943. 
Suppose that and are digits, not both nine and not both zero, and the repeating decimal is expressed as a fraction in lowest terms. How many different denominators are possible?
This problem is copyrighted by the American Mathematics Competitions.

Instructions for entering answers:
For questions or comments, please email markan@eudelic.com.
Try our new, free contest math practice test. All new, neverseenbefore problems.
I offer online AMC/AIME classes periodically. Join the mailing list to be informed next time they're offered.
Private coaching is also available.