1594. 
At a twins and triplets convention, there were sets of twins and sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?
This problem is copyrighted by the American Mathematics Competitions.

Instructions for entering answers:
For questions or comments, please email markan@eudelic.com.