The answer is $ n = 100$. Consider an arbitrary person $ A$. Let $ F(A)$ be the set of friends of $ A$ and $ S(A)$ be the set of strangers of $ A$. Then $ |F(A)| = 22$ and $ |S(A)| = n - 23$. Consider a person $ S\in S(A)$. Since $ S$ does not know $ A$, $ S$ and $ A$ must have $ 6$ friends in common. Thus, each person $ S\in S(A)$ knows exactly $ 6$ people in $ F(A)$. Hence, the number of the relationship $ F(A) - S(A)$ is $ 6(n - 23)$. On the other hand, every two people in $ F(A)$ do not know each other (since they all know $ A$), therefore, every people in $ F(A)$ knows exactly $ 21$ people in $ S(A)$. This means that the number of relationship $ F(A) - S(A)$ is $ 21\cdot 22$. From the above argument, we deduce that $ 6(n - 23) = 21\cdot 22$, which yields $ n = 100$, QED.

Any construction for $100$ people?