Question 136
$n\gt 10$ teams take part in a soccer tournament. Each team plays against each other exactly once. A win gives you two points, a draw gives you one point, and a loss gives you no point. After the tournament, it turns out that each team won exactly half of their points in the games against the 10 worst teams (in particular, each of these 10 teams won half of their points against the 9 remaining). Determine all possible values of $n$ and give an example of such a tournament for these values.