Subcontests
(6)Trios of handshakes
Five people are gathered in a meeting. Some pairs of people shakes hands. An ordered triple of people (A,B,C) is a trio if one of the following is true:
[*]A shakes hands with B, and B shakes hands with C, or
[*]A doesn't shake hands with B, and B doesn't shake hands with C.
If we consider (A,B,C) and (C,B,A) as the same trio, find the minimum possible number of trios.