Does this problem have a name:
"Given the final points table of a sports league having $n$ teams, enumerate the possible results leading up to it, or at least provide the number of possible results".
So suppose there were 3 teams X, Y, Z which played each other twice (once at home and once away). A win meant 2 points, a draw/tie meant 1 and a loss meant 0 points.
At the end the points table was as follows:
X had 3 points
Y had 3 points
Z had 6 points
Given this info what are all the possible results?
One possibility is that X defeated Y at home but drew away. Z defeated X both times, & Y and Z drew both their games. In this way, one can enumerate all the possibilities. How many possibilities will be there in total?
I wish to know whether this problem can be solved easily, or not (for $n$ teams where winning yields $p$ points, drawing $q$ points and losing $r$ points). In the latter case, is it equivalent to some other problem that has a name?
You can use binary decision variables and constraint programming (or integer linear programming) to find all feasible solutions. Here is how to do it in SAS:
For your example, here are the resulting 24 feasible solutions (solution s=7 is the one you mentioned), where the three columns are away team, home team, and outcome: