10 Jun 12
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?
10 Jun 12
1 edit
Originally posted by talzamirI can answer the first two questions.
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?
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.