import java.util.Scanner;

public class FactoringAlgorithm {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int[] a = {6,9,20};
       
        while (true) {
            System.out.print("Number: ");
            int n = in.nextInt();
            if (n == 0)     break;
            System.out.println(checkFactoring(n, a));
        }
    }

    private static boolean checkFactoring(int target, int[] factors) {
        for (int i = 1; i <= factors.length; i++) {
            if (checkRegression(target, factors, i) == true)     return true;
        }
        return false;
    }
   
    private static boolean checkRegression(int target, int[] factors, int len) {
        if (factors.length <= 1) {
            if (target % factors[0] == 0)     return true;
            else                             return false;
        }
       
        for (int i = 1; i < factors.length; i++) {
            if (i + len - 1 > factors.length)     return false;
           
            int factor = factors[0];
            int j = i;
            for (int z = 1; z < len; z++) {
                factor += factors[j];
                j++;
            }
           
            if (target % factor == 0)     return true;
        }
       
        // Shorten the array
        if (factors.length > 1) {
            int[] n = new int[factors.length - 1];
            for (int i = 1; i < factors.length; i++) {
                n[i-1] = factors[i];
            }
            if (checkRegression(target,n,len) == true)     return true;
        }
       
        return false;
    }
}

/**
* McFuPucks is a java class that decides whether the user's input amount of pucks is obtainable via boxes of 6,9 and/or 20
*
* Rowan Collins
* Version 1.0
*/

import java.util.Scanner;

public class McFuPucks
{   //start of McFuPucks class
   public static void main(String[] args)
   {   //start of main method
       /**
        * Main acquires the users desired pucks and initiates the recurring method "buyable"
        */
       Scanner input = new Scanner(System.in);     //input is the scanner object used to obtain user input
       System.out.print("Input the number of McFuPucks you'd like to purchase: ");
       int i = input.nextInt();    //i is the desired amount of McFuPucks
       int[] boxSizes = {6,9,20};  //boxSizes is the different variety of box sizes
       if(buyable(i, boxSizes) == true)
       {
           System.out.println("This is buyable");
       }
       else
       {
           System.out.println("This is not buyable");
       }
   }   //end of main method

   private static boolean buyable(int x, int[] array)
   {   //start of buyable method
       /**
        * buyable is a method that reccurs in order to find if the desired amount of pucks is obtainable using a variety of boxsizes
        *
        * @param int x is the desired amount of McFuPucks
        * @param int[] array is the different boxsizes
        *
        * @return true or false depending on whether or not it is purchasable
        */
       int n = 0;  //n is the temporary value used in comparison against x (target value) to decide if n is too low, too high or 'buyable'
       while (true)
       {   //start of recursive loop
           if (n == x)
           {
               return true;
           }
       
           if (array.length > 1)
           {
               int[] shortArray = new int[array.length - 1];
               for (int i = 1; i < array.length; i++)
               {
                   shortArray[i - 1] = array[i];
               }
               if (buyable(x - n, shortArray))
               {
                   return true;
               }
           }

           n += array[0];
           if (n > x)
           {
               return false;
           }
       }   //end of recursive loop
   }   //end of buyable method
}   //end of McFuPucks class

if(buyable(i, boxSizes) == true)

if(buyable(i, boxSizes))