Question 74
Let 300 students participate to the Olympiad. Between each 3 participants there is a pair that are not friends. Hamza enumerates participants in some order and denotes by $x_{i}$ the number of friends of $i$-th participant. It occurs that
$$
\left\{x_{1}, x_{2}, \ldots, x_{299}, x_{300}\right\}=\{1,2, \ldots, N-1, N\} .
$$
Find the biggest possible value for $N$.
$$
\left\{x_{1}, x_{2}, \ldots, x_{299}, x_{300}\right\}=\{1,2, \ldots, N-1, N\} .
$$
Find the biggest possible value for $N$.