Question 86
Five people are at a party. Each pair of them are friends, enemies, or frenemies (which is equivalent to being both friends and enemies). It is known that given any three people $A$, $B$, $C$:
- If $A$ and $B$ are friends and $B$ and $C$ are friends, then $A$ and $C$ are friends;
- If $A$ and $B$ are enemies and $B$ and $C$ are enemies, then $A$ and $C$ are friends;
- If $A$ and $B$ are friends and $B$ and $C$ are enemies, then $A$ and $C$ are enemies.
How many possible relationship configurations are there among the five people?
- If $A$ and $B$ are friends and $B$ and $C$ are friends, then $A$ and $C$ are friends;
- If $A$ and $B$ are enemies and $B$ and $C$ are enemies, then $A$ and $C$ are friends;
- If $A$ and $B$ are friends and $B$ and $C$ are enemies, then $A$ and $C$ are enemies.
How many possible relationship configurations are there among the five people?