How to create a Magic square in python?

Question

A magic square is a matrix in which the sum of rows, columns and diagonals are equal.

I had created a matrix using nested list but unable to equal the sum of the rows, columns and diagonals.

Answer 1

''' This is a project made by students of lovely professional university: Akula Anjiyya, Gudla Srikanth,Mahammad Umar Farooq . Project is used to make a basket and arrange the eggs in it in such a way that the sum of each row,column and diagnol is equal. We used some of the in built functions and logics to built this code .''' def Odd_Order(n): '''Creating a matrix of n order with all entries as "0" where the variable "c" is the number of columns and the variable r is the number of rows''' matrix=[ [0 for c in range(n)] for r in range(n)]

#Applying the first condition to check that n is Even or Odd or "0"

 # if "n" is  an odd integer

            #Starting from the first position after verifying it's Odd 

r=n//2
c=n-1
i=1 
limit=n**2
    
    #here limit is the range of eggs that we can arrange in the basket

while i<=limit:
    if r==-1 and c==n: # Condition if both the rows and columns are out of range 
        r=0
        c=n-2
    else:
            
        if r<0: #Condition if rows are out of range
            r=n-1
                
        if c==n: #Condition if column out of range
            c=0
                
    if matrix[r][c]: # Starting to arrange
        c=c-2
        r=r+1
        continue
        
    else: #Condition if the before condition becomes False
        matrix[r][c]=i
            
        i+=1 #Increment of the " i " value
            
    c+=1 #Increment of column
        
    r-=1 # Decrement of rows to skip to another value

    '''Printing the number of Rows '''
print ("basket for n =", n)
    
    #Print the sum of each row and column of n order matrix
    
print ("Sum of each row or column",n * (n * n + 1) / 2, "\n")
    
'''Printing the Basket '''

print("Basket with arrangement of EGGS is : ")
    
    #Used Nested list
for r in range(0,n):
    for c in range(0,n):
        print("%2d"%(matrix[r][c]),end="    ")
                    # To display output  
                    # in matrix form 
        if c==n-1:
            print()
    

def Even_Order(n): '''Creating a matrix of n order with all "0" entries where the varaiable "c" is the columns and variable "r" is the rows''' matrix=[ [(n*r)+c+1 for c in range(n)] for r in range(n)]

    #Condition to change the zero elements is (n*n+1)-matrix[r][c]
    # Starting with Top left corner 
for r in range(n//4): #setting a range to rows
        
    for c in range(n//4): #setting a range to column
            
        matrix[r][c]=(n*n-1)-matrix[r][c]; 

    # Moving to Top right corner 

for r in range(n//4):

    for c in range(3*(n//4),n):

        matrix[r][c]=(n*n+1)-matrix[r][c];

    # Moving Bottom Left corner

for r in range(3*(n//4),n):

    for c in range(0,n//4):

        matrix[r][c]=(n*n+1)-matrix[r][c];

    #Moving to Bottom Right corner 

for r in range(3*(n//4),n):

    for c in range(3*(n//4),n):

        matrix[r][c]=(n*n-1)-matrix[r][c];

    #Center of matrix,order(n/2)*(n/2)

for r in range(n//4,3*(n//4)):

    for c in range(n//4,3*(n//4)):

        matrix[r][c]=(n*n-1)-matrix[r][c];



print ("basket for n =", n)

print ("Sum of each row or column",n * (n * n + 1) / 2, "\n")

#Printing the Basket

print("Basket with arrangement of EGGS is : ")

for r in range(n):

    for c in range(n):

        print("%2d"%(matrix[r][c]),end="    ")

    print()

n=int(input("Enter the number of Rows and Columns : "))

if n%2==0:

Even_Order(n)

elif n<=0: # Condition when the input of "n" is less than zero or equal to zero

    print("Enter the positve numbers for result")

else:

Odd_Order(n)

Answer 2

SciPython have a webpage about this that they explain well and the code they use is as follows.

# Create an N x N magic square. N must be odd.
import numpy as np

N  = 5
magic_square = np.zeros((N,N), dtype=int)

n = 1
i, j = 0, N//2

while n <= N**2:
    magic_square[i, j] = n
    n += 1
    newi, newj = (i-1) % N, (j+1)% N
    if magic_square[newi, newj]:
        i += 1
    else:
        i, j = newi, newj

print(magic_square)