on my Twitter.
    It looks like the code will produce the same numbers
    every time though, which makes it a bit limited,
    I was thinking of doing a GUI on the code and
    making a puzzle game from it, but I’m not
    experienced enough yet to modify it to make
    up different solutions each time.
    Nice job though.

  2. ar.drso says:
    March 19, 2020 at 1:46 pm

    it just work for odd numbers.if you input an even number,You will encounter an error on the 25th line

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