Magic Square of Odd Order
![Example magic square of odd order [7X7]](./px/matrix/example-magic-square-of-odd-order-7x7.png "Example magic square of odd order [7X7]")
Here given code implementation process.
// C Program
// Magic Square of Odd length
#include <stdio.h>
// Find magic square of Odd length
void magicSquare(int n)
{
if (n <= 1 || n % 2 == 0)
{
// This are not work when number is Even and less than 3
return;
}
int matrix[n][n];
int row = 0;
int col = 0;
int value = 1;
// Set default value
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
matrix[row][col] = 0;
}
}
// Get first location
row = n / 2;
col = n - 1;
// Execute loop through by n*n
while (value <= n *n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
// Change element value
value++;
}
else
{
row = row + 1;
col = col - 2;
}
}
printf(" Magic square of size (%dX%d) \n", n, n);
// Display result
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
printf(" %d", matrix[row][col]);
}
printf("\n");
}
printf(" Sum of each rows and columns is %d \n\n", (n *(n *n + 1) / 2));
}
int main(int argc, char
const *argv[])
{
magicSquare(7);
magicSquare(9);
magicSquare(3);
return 0;
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
/*
Java Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
public void magicSquare(int n)
{
if (n <= 1 || n % 2 == 0)
{
// This are not work when number is Even and less than 3
return;
}
int[][] matrix = new int[n][n];
int row = 0;
int col = 0;
int value = 1;
// Set default value
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
matrix[row][col] = 0;
}
}
// Get first location
row = n / 2;
col = n - 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
// Change element value
value++;
}
else
{
row = row + 1;
col = col - 2;
}
}
System.out.print(" Magic square of size (" + n + "X" + n + ") \n");
// Display result
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
System.out.print(" " + matrix[row][col]);
}
System.out.print("\n");
}
System.out.print(" Sum of each rows and columns is " + (n * (n * n + 1) / 2) + " \n\n");
}
public static void main(String[] args)
{
Square task = new Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
// Include header file
#include <iostream>
using namespace std;
/*
C++ Program for
Magic Square of Odd length
*/
class Square
{
public:
// Find magic square of Odd length
void magicSquare(int n)
{
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
int matrix[n][n];
int row = 0;
int col = 0;
int value = 1;
// Set default value
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
matrix[row][col] = 0;
}
}
// Get first location
row = n / 2;
col = n - 1;
// Execute loop through by n*n
while (value <= n *n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Change element value
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
value++;
}
else
{
row = row + 1;
col = col - 2;
}
}
cout << " Magic square of size (" << n << "X" << n << ") \n";
// Display result
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
cout << " " << matrix[row][col];
}
cout << "\n";
}
cout << " Sum of each rows and columns is " << (n *(n *n + 1) / 2) << " \n\n";
}
};
int main()
{
Square task = Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
return 0;
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
// Include namespace system
using System;
/*
C# Program for
Magic Square of Odd length
*/
public class Square
{
// Find magic square of Odd length
public void magicSquare(int n)
{
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
int[,] matrix = new int[n,n];
int row = 0;
int col = 0;
int value = 1;
// Set default value
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
matrix[row,col] = 0;
}
}
// Get first location
row = n / 2;
col = n - 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row,col] == 0)
{
// Change element value
// Put value
matrix[row,col] = value;
row = row - 1;
col = col + 1;
value++;
}
else
{
row = row + 1;
col = col - 2;
}
}
Console.Write(" Magic square of size (" + n + "X" + n + ") \n");
// Display result
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
Console.Write(" " + matrix[row,col]);
}
Console.Write("\n");
}
Console.Write(" Sum of each rows and columns is " + (n * (n * n + 1) / 2) + " \n\n");
}
public static void Main(String[] args)
{
Square task = new Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
<?php
/*
Php Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
public function magicSquare($n)
{
// This are not work when number is Even and less than 3
if ($n <= 1 || $n % 2 == 0)
{
