Can someone clarify how this mysterious game works?

http://bored.com/mysticalball/index.htm





My theory was wrong. Can anyone figure it out?Can someone clarify how this mysterious game works?
Your two-digit number can be represented by 10a + b, where b is the one's digit and a is the ten's digit.





Then, what they ask you to do is calculate:





(10a + b) - (a + b) = 9a





So you will always end up with a multiple of 9. Check and see that every multiple of 9 on that chart has the same symbol, and it changes every time you do it.Can someone clarify how this mysterious game works?
The answer is simple. Pick any two digit number, add the digits, and subtract the answer from the original number. Find the symbol for the new number. Now, before you click on the stupid ball thingy, do the same thing with another number, and find the symbol. Now do it again. Notice a pattern? They're all the same symbol. This is because any given time that you click the ball, all the symbols for the numbers change so that this time you pick a number, the corresponding symbol has to be a certain one. Once you click the ball again, all the symbols change, and the answer to your next number choice has to be a certain one. It's a simple answer, really. It just takes a little free time to figure out.
Easy. Every multiple of nine has the same symbol within each round, however the symbol changes each round so as to avoid arousing suspicion. Due to the nature of numbers, adding the digits of any 2-digit number and subtracting this number from the original always yields a multiple of nine. Since every multiple of nine has the same symbol in each round, the ';magic ball'; displays that symbol each time.





Examples:





11 = 11 - 2 = 9 times 1


12 = 12 - 3 = 9 times 1





21 = 21 - 3 = 18 = 9 times 2





34 = 34 - 7 = 27 = 9 times 3





As you can see, this will work for every two digit number.
i think that there are only a few possible numbers which can result from the formula they give you. The numbers that work are only multiples of 9. They give all of these numbers the same symbol and the rest are given random symbols. If you retry you can notice that all of the multiples of 9 switch to the same symbol, while the rest are apparently random.