If everyone shakes hands with each other person we essentially have a complete graph. If there are 12 original guests, then there are handshakes. So what about the late comer?
Near the end of a party, everyone shakes hands with everbody else. A straggler arrives and shakes hands with only those he people whom the straggler knows. Altogether, sixty-eight handshakes occured. How many people at the party did the straggler know?