Question 13
Let $n$ be a positive integer greater than 3. There are $n$ people in a room, and some pairs of them are enemies (enmity is mutual). Suppose we know that this group of people satisfies both of the following properties:
a. Among any 4 people, there are always two who are not enemies of each other.
b. For any positive integer $m \ge 1$, if we can find $m$ of the people who are pairwise not enemies, then among the remaining $n-m$ people there must be 3 people any two of whom are enemies of each other. (Note: nobody is an enemy of himself or herself.)
Find the smallest possible value of $n$.
a. Among any 4 people, there are always two who are not enemies of each other.
b. For any positive integer $m \ge 1$, if we can find $m$ of the people who are pairwise not enemies, then among the remaining $n-m$ people there must be 3 people any two of whom are enemies of each other. (Note: nobody is an enemy of himself or herself.)
Find the smallest possible value of $n$.