I have a fantasy football league with 8 members. The regular season of the league goes for 14 weeks, so each team plays the other seven teams exactly twice (once in a randomized order, and then over again in the same order). So for instance, if I am team 1, my list of opponents for the 14 weeks might look like this:
3,5,6,2,8,4,7,3,5,6,2,8,4,7
It is trivial to assess how many different schedules I as one player could face (7!, or 5,040). But for each of those schedules, there are some number of compatible schedules for the other players, which add up to a whole season schedule, and I am looking to find this number (the number of total schedules available for all players, not just one), and a way to generate these schedules in Excel. Any help would be greatly appreciated!
Notes: So far I have been able to assess that for any one sequence of opponents for one player, only 265 of 5040 sequences for a second player will be compatible. From there it gets dicey, since those 265*5040 combinations are not all isomorphic to one another.
