Python Math: Calculate magic square

Last update on April 24 2025 12:35:18 (UTC/GMT +8 hours)

20. Magic Square Calculator

Write a Python program to calculate the magic square.

A magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the "magic constant." A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n".

Pictorial presentation:

Sample Solution:

Python Code:

def magic_square_test(my_matrix):
    iSize = len(my_matrix[0])
    sum_list = []
    
    #Horizontal Part:
    sum_list.extend([sum (lines) for lines in my_matrix])   

    #Vertical Part:
    for col in range(iSize):
        sum_list.append(sum(row[col] for row in my_matrix))
    
    #Diagonals Part
    result1 = 0
    for i in range(0,iSize):
        result1 +=my_matrix[i][i]
    sum_list.append(result1)  
    
    result2 = 0
    for i in range(iSize-1,-1,-1):
        result2 +=my_matrix[i][i]
    sum_list.append(result2)

    if len(set(sum_list))>1:
        return False
    return True

m=[[7, 12, 1, 14], [2, 13, 8, 11], [16, 3, 10, 5], [9, 6, 15, 4]] 
print(magic_square_test(m));

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

m=[[2, 7, 6], [9, 5, 1], [4, 3, 7]]
print(magic_square_test(m));

Sample Output:

True                                                                                                          
True                                                                                                          
False

Flowchart:

$Flowchart: Calculate magic square$

For more Practice: Solve these Related Problems:

Write a Python program to generate a 3x3 magic square where the sums of rows, columns, and diagonals are equal, and then print the square.
Write a Python function that calculates a magic square of order n and prints the grid in a formatted table.
Write a Python script to validate a given square matrix as a magic square by checking the sums of its rows, columns, and diagonals.
Write a Python program to generate and display all possible 3x3 magic squares using backtracking.

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Next: Write a Python program to print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number.

Python Code Editor:

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