Disclaimer: I didn't read through all your code cuz I've been drinking too much.

Just looking at the amount of code you wrote for getMove and mazeSolution smelled kind of funny
The concept is pretty straight forward

With your assumtions
X - SOLID WALL (no passage allowed)

O - PATH (passage allowed)

. - TRAVELED (path traveled to find the exit)

and F for exit

pseudo code

boolean solveMaze(int x, int y) {
  if(maze[x][y] == 'F' {
    return true;
  } else if (maze[x][y] == '.' || maze[x][y] == 'X') {
    return false
  } else {
  // otherwise try each of the 4 possible steps
    maze[x][y] = '.'
    if(solveMaze(x + 1, y)) return true;
    if(solveMaze(x, y + 1)) return true;
    if(solveMaze(x, y - 1)) return true;
    if(solveMaze(x - 1, y)) return true;

    // couldn't find a from this position
    maze[x][y] = 'O';
    return false;

  }  

}

hopefully this clears somethings up

There looks to be several problems here.
1) At line 40 you try to add an action listener to an object that hasn't yet been initialized
2) At line 63 you try and initialize the JComboBox with a primitive array. However no such constructor exists for JComboBox. JComboBox(Object[] items) is what you want

You can fix this by declaring stringChoice to be Integer[] stringChoice. Though you may want this String[] stringChoice

To simplify thing remove all that code of trying to read from a file because it doesn't look like you need it.

lines 40 to 56 can be replace with

stringChoice =  new Integer[] {1, 2, 3};

This should load the comboBox with 3 numbers.
You can then replace that with something like this

stringChoice = getChoices();

Where getChoices() reads from the file the data that you need populated

Something is wrong with your pseudo code.
I'm now sure what tail() returns but something doesn't feel right with
samelist(tail(L1), tail(L2))

The way I look at this problem is that we just simply want to check if each element in
the list is the same.

Pseudo code:
L1 = {1, 2, 3, 4}
L2 = {1, 2, 3, 4}

sameList(L1, L2, 0)

boolean sameList(L1, L2, index) {
// note NOT check for indexing exceptions
return (L1[index] == L2[index] && sameList(L1, L2, index + 1)
}

}

The whole point of MVC is separation of concerns. What is meant by this, is that the different components of your application should know as little as possible about the other components to that you don't have a highly coupled system.

With MVC, The controller generally knows about both the view and model.
When implementing the controller you will usually do something like this

public class MyController {
    MyView view;
    Model model;
    
    public MyController(MyView view, Model model) {
        view.addCoolEventListener(new ActionListener() { ... })
    }
...
}

The controller above has a "direct" association with both the Model and View because it has to know about them.

The "indirect" association is generally done using the observer pattern.
The example is the View in MVC

public class MyView {

  public void addCoolEventListener(ActionListener event) {...}
}

Here the view allows other objects to know that the view did something.
In our case the controller created an "indirect" relationship by registering for the "CoolEvent" event.

Looking at the java.util.concurrent package and documentation is a good place to start.

http://docs.oracle.c...ency/pools.html