9.5. In a company of $n>1$ people, some of its members are acquainted with each other, while others are not. If X is acquainted with Y, then Y is also acquainted with X, and a person is neither considered their own acquaintance nor non-acquaintance. Find all $n$ for which in the company there will always be two people A and B who have the same number of acquaintances in this company, and such that there will be either a person C who is acquainted with both A and B, or a person $\Gamma$, who is not acquainted with both A and B.
Answer. All $\boldsymbol{n}$, not equal to 2 and 4.

Proof. 1. Examples. When $\boldsymbol{n}=2$, in any case, both participants have the same number of acquaintances, 0 or 1, but there are no candidates for a common acquaintance or stranger. When $\boldsymbol{n}=4$, the only example where it is impossible to find V or G is a group where the first is acquainted with the second, the second with the third, and the third with the fourth, and there are no other acquaintances.