# We have a sequencing problem

We have a competition with $$9$$ different teams (team $$1$$ to team $$9$$). They are competing in a round robin contest using $$2$$ different (venues $$A$$ and $$B$$). So every team will play the others once. Each venue is run at the same time so eg Team $$1$$ v Team $$2$$ at Venue $$A$$ at the same time as Team $$3$$ v Team $$4$$ in Venue $$B$$.

All teams will end up with $$8$$ different contest scores, playing all teams, but once playing each once.

However the key part is no team should play in consecutive contests. So if following on from the above set of games is $$1$$v$$2$$ at the same time as $$3$$v$$4$$, the next set of games must not contain any of those $$4$$ teams.

Using the above parameters there should be $$36$$ games, so $$18$$ pairs of games in Venue $$A$$ and Venue $$B$$.

Can a schedule be devised that can meet all those restrictions?

• I changed the tags. This isn't what a mathematician means by "sequences and series." – saulspatz May 21 '19 at 16:35

Yes, there seems to be a lot of solutions. Even though I specified the players in the first two rounds, I got tired of waiting for my python script to generate them all. Here is one solution.

The first match listed in each round is at venue A and the second at venue B. Each team plays $$4$$ times at each of the venues.

 1 :  1 - 2  and  3 - 4
2 :  5 - 6  and  7 - 8
3 :  1 - 3  and  2 - 9
4 :  6 - 7  and  4 - 8
5 :  1 - 9  and  3 - 5
6 :  2 - 8  and  4 - 6
7 :  5 - 7  and  3 - 9
8 :  6 - 8  and  2 - 4
9 :  7 - 9  and  1 - 5
10 :  3 - 8  and  2 - 6
11 :  4 - 7  and  5 - 9
12 :  3 - 6  and  1 - 8
13 :  4 - 5  and  2 - 7
14 :  8 - 9  and  1 - 6
15 :  2 - 5  and  3 - 7
16 :  1 - 4  and  6 - 9
17 :  2 - 3  and  5 - 8
18 :  4 - 9  and  1 - 7

• Thank you very much, this is really helpful. – Patrick Cook May 22 '19 at 7:50
• If the answer solves your problem, you should accept it by clicking on the checkmark. That way, it no loner shows as open. – saulspatz May 22 '19 at 14:11