some of you might not be familiar with this particular case of combination/permutation
So, basically, there is a popular game in Europe that involves many many groups of friends and is about soccer. I think that it might be similar to the American “fantasy football”, and the rules are pretty simple: 1 - you have a budget to build your team made of 25 real players 2 - every Saturday you choose 11 players who get grades based on their performance in real-life games (let’s say that grades are in the range between soccer tipster 0 and 10, but could be higher or lower depending on bonuses and malus) 3 - the sum of the 11 grades = your total score 4 - the goals that you score depend on the range of your total score (66 = 1 goal, 72 = 2 goal and so on) 5 - winning one match gives you 3 points in the league table/ ranking, a draw gives you 1 point and a lose give you 0 point. At the end of the season, the friend with the highest score wins.
The average case is a league made of 8 friends: A B C D E F G H. Every Saturday there are 4 games since two teams confront each other, let’s say:
1st Saturday A vs BC vs D E vs F G vs H
2nd Saturday A vs H C vs F E vs D G vs B
And so on... So every player needs to confront each of the other players, week after week.
This order of confrontation makes a huge difference in the final result of the league because I can get a draw 3-3 and get 1 point in the league table/ ranking, while my lucky friend can earn 3 points winning with a simple 1-0. The basic assumption is that every Saturday you choose 11 players regardless of the friend you are going to confront, but instead you make your decision based on the real-life games of the day. (If Real Madrid confronts the shittiest team of the league this Saturday, you will for sure pick all the Real Madrid players that you got and include them in the 11 chosen). After I gave you all this background information, here is the real question:
How many calendars (order of confrontation) exist in a league made of 8 friends? Consider that we do not differentiate away and home games, and it is important to consider all the points of view, not only mine (if A vs B, it matters if C vs D or C vs E)
I hope this is clear, forgive me for my poor English.
So, basically, there is a popular game in Europe that involves many many groups of friends and is about soccer. I think that it might be similar to the American “fantasy football”, and the rules are pretty simple: 1 - you have a budget to build your team made of 25 real players 2 - every Saturday you choose 11 players who get grades based on their performance in real-life games (let’s say that grades are in the range between soccer tipster 0 and 10, but could be higher or lower depending on bonuses and malus) 3 - the sum of the 11 grades = your total score 4 - the goals that you score depend on the range of your total score (66 = 1 goal, 72 = 2 goal and so on) 5 - winning one match gives you 3 points in the league table/ ranking, a draw gives you 1 point and a lose give you 0 point. At the end of the season, the friend with the highest score wins.
The average case is a league made of 8 friends: A B C D E F G H. Every Saturday there are 4 games since two teams confront each other, let’s say:
1st Saturday A vs BC vs D E vs F G vs H
2nd Saturday A vs H C vs F E vs D G vs B
And so on... So every player needs to confront each of the other players, week after week.
This order of confrontation makes a huge difference in the final result of the league because I can get a draw 3-3 and get 1 point in the league table/ ranking, while my lucky friend can earn 3 points winning with a simple 1-0. The basic assumption is that every Saturday you choose 11 players regardless of the friend you are going to confront, but instead you make your decision based on the real-life games of the day. (If Real Madrid confronts the shittiest team of the league this Saturday, you will for sure pick all the Real Madrid players that you got and include them in the 11 chosen). After I gave you all this background information, here is the real question:
How many calendars (order of confrontation) exist in a league made of 8 friends? Consider that we do not differentiate away and home games, and it is important to consider all the points of view, not only mine (if A vs B, it matters if C vs D or C vs E)
I hope this is clear, forgive me for my poor English.
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