Raholt figured it out a while back.
Of all the possible numbers you can begin with, there's a limited number of answers that can result from the calculation, and actually the answer will always be a multiple of 9. Though the symbols appear to be random, each time you refresh the page by clicking the crystal ball, the symbols next to the multiples of 9 (9, 18, 27, etc.) will become a new symbol that they'll all share.
In other words, you click the crystal ball and all multiples of 9 might then have a book next to them. Next time, they all might have a star next to them, and so on.