Argh, I can't remember the mathematical proof, but it works like this:
Whatever numbers you pick, adding them up and taking away the original number always comes a set pattern of numbers. Look at the example they give:
23. => 2+3 = 5 and 23-5 = 18. Every time you click the ball, check to see what symbol the number 18 has next to it. That's the symbol that'll appear in the ball. Every time. Clever, but not psychic.