Simple encryption algorithm for homework. not getting decryption working properly

This is a homework question that I can't get my head around at all

Its a very simple encryption algorithm. You start with a string of characters as your alphabet:

ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!, .

Then ask the user to enter there own string that will act as a map such as:

0987654321! .,POIUYTREWQASDFGHJKLMNBVCXZ

Then the program uses this to make a map and allows you to enter text that gets encrypted.

For example MY NAME IS JOSEPH would be encrypted as .AX,0.6X2YX1PY6O3

This is all very easy, however he said that its a one to one mapping and thus implied that if I enter .AX,0.6X2YX1PY6O3 back into the program I will get out MY NAME IS JOSEPH

This doesn't happen, because .AX,0.6X2YX1PY6O3 becomes Z0QCDZQGAQFOALDH

The mapping only works to decrypt when you go backwards but the question implies that the program just loops and runs the one algorithm every time.

Even if some could say that it is possible I would be happy, I have pages and pages of paper filled up with possible workings, but I came up with nothing, the only solution to run the algorithm backwards back I don't think we are allowed to do that.

Any ideas?

Edit:

Unfortunately I can't get this to work (Using the orbit computation idea) What am I doing wrong?

//import scanner class
import java.util.Scanner;

public class Encryption {

    static Scanner inputString = new Scanner(System.in);
    //define alphabet
    private static String alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!, .";
    private static String map;
    private static int[] encryptionMap = new int[40];//mapping int array
    private static boolean exit = false;
    private static boolean valid = true;

    public static void main(String[] args) {

        String encrypt, userInput;
        userInput = new String();

        System.out.println("This program takes a large reordered string");
        System.out.println("and uses it to encrypt your data");
        System.out.println("Please enter a mapping string of 40 length and the same characters as below but in different order:");
        System.out.println(alpha);

        //getMap();//don't get user input for map, for testing!
        map=".ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!, ";//forced input for testing only!
        do{
            if (valid == true){
                System.out.println("Enter Q to quit, otherwise enter a string:");
                userInput = getInput();
                if (userInput.charAt(0) != 'Q' ){//&& userInput.length()<2){

                    encrypt = encrypt(userInput);
                    for (int x=0; x<39; x++){//here I am trying to get the orbit computation going
                        encrypt = encrypt(encrypt);
                    }
                    System.out.println("You entered: "+userInput);
                    System.out.println("Encrypted Version: "+encrypt);
                }else if (userInput.charAt(0) == 'Q'){//&& userInput.length()<2){
                    exit = true;
                }

            }
            else if (valid == false){
                System.out.println("Error, your string for mapping is incorrect");
                valid = true;//reset condition to repeat
            }
        }while(exit == false);
        System.out.println("Good bye");
    }

    static String encrypt(String userInput){
        //use mapping array to encypt data
        String encrypt;
        StringBuffer tmp = new StringBuffer();
        char current;
        int alphaPosition;
        int temp;


        //run through the user string
        for (int x=0; x<userInput.length(); x++){
            //get character
            current = userInput.charAt(x);


            //get location of current character in alphabet
            alphaPosition = alpha.indexOf(current);
            //encryptionMap.charAt(alphaPosition)

            tmp.append(map.charAt(alphaPosition));

        }
        encrypt = tmp.toString();
        return(encrypt);
    }

    static void getMap(){
        //get a mapping string and validate from the user
        map = getInput();
        //validate code
        if (map.length() != 40){
            valid = false;
        }
        else{
            for (int x=0; x<40; x++){
                if (map.indexOf(alpha.charAt(x)) == -1){
                    valid = false;
                }
            }
        }
        if (valid == true){
            for (int x=0; x<40; x++){
                int a = (int)(alpha.charAt(x));
                int y = (int)( map.charAt(x));
                //create encryption map
                encryptionMap[x]=(a-y);
            }
        }
    }

    static String getInput(){
        //get input(this repeats)
        String input = inputString.nextLine();
        input = input.toUpperCase();
        if ("QUIT".equals(input) || "END".equals(input) || "NO".equals(input) || "N".equals(input)){
            StringBuffer tmp = new StringBuffer();
            tmp.append('Q');
            input = tmp.toString();
        }
        return(input);
    }




}