(a / (b + c)) + (d / (e + f)) + (g / (h + i)) = 1

import java.util.Iterator;
import java.util.NoSuchElementException;
import java.lang.reflect.Array;
import java.util.ArrayList;

public class Permutations implements Iterator
{

    private final int size;
    private final Object[] elements;
    private final Object output;
    private final int[] permutation;
    private static ArrayList<String> solutions = new ArrayList<>();

    private boolean next = true;

    public static boolean function(int[] a)
    {
        int[] b = new int[3];
        b[0] = a[1] + a[2]; // add denominators
        b[1] = a[4] + a[5]; // second set
        b[2] = a[7] + a[8]; // third set
        int d = b[0] * b[1] * b[2]; // multiply them together
        int n = (a[0] * (d/b[0])) + (a[3] * (d/b[1])) + (a[6] * (d/b[2])); // get numerator to match common denominator
        //System.out.println("Numerator" + n + " : Denominator:" + d);
        if (n == d)
        {
            return true;
        }
        return false;

    }

    public static int[] stringArrayToIntArray(String[] s)
    {
        int[] r = new int[s.length];
        for (int i = 0; i < s.length; i++)
        {
            r[i] = Integer.parseInt(s[i]);
        }
        return r;
    }


    public Permutations (Object [] e)
    {
      size = e.length;
      elements = new Object [size];    // not suitable for primitives
      System.arraycopy (e, 0, elements, 0, size);
      output = Array.newInstance (e.getClass().getComponentType(), size);
      System.arraycopy (e, 0, output, 0, size);
      permutation = new int [size+1];
      for (int i=0; i<size+1; i++) {
         permutation [i]=i;
      }
    }

    private void formNextPermutation () {
      for (int i=0; i<size; i++) {
         // i+1 because perm[0] always = 0
         // perm[]-1 because the numbers 1..size are being permuted
         Array.set (output, i, elements[permutation[i+1]-1]);
      }
    }

    public boolean hasNext() {
      return next;
    }

    public void remove() throws UnsupportedOperationException {
      throw new UnsupportedOperationException();
    }

    private void swap (final int i, final int j) {
      final int x = permutation[i];
      permutation[i] = permutation [j];
      permutation[j] = x;
    }

    // does not throw NoSuchElement; it wraps around!
    public Object next() throws NoSuchElementException {

      formNextPermutation ();  // copy original elements

      int i = size-1;
      while (permutation[i]>permutation[i+1]) i--;

      if (i==0) {
         next = false;
         for (int j=0; j<size+1; j++) {
            permutation [j]=j;
         }
         return output;
      }

      int j = size;

      while (permutation[i]>permutation[j]) j--;
      swap (i,j);
      int r = size;
      int s = i+1;
      while (r>s) { swap(r,s); r--; s++; }

      return output;
    }

    public String toString () {
      final int n = Array.getLength(output);
      final StringBuffer sb = new StringBuffer ("[");
      for (int j=0; j<n; j++) {
         sb.append (Array.get(output,j).toString());
         if (j<n-1) sb.append (",");
      }
      sb.append("]");
      return new String (sb);
    }

    public static void main (String [] args) {
       String[] p = {"1","2","3","4","5","6","7","8","9"};
       int count = 0;

      for (Iterator i = new Permutations(p); i.hasNext(); ) {
         final String [] a = (String []) i.next();
         if (function(stringArrayToIntArray(a)))
         {
             solutions.add(i.toString());
             count++;
         }
         System.out.println (i);

      }
      System.out.println("Solutions:" + count);
      for (String current : solutions)
      {
          System.out.println(current);
      }
    }
}