Originally posted by talzamir
Or soccer, for the new world cousins. Each division has four team in it, every team plays against the other three once. Win for 3 pts, draw for 1 point. The top two teams advance.
How many points at minimum can suffice to advance?
How many points at maximum can a team get and still fail to advance?
How to generalize the solution for k teams advance out of n?
I can answer the first two questions.
You can get 2 points minimum to advance. You can get 6 points maximum and fail to advance.
In the first scenario if the top team gets a maximum 9 points and the other teams draw amongst themselves there will be three teams that have 2 points. It will then depend on the tie breakers to separate the teams.
In the second scenario, the bottom team would have to get 0 points and the other three teams would get a win and a loss against the other two teams in the group. Three teams would have 6 points and tie breakers would separate them.
I need more time for the third question.