return;
}
$matrix = array_fill(0, $n, array_fill(0, $n, 0));
// Get first location
$row = intval($n / 2);
$col = $n - 1;
$value = 1;
// Execute loop through by n*n
while ($value <= $n * $n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if ($row == -1 && $col == $n)
{
// When row is -1 and column is equal to given n
$col = $n - 2;
$row = 0;
}
if ($col == $n)
{
// When columns are out of range
$col = 0;
}
if ($row < 0)
{
// When row value less than zero
$row = $n - 1;
}
if ($row == $n)
{
// When row are out of range
$row = 0;
}
if ($matrix[$row][$col] == 0)
{
// Change element value
// Put value
$matrix[$row][$col] = $value;
$row = $row - 1;
$col = $col + 1;
$value++;
}
else
{
$row = $row + 1;
$col = $col - 2;
}
}
echo " Magic square of size (". $n ."X". $n .") \n";
// Display result
for ($row = 0; $row < $n; ++$row)
{
for ($col = 0; $col < $n; ++$col)
{
echo " ". $matrix[$row][$col];
}
echo "\n";
}
echo " Sum of each rows and columns is ". (intval($n * ($n * $n + 1) / 2)) ." \n\n";
}
}
function main()
{
$task = new Square();
$task->magicSquare(7);
$task->magicSquare(9);
$task->magicSquare(3);
}
main();Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
/*
Node Js Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
magicSquare(n)
{
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
var matrix = Array(n).fill(0).map(() => new Array(n).fill(0));
// Get first location
var row = parseInt(n / 2);
var col = n - 1;
var value = 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Change element value
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
value++;
}
else
{
row = row + 1;
col = col - 2;
}
}
process.stdout.write(" Magic square of size (" + n + "X" + n + ") \n");
// Display result
for (row = 0; row < n; ++row)
{
for (col = 0; col < n; ++col)
{
process.stdout.write(" " + matrix[row][col]);
}
process.stdout.write("\n");
}
process.stdout.write(" Sum of each rows and columns is " + (parseInt(n * (n * n + 1) / 2)) + " \n\n");
}
}
function main()
{
var task = new Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}
main();Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
# Python 3 Program for
# Magic Square of Odd length
class Square :
# Find magic square of Odd length
def magicSquare(self, n) :
# This are not work when number is Even and less than 3
if (n <= 1 or n % 2 == 0) :
return
matrix = [[0] * (n) for _ in range(n) ]
# Get first location
row = int(n / 2)
col = n - 1
value = 1
# Execute loop through by n*n
while (value <= n * n) :
# row and column indicate element position but
# Before accessing the elements we check its valid limit
if (row == -1 and col == n) :
# When row is -1 and column is equal to given n
col = n - 2
row = 0
if (col == n) :
# When columns are out of range
col = 0
if (row < 0) :
# When row value less than zero
row = n - 1
if (row == n) :
# When row are out of range
row = 0
if (matrix[row][col] == 0) :
# Change element value
# Put value
matrix[row][col] = value
row = row - 1
col = col + 1
value += 1
else :
row = row + 1
col = col - 2
print(" Magic square of size (", n ,"X", n ,") ")
# Display result
row = 0
while (row < n) :
col = 0
while (col < n) :
print(" ", matrix[row][col], end = "")
col += 1
print(end = "\n")
row += 1
print(" Sum of each rows and columns is ", (int(n * (n * n + 1) / 2)) ," \n")
def main() :
task = Square()
task.magicSquare(7)
task.magicSquare(9)
task.magicSquare(3)
if __name__ == "__main__": main()Output
Magic square of size ( 7 X 7 )
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
Sum of each rows and columns is 175
Magic square of size ( 9 X 9 )
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size ( 3 X 3 )
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
# Ruby Program for
# Magic Square of Odd length
class Square
# Find magic square of Odd length
def magicSquare(n)
# This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
return
end
matrix = Array.new(n) {Array.new(n) {0}}
# Get first location
row = n / 2
col = n - 1
value = 1
# Execute loop through by n*n
while (value <= n * n)
# row and column indicate element position but
# Before accessing the elements we check its valid limit
if (row == -1 && col == n)
# When row is -1 and column is equal to given n
col = n - 2
row = 0
end
if (col == n)
# When columns are out of range
col = 0
end
if (row < 0)
# When row value less than zero
row = n - 1
end
if (row == n)
# When row are out of range
row = 0
end
if (matrix[row][col] == 0)
# Change element value
# Put value
matrix[row][col] = value
row = row - 1
col = col + 1
