Five married couples gather for a party, 10 people total.
One of them is a sociologist, and he desides to make a little
research: at the end of the party he asks how many handshakes
each of the participants made during the party.
He gets 9 answers, all different, namely all integers
from zero to eight. How many handshakes his wife made?
1. Nobody shakes hands with himself/herself or with his/her
2. Each pair of people makes zero or one handshakes during the party.