can South Africa qualify? a study of mathematical possibility

The first stage of the World Cup Finals consists of a number of groups of 4 who all play each other. The top two teams of each group qualify for the next round. A win is worth 3 pts, a draw 1pt.

9 pts, i.e. 3-0-0: 1st place guaranteed
7 pts, i.e. 2-1-0: 1st place not guaranteed but likely; qualification guaranteed
6 pts, i.e. 2-0-1: anything can happen, but qualification is very likely (not guaranteed: in case the 3 top teams all lose 1 game and win 2, one of them has to stay out. example)
5 pts, i.e. 1-2-0: anything can happen (in case the top 3 teams all draw with each other, 1 has to stay out)
4 pts, i.e. 1-1-1: anything can happen, e.g. all teams could end up with 4 points. example
3 pts, i.e. 1-0-2, 0-3-0: 1st place impossible, qualification is unlikely but possible (in the 0-3-0 situation, 1 non-draw between other teams makes first place impossible; 2 non-draws between other teams makes qualification impossible) The 1-0-2 situation is symmetrical to the 2-0-1 above.
2 pts, i.e. 0-2-1: 1st place impossible, qualification is very unlikely but possible (in case the 3 bottom teams all draw with each other, 1 must still rise)
1 pt or less: qualification is impossible

(Back when they had 24 teams, 4 out of 6 3rd-places would make it to the playoffs)

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spontaneous remission

Just as I was about to describe my apt-get problem to #ubuntu, it went away... now I have pdflatex working, and installed a couple of other goodies: sshfs and synaptic.

Now, let's get ESS working!