Question 36
There are 300 contestants at the competition. Each pair of the contestants is either acquainted (knows each other) or unfamiliar with each other, and there are no three contestants who all know each other. Determine the maximum possible $n$ such that the following conditions hold:
* Every contestant is acquainted with at most $n$ other contestants.
* For every positive integer $m$ such that $1 \le m \le n$, there is at least one contestant who is acquainted with exactly $m$ other contestants.
(Mongolia 2017)
* Every contestant is acquainted with at most $n$ other contestants.
* For every positive integer $m$ such that $1 \le m \le n$, there is at least one contestant who is acquainted with exactly $m$ other contestants.
(Mongolia 2017)