Magic chain solutions

This applet generates solutions to a "magic chain" puzzle in which each of 9 squares must be filled with the numbers 1 to 9 such that each row and column (arranged as shown below) add up to the same total:

The Java applet on this page tests each of the 362,880 (i.e. 9!) ways of placing the numbers in the squares.   Out of the 96 solutions, 12 are unique (discarding solutions that differ only in order of the first or last two digits or in being a reverse of a previous solution).  Interestingly, 13 was the row/column total in one solution, 17 in one, 14 in five, 16 in five but there are no solutions totaling 15. 

Program output (the first solution is illustrated in the figure above):

439526817
548362917
529436718
536719428
754391628
716539248
635728419
745382619
851674329
652748139
761584239
628175439

If you have any insights or comments about this page please contact Mickey Segal.  A listing of  many Java resources is at this link.

Source code

import java.applet.*;
import java.awt.*;

public class FastChain9 extends Applet {

int[] digit;
int length = 9;

public void init()
{
    digit = new int[length];
    PermutationGenerator permutationGenerator = new PermutationGenerator(length);
    int perms = permutationGenerator.factorial(length);
    digit = permutationGenerator.getThis();
    if (!redundant() && isMagichain9()) print9();
    for (int i = 1; i < perms; i++)
    {
        digit = permutationGenerator.getNext();
        if (!redundant() && isMagichain9()) print9();
    }
}

boolean redundant()
{
    return (digit[0] < digit[1] || digit[0] < digit[8] || digit[8] < digit[7]);
}

boolean isMagichain9() // chain with same column and row sums
{
    int total = digit[0] + digit[1] + digit[2];
    if (total != digit[2] + digit[3] + digit[4]) return false;
    if (total != digit[4] + digit[5] + digit[6]) return false;
    if (total != digit[6] + digit[7] + digit[8]) return false;
    return true;
}

void print9() // prints sequence
{
    String s = "";
    for (int i=length-1; i>= 0; i--) s += String.valueOf(digit[i] + 1);
    System.out.println(s);
}

public void paint(Graphics g)
{
    g.drawString("Results appear in the Java console", 20 , 25);
}
} // END OF Class FastChain9



class PermutationGenerator {

int[] digit;
int length;

PermutationGenerator(int length)
{
    this.length = length;
    digit = new int[length];
    for (int i = 0; i < length; i++) digit[i] = i;
}

int[] getThis()
{
    return(digit);
}

int[] getNext()
{
    int i = length - 1;
    while (digit[i-1] > digit[i]) i--;
    int j = length;
    while (digit[j-1] <= digit[i-1]) j--;
    swap(i-1, j-1);
    i++;
    j = length;
    while (i < j)
    {
        swap(i-1, j-1);
        i++;
        j--;
    }
    return(digit);
}

void swap(int first, int second)
{
    int temp = digit[first];
    digit[first] = digit[second];
    digit[second] = temp;
}

int factorial(int number)
{
    int result = 1;
    for (int i = 1; i <= number; i++) result *= i;
    return result;
}
} // END OF Class PermutationGenerator