Question 114
300 participants take part in a mathematics competition. After the competition, some participants play some games of chess. Every two participants play against each other at most once. There are no three participants in this competition who all play chess against each other. Determine the maximal $n$ for which it is possible that the following conditions are satisfied simultaneously: every participant plays at most $n$ games of chess, and for every $m$ with $1 \leq m \leq n$ there is a participant who plays exactly $m$ games of chess.