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Java Math Exercises: Generate a magic square of order n

Java Math Exercises: Exercise-19 with Solution

Write a Java program to generate a magic square of order n (all row, column, and diagonal sums are equal).
From Wikipedia,
In recreational mathematics and combinatorial design, a magic square is a n x n square grid (where n is the number of cells on each side) filled with distinct positive integers in the range 1, 2, ..., n2 such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal. The sum is called the magic constant or magic sum of the magic square. A square grid with n cells on each side is said to have order n.

Sample Solution:

Java Code:

import java.util.*;
public class solution {

    public static void main(String[] args) { 
	
	    Scanner scan = new Scanner(System.in);
        System.out.print("Input a number: ");
        int num = scan.nextInt();
        if ((num % 2 == 0) || (num <=0 ))
        {
            System.out.print("Input number must be odd and >0"); 			
			System.exit(0); 
		}

        int[][] magic_square = new int[num][num];

        int row_num = num-1;
        int col_num = num/2;
        magic_square[row_num][col_num] = 1;

        for (int i = 2; i <= num*num; i++) {
            if (magic_square[(row_num + 1) % num][(col_num + 1) % num] == 0) {
                row_num = (row_num + 1) % num;
                col_num = (col_num + 1) % num;
            }
            else {
                row_num = (row_num - 1 + num) % num;                
            }
            magic_square[row_num][col_num] = i;
        }

        // print the square
        for (int i = 0; i < num; i++) {
            for (int j = 0; j < num; j++) {
                if (magic_square[i][j] < 10)  System.out.print(" ");   
                if (magic_square[i][j] < 100) System.out.print(" ");  
                System.out.print(magic_square[i][j] + " ");
            }
            System.out.println();
        }

    }
}

Sample Output:

 Input a number:  13
 79  94 109 124 139 154 169   2  17  32  47  62  77 
 78  80  95 110 125 140 155 157   3  18  33  48  63 
 64  66  81  96 111 126 141 156 158   4  19  34  49 
 50  65  67  82  97 112 127 142 144 159   5  20  35 
 36  51  53  68  83  98 113 128 143 145 160   6  21 
 22  37  52  54  69  84  99 114 129 131 146 161   7 
  8  23  38  40  55  70  85 100 115 130 132 147 162 
163   9  24  39  41  56  71  86 101 116 118 133 148 
149 164  10  25  27  42  57  72  87 102 117 119 134 
135 150 165  11  26  28  43  58  73  88 103 105 120 
121 136 151 166  12  14  29  44  59  74  89 104 106 
107 122 137 152 167  13  15  30  45  60  75  90  92 
 93 108 123 138 153 168   1  16  31  46  61  76  91

Flowchart:

Flowchart: Generate a magic square of order n.

Java Code Editor:

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Previous: Write a Java program to count the numbers without digit 7, from 1 to a given number.
Next: Write a Java program to print all primes smaller than or equal to any given number.

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