Question 41
In a chess tournament there were $n$ ($n \gt 10$) participants. Each participant plays against another exactly once. If a game ends in a draw, each participant gets 1 point, otherwise the winner gets 2 points and the loser gets none. At the end of the tournament, every participant found that half of his/her score came from games played against the ten participants with the lowest scores. This is true even for each of the ten participants with the lowest scores, (i.e. half of the scores of each of the 10 lowest scorers comes from playing with other 9 lowest scorers). Find the possible value(s) of $n$.