1796. 
Daphne is visited periodically by her three best friends: Alice, Beatrix, and Claire. Alice visits every third day, Beatrix visits every fourth day, and Claire visits every fifth day. All three friends visited Daphne yesterday. How many days of the next 365day period will exactly two friends visit her?
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.