9 is a very interesting number, too. Any factor of nine, its digits can be added to result in nine, or a number divisible by nine, in which case you add those digits together, and repeat as necessary. Examples:
3x9=27. 2+7=9
27x27=729. 7+2+9=18. 1+8=9
etc. it always works. (try it with any factor of nine) I'm pretty sure that's where your pattern lies. which still leads me to believe the answer is 4. Because you will have a remainder of 1 (9-8), plus the first 3 that got added in the very beginning.
Off to google I go! :)