BD-BDMO 2018 Problem 8

a tournament is playing between n persons. Everybody plays with everybody one time. There is no draw here. A number $k$ is called $n$ good if there is any tournament such that in that tournament they have any player in the tournament that has lost all of $k$ 's. prove that

1. $n$ is greater than or equal to $2^{k+1}-1$ 2.Find all $n$ such that $2$ is a n-good