Magical Mind Reader - Multiples Of Nine

Pick a 2-digit number...

• Add the two digits together.
• Subtract that sum of digits from the original number.
• Look up the symbol corresponding to the result in a special table. 

How can the  magician  predict what that symbol is? The trick will become boring  (or obvious)  if the same table is used repeatedly.  Thus, a new table must be provided each time.  Several online implementation do this quite effectively, with nice graphics.  Examples:

 
 Magic Gopher  (British Council)

How fast can you discover the  secret  which makes this work?   [ Answer ] 

Answer :

The difference between a number and the sum of its digits
is always divisible by 9. The same symbol appears at all positions that are multiples of 9.