value += 1
else
row = row + 1
col = col - 2
end
end
print(" Magic square of size (", n ,"X", n ,") \n")
# Display result
row = 0
while (row < n)
col = 0
while (col < n)
print(" ", matrix[row][col])
col += 1
end
print("\n")
row += 1
end
print(" Sum of each rows and columns is ", (n * (n * n + 1) / 2) ," \n\n")
end
end
def main()
task = Square.new()
task.magicSquare(7)
task.magicSquare(9)
task.magicSquare(3)
end
main()Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
/*
Scala Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
def magicSquare(n: Int): Unit = {
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
var matrix: Array[Array[Int]] = Array.fill[Int](n, n)(0);
// Get first location
var row: Int = (n / 2).toInt;
var col: Int = n - 1;
var value: Int = 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix(row)(col) == 0)
{
// Change element value
// Put value
matrix(row)(col) = value;
row = row - 1;
col = col + 1;
value += 1;
}
else
{
row = row + 1;
col = col - 2;
}
}
print(" Magic square of size (" + n + "X" + n + ") \n");
// Display result
row = 0;
while (row < n)
{
col = 0;
while (col < n)
{
print(" " + matrix(row)(col));
col += 1;
}
print("\n");
row += 1;
}
print(" Sum of each rows and columns is " + ((n * (n * n + 1) / 2).toInt) + " \n\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Square = new Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
/*
Swift 4 Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
func magicSquare(_ n: Int)
{
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
var matrix: [[Int]] = Array(repeating: Array(repeating: 0, count: n), count: n);
// Get first location
var row: Int = n / 2;
var col: Int = n - 1;
var value: Int = 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Change element value
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
value += 1;
}
else
{
row = row + 1;
col = col - 2;
}
}
print(" Magic square of size (", n ,"X", n ,") ");
// Display result
row = 0;
while (row < n)
{
col = 0;
while (col < n)
{
print(" ", matrix[row][col], terminator: "");
col += 1;
}
print(terminator: "\n");
row += 1;
}
print(" Sum of each rows and columns is ", (n * (n * n + 1) / 2) ," \n");
}
}
func main()
{
let task: Square = Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}
main();Output
Magic square of size ( 7 X 7 )
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
Sum of each rows and columns is 175
Magic square of size ( 9 X 9 )
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size ( 3 X 3 )
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
/*
Kotlin Program for
Magic Square of Odd length
*/
class Square
{
// Find magic square of Odd length
fun magicSquare(n: Int): Unit
{
// This are not work when number is Even and less than 3
if (n <= 1 || n % 2 == 0)
{
return;
}
var matrix: Array <Array<Int>> = Array(n){Array(n){0}};
// Get first location
var row: Int = n / 2;
var col: Int = n - 1;
var value: Int = 1;
// Execute loop through by n*n
while (value <= n * n)
{
// row and column indicate element position but
// Before accessing the elements we check its valid limit
if (row == -1 && col == n)
{
// When row is -1 and column is equal to given n
col = n - 2;
row = 0;
}
if (col == n)
{
// When columns are out of range
col = 0;
}
if (row < 0)
{
// When row value less than zero
row = n - 1;
}
if (row == n)
{
// When row are out of range
row = 0;
}
if (matrix[row][col] == 0)
{
// Change element value
// Put value
matrix[row][col] = value;
row = row - 1;
col = col + 1;
value += 1;
}
else
{
row = row + 1;
col = col - 2;
}
}
print(" Magic square of size (" + n + "X" + n + ") \n");
// Display result
row = 0;
while (row < n)
{
col = 0;
while (col < n)
{
print(" " + matrix[row][col]);
col += 1;
}
print("\n");
row += 1;
}
print(" Sum of each rows and columns is " + (n * (n * n + 1) / 2) + " \n\n");
}
}
fun main(args: Array < String > ): Unit
{
var task: Square = Square();
task.magicSquare(7);
task.magicSquare(9);
task.magicSquare(3);
}Output
Magic square of size (7X7)
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
Sum of each rows and columns is 175
Magic square of size (9X9)
35 25 15 5 76 66 56 46 45
24 14 4 75 65 55 54 44 34
13 3 74 64 63 53 43 33 23
2 73 72 62 52 42 32 22 12
81 71 61 51 41 31 21 11 1
70 60 50 40 30 20 10 9 80
59 49 39 29 19 18 8 79 69
48 38 28 27 17 7 78 68 58
37 36 26 16 6 77 67 57 47
Sum of each rows and columns is 369
Magic square of size (3X3)
2 7 6
9 5 1
4 3 8
Sum of each rows and columns is 15
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