learnmathcode.com

🧮 Python Code: 3×3 Magic Square Generator (Siamese Method)version of the Magic Square Generator in Python, using the Siamese Method, which works for any odd-ordered square (3×3, 5×5, etc.).

def generate_magic_square(n):
    if n % 2 == 0:
        raise ValueError("This method works only for odd-order magic squares.")

    magic_square = [[0 for _ in range(n)] for _ in range(n)]

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

    while num <= n**2:
        magic_square[i][j] = num
        num += 1
        new_i = (i - 1) % n
        new_j = (j + 1) % n
        if magic_square[new_i][new_j]:
            i = (i + 1) % n
        else:
            i, j = new_i, new_j

    return magic_square

def print_square(square):
    n = len(square)
    for row in square:
        print(" ".join(f"{num:2d}" for num in row))
    print(f"Magic constant: {n * (n**2 + 1) // 2}")

def is_magic(square):
    n = len(square)
    magic_sum = sum(square[0])
    for row in square:
        if sum(row) != magic_sum:
            return False
    for col in zip(*square):
        if sum(col) != magic_sum:
            return False
    if sum(square[i][i] for i in range(n)) != magic_sum:
        return False
    if sum(square[i][n - i - 1] for i in range(n)) != magic_sum:
        return False
    return True

# Generate and display the magic square
n = 3
magic_square = generate_magic_square(n)
print("Generated Magic Square:")
print_square(magic_square)

# Verify the square
if is_magic(magic_square):
    print("✅ This is a valid magic square.")
else:
    print("❌ This is not a valid magic square.")

✅ Expected Output for n = 3:

 2  7  6
 9  5  1
 4  3  8
Magic constant: 15
✅ This is a valid magic square.