Java Applet puzzle picture game

Question

I am making a java sliding puzzle for my project, and i have managed to crop the images and making it move to a blank space, however i am still puzzled on how to know whether the user got the correct solution or not. i wanted to congratulate the user when he gets the correct pattern.

 import java.applet.*; 
 import java.util.*;
 import java.awt.*; 
 import java.awt.event.*;
 import java.awt.image.*;


 public class SlidePuzz extends Applet implements MouseMotionListener,MouseListener {
 int gridDim = 3;
 int animal = -1;
 int pieceDim = 0;
 int a; int b;
 int gapX = -1; int gapY = -1;
 int moveX = -1; int moveY = -1;
 Image[][] pieces = new Image[7][7];
 int[][] placement = new int[7][7];
 String [] images = {"mouse","cat","dog"};

 String stage = "grid";
 Image img;


  public void init() {
  setSize(420, 420);
  addMouseMotionListener(this);
  addMouseListener(this);
  }

 public void paint(Graphics g) {
 if(stage=="grid") {
 g.setColor(Color.lightGray);
 g.fillRect(0,0,60*gridDim,60*gridDim);

 g.setColor(Color.white);
 g.fillRect(60*gridDim,0,(7-gridDim)*60,420);
 g.fillRect(0,60*gridDim,60*gridDim,(7-gridDim)*60);

 g.setColor(Color.black);

 for (int i=1; i<7; i++) {
  g.drawLine(i*60,0,i*60,460);
  g.drawLine(0,i*60,460,i*60);
 }

  g.setColor(Color.black);
  g.fillRect(120,0,180,20);

  g.setColor(Color.white);
  g.drawString("click to choose "+gridDim+"x"+gridDim+" grid", 145, 15);
  } else if (stage=="animal") {
  g.setColor(Color.white);
  g.fillRect(0,0,420,420);

  g.setColor(Color.black);    
  g.drawString("Please click an animal...", 80, 100);
  g.setFont(new Font("Courier New", Font.BOLD,  22));
  g.drawString("Mouse", 80, 150);
  g.drawString("Cat", 80, 200);
  g.drawString("Dog", 80, 250);
  } else if (stage=="game") {


  if (gapX<0) {
    g.setColor(Color.white);
    g.fillRect(0,0,420,420);
    g.setColor(Color.black);
    g.setFont(new Font("Courier New", Font.PLAIN,  12));
    g.drawString("Loading image...", 120, 50);

    tr = new MediaTracker(this);
    img = getImage(getCodeBase(),  images[animal]+".jpg");
    tr.addImage(img,0);


    for(int x=0; x<gridDim; x++) {
      for(int y=0; y<gridDim; y++) {
        pieces[x][y] = createImage(new FilteredImageSource(img.getSource(),
            new CropImageFilter(x*pieceDim, y*pieceDim, pieceDim, pieceDim)));
    placement[x][y] = (x==gridDim-1 && y==gridDim-1) ? -2 : -1;
    tr.addImage(pieces[x][y],0);
  }
}


    Random r = new Random();
    Boolean placed;
    for(int x=0; x<gridDim; x++) {
      for(int y=0; y<gridDim; y++) {
    // if its the gap, no need to draw anything
    if (placement[x][y]==-2) break;

    // keep looping until piece is selected thats not already drawn
    do {
      do {
        a = r.nextInt(gridDim);
        b = r.nextInt(gridDim);
      } while (a==gridDim-1 && b==gridDim-1);
      placed = false;
      for(int c=0; c<gridDim; c++) {
        for(int d=0; d<gridDim; d++) {
          if(placement[c][d]==a*10+b) placed=true;
        }
      }
    } while (placed);

    // draw on the screen and record what's gone here
    g.drawImage(pieces[a][b], x*pieceDim, y*pieceDim, this);
    placement[x][y] = a*10+b;
      }
    }
    // record where the gap is
    gapX = gridDim-1; gapY = gridDim-1;

  // a piece needs to be moved
  } else if (moveX>=0){
    g.setColor(Color.white);
    g.fillRect(moveX*pieceDim, moveY*pieceDim, pieceDim, pieceDim);

    b = placement[moveX][moveY]%10;
    a = (placement[moveX][moveY]-b)/10;

    g.drawImage(pieces[a][b], gapX*pieceDim, gapY*pieceDim, this);
    placement[gapX][gapY] = a*10+b;
    placement[moveX][moveY] = -2;
    gapX = moveX; gapY = moveY;
    moveX = -1; moveY = -1;


  } else {
    for(int x=0; x<gridDim; x++) {
      for(int y=0; y<gridDim; y++) {
    if (placement[x][y]==-2) continue;
    b = placement[x][y]%10;
    a = (placement[x][y]-b)/10;
    g.drawImage(pieces[a][b], x*pieceDim, y*pieceDim, this);
      }
     }
    }
   }
  }

 public void mouseMoved(MouseEvent me) {
 if(stage=="grid") {
  int mousePos = me.getX()>me.getY() ? me.getX() : me.getY();
  int oldGridSize = gridDim;

  gridDim = (mousePos/60)+1;

  if(gridDim<3) gridDim=3;
  if (gridDim!=oldGridSize) repaint();
  }
  }

 public void mousePressed (MouseEvent me) {
  int x = me.getX();
  int y = me.getY();
  if(stage=="grid") {
  stage = "animal";
  repaint();
   } else if(stage=="animal") {
    if(x<150 && x>80 && y<150 && y>130) animal=0;
    else if(x<150 && x>80 && y<200 && y>180) animal=1;
    else if(x<150 && x>80 && y<250 && y>130) animal=2;
    if (animal>-1) {
    stage="game";
    pieceDim = 420/gridDim;
    repaint();
   }
  } else if(stage=="game") {
  x /= pieceDim;
  y /= pieceDim;

  Boolean right = (x-1==gapX && y==gapY);
  Boolean left = (x+1==gapX && y==gapY);
  Boolean down = (x==gapX && y-1==gapY);
  Boolean up = (x==gapX && y+1==gapY);
  if (right || left || down || up) {
    moveX = x;
    moveY = y;
    repaint();
  }
  }
  }

 public void update(Graphics g) { paint(g); }

 public void mouseDragged (MouseEvent me) {}
 public void mouseExited (MouseEvent me) {}
 public void mouseEntered (MouseEvent me) {}
 public void mouseClicked (MouseEvent me) {}
 public void mouseReleased (MouseEvent me) {}
 }