As you maybe know, the qualification for the European Soccer Championship 2000 is a tournament where in each group each team plays against each other team twice. Germany is in group 3 together with Turkey, Finland, Moldova and Northern Ireland. 14 games have been played and 6 are still to come. (See attachment.)
A quick look at the current standings might make you think that Northern Ireland is already out of the race. But that's wrong! Imagine Northern Ireland wins their three remaining games, Germany plays remis against Turkey and loses against Finland, and Moldova defeats Turkey. Then Northern Ireland is number one!
For those who are not familiar with the scoring model: In each game a team gains 3 points for a victory, 1 point for a remis or 0 points for a loss. After all games have been played, teams are ranked according to points. In case of a tie, the additional tie breakers are: goal difference (i.e. goals scored - goals against), goals scored, and random choice, in that order.
The question your program should answer is:
Regarding all possibilities of how the remaining games could end, what is the highest and lowest possible rank of each team in the group after the tournament is over?
2 A B 1 A B 1 0 5 Ger Tur Fin Nor Mol 14 Fin Mol 3 2 Tur Nor 3 0 Tur Ger 1 0 Nor Fin 1 0 Mol Ger 1 3 Tur Fin 1 3 Nor Mol 2 2 Nor Ger 0 3 Tur Mol 2 0 Ger Fin 2 0 Mol Fin 0 0 Ger Mol 6 1 Fin Tur 2 4 Mol Nor 0 0
Group #1 A 1-2 B 1-2 Group #2 Ger 1-3 Tur 1-3 Fin 1-4 Nor 1-5 Mol 4-5