The Smiths, the Andrings and the Cliffords all hold a big party. Everyone shakes hands with every member of the other two families (no one shakes hands with members of their own family), 142 handshakes in all.
Assuming that there at least as many Andrings as Smiths, and at least as many Cliffords as Andrings, how many of each family are present?
The members present at the party are as follows:
Andrings family ---- 10 members
Clifford family----- 12 members
Smith family --------1 member