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Posers and Puzzles

Posers and Puzzles

  1. Standard member talzamir
    Art, not a Toil
    10 Jun '12 19:11
    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?
  2. 10 Jun '12 21:46 / 1 edit
    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.