Can someone explain how to solve or start with this challenging equation? I have come to one conclusion which is to try the pigeonhole principle but can't get it right.
Harry, being ahead of a student union, plans a meeting with other members. In order to facilitate discussions, he wants to seat attendees (Harry, Alisa, Ann, Don, Karl, Monti, George, Monica) properly. The attendees, along with the corresponding list of adversaries, are as follows:
Harry - Alisa, Ann, Don
Karl - Alisa, Monti, George
Alisa - Harry, Karl, Ann
Monti - Karl, Monica, Don
Monica - Monti, Don, George
Ann - Harry, Alisa, George
Don - Harry, Monti, Monica
George - Karl, Monica, Ann
Draw the graph representing these eight guests and their friends, and find a seating arrangement where each person sits between two friends (i.e., no-one sits next to one of their adversaries).
As the problem says, you are to draw a graph. The people are the vertices. You draw an edge between two people if they are not adversaries. As each person has three adversaries, each point will have four edges connected to it. Then if you can find a Hamiltonian circuit in the graph you will have a way to seat people.