1449. 
Ten chairs are evenly spaced around a round table and numbered clockwise from through . Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements 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.