Finding a defective ball out of 12 in three weighings

/*
Methodology for finding the odd ball in three weighings:

Name the balls 1,2,3...12.
In the following paragraphs,
> means heavier
= means equal
< means lighter
(1,2,3,4) means the group of 4 balls.
- in the left margin means the first weighing
-- second weighing
*-- third and final weighing
=> inference

-(1,2,3,4)=(5,6,7,8) => odd one in (9,10,11,12)
-- (9,10)=(11,8) => odd one is 12
*-- (12)>(1) => 12 is heavier
*-- (12)>(1) => 12 is lighter
-- (9,10)>(11,8) => 11 lighter, or, one of 9 or 10 heavier
*-- (9)>(10) => 9 heavier
*-- (9)<(10) => 10 heavier
*-- (9)=(10) => 11 lighter
-- (9,10)<(11,8) => 11 heavier, or, one of 9 or 10 lighter
*-- (9)>(10) => 10 lighter
*-- (9)<(10) => 9 lighter
*-- (9)=(10) => 11 heavier

-(1,2,3,4)>(5,6,7,8) => one of 1,2,3,4 heavier, or, one of 5,6,7,8 lighter
-- (1,2,5)=(3,6,9) => 4 is heavier, or 7 is light, or 8 is light
*-- (7)=(8) => 4 is heavier
*-- (7)>(8) => 8 is light
*-- (7)<(8) => 7 is light
-- (1,2,5)>(3,6,9) => one of 1,2 heavy, or 6 light
*-- (1)=(2) => 6 is light
*-- (1)>(2) => 1 is heavier
*-- (1)<(2) => 2 is heavier
-- (1,2,5)<(3,6,9) => 5 light, or, 3 heavy
*-- (1)=(5) =>3 is heavy
*-- (1)>(5) =>5 is light

-(1,2,3,4)<(5,6,7,8) => one of 1,2,3,4 is lighter, or, one of 5,6,7,8 is heavier
-- (1,2,5)=(3,6,9) => 4 is lighter, or 7 is heavier, or 8 is heavier
*-- (7)=(8) => 4 is lighter
*-- (7)>(8) => 8 is heavier
*-- (7)<(8) => 7 is heavier
-- (1,2,5)>(3,6,9) => 5 is heavier, or 3 is lighter
*-- (1)=(5) => 3 is lighter
*-- (1)<(5) => 5 is heavier
-- (1,2,5)<(3,6,9) => 1,2 ligher, 6 heavier
*-- (1)=(2) => 6 is heavier
*-- (1)>(2) => 2 is lighter
*-- (1)<(2) => 1 is lighter

As the reader can see, there are 24 third and final weighings, reflecting the 24 possible outcomes.

Reference:
http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH007.HTM
*/
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.lang.Math.*;
import java.math.BigInteger;

public class Weighing extends JApplet implements ActionListener{
	JTextArea tInstructions;
	//JButton bL=new JButton("L"),	bR=new JButton("R");
	JButton bBalls[]=new JButton[12];
	JButton bWeigh=new JButton("WEIGH");
	JButton bAnswer=new JButton("ANSWER");
	JButton bReset=new JButton("RESET");
	JTextArea tDisplay=new JTextArea(600,100);
	Color red=new Color(255,200,200);
	Color blue=new Color(200,200,255);
	Color white=new Color(255,255,255);
	Color col[]={white,red,blue};
	int sizeX=50, sizeY=50;
	String Instr="Each of 12 balls of identical appearance has the same weight except for an odd\none, which can be heavier or lighter than the other ones.\nGiven a balance, try to find the odd ball with a minimum number of weighings.\nNote: successively clicking on the boxes will put balls on left side (pink),\nright side (blue) or off balance\n";
	Container c=getContentPane();
	int side[]=new int[12];				// 0=off balance, 1=left, 2=right;
	int weight[]=new int[12];
	int weighCount;
	final int NORMAL_WEIGHT=10;

	public void makeBoxes(JButton b[],int n, int origX, int origY, boolean visible){
		// initialize an array of buttons
		for(int i=0; i1)left+=";";	left+=i+1;
				} else {
					sum-=weight[i];
					if(right.length()>1)right+=";";	right+=i+1;
				}
			}
			weighCount++;
			left+=")"; right+=")";
			if(sum==0)relation=" is equal to ";
			else if(sum<0)relation=" is lighter than ";
			else relation=" is heavier than ";
			tDisplay.append(left+relation+right+"\n");
	}
	public void init(){
		int yInst=90, yMarg=10;
		c.setLayout(null);
		tInstructions=new JTextArea();
		tInstructions.setText(Instr);
		tInstructions.setEditable(false);
		tInstructions.setLocation(2*sizeX,0);
		tInstructions.setSize(450,yInst-10);
		c.add(tInstructions);
		makeBoxes(bBalls,12,sizeX/2,yInst,true);

		makeBox(bWeigh,sizeX*2,yInst+1*(sizeY+yMarg),true);
		bWeigh.setSize(2*sizeX,sizeY);
		bWeigh.setToolTipText("Make another weighing");

		makeBox(bAnswer,sizeX*5,yInst+1*(sizeY+yMarg),true);
		bAnswer.setSize(2*sizeX,sizeY);
		bAnswer.setToolTipText("Display answer, press reset to start new game");

		makeBox(bReset,sizeX*8,yInst+1*(sizeY+yMarg),true);
		bReset.setSize(2*sizeX,sizeY);
		bReset.setToolTipText("New Game");

	  ScrollPane scr=new ScrollPane();
    scr.add(tDisplay);
    scr.setSize(700,150);
    scr.setLocation(0,yInst+2*(sizeY+10));
    tDisplay.setEditable(false);
    c.add(scr);

		newGame();

    setSize(700,380);
    setVisible(true);
    showStatus("Choose balls to weigh");

	}

  public void actionPerformed(ActionEvent event){
		if(event.getSource()==bAnswer){
			displayAnswer();
			return;
		}
		if(event.getSource()==bReset){
			newGame();
		}
		if(event.getSource()==bWeigh){
			weighBalls();
			resetBalls(side);
		}
		int nBall;
		for(nBall=0; nBall<12;nBall++){
  	  if(event.getSource()==bBalls[nBall]){
				side[nBall]=(side[nBall]+1)%3;
				bBalls[nBall].setBackground(col[side[nBall]]);
				return;
			}
		}
	}
}