The thing you're asked to do with your number always produces a multiple of 9 (see note below.) On a given chart, the symbol placed next to your multiple of 9 is the same as the symbol placed next to every other multiple of 9. When you click the crystal ball, this symbol appears.

Numbers and symbols associated with non multiples of 9 are irrelevant.

If you play the game again, a new chart is presented and once again all multiples of 9 are associated with the same symbol (which is probably different than the previous chart's symbol.) The crystal ball is programmed to show the symbol associated with the currently displayed chart.

Note: Any two digit number xy can be represented as 10*x + y. For example, 57 = 10*5 + 7. If you subtract from a two digit number the sum of its digits you get 10*x + y - (x + y) = 9*x, ie. a multiple of 9. In our example, 57 - (5 + 7) = 57 - 12 = 45 = 9*5. The symbol used for 45 (and 9, 18, 27, ... , 81) in the example chart below is .