At a party, you realise that everyone, except you, has shaken hands with exactly three other people; you have shaken hands with only one other person. Determine the minimum number of attendees at this party.
So i know that if n is the minimum number of attendees, it must be an even number. And the total number of handshakes has to be (3n-2)/2. No leads after this.
This came up while solving an old question paper for an entrance exam.I dont know graph theory so I am trying to attempt this using pigeon hole principle or some general logic that doesnt involve very advanced knowledge of graph theory. Can anyone give a hint or help solve this?