KöMaL 2021 B5142

In a football championship, there are four teams in a group. Within the group, each team plays every other team once. The teams receive 3 points for winning, 1 point for a draw and 0 points for losing a game. The two teams scoring the highest qualify for the semi-finals, and the other two teams are eliminated. In the case of equal scores, the qualification is decided by chance. Determine those values of the number $p$ for which it may happen that a qualifying team and an eliminated team both have $p$ points.