4 teams per game

[jwb216]

Hello!  I am attempting to set-up a double round robin tournament involving 8 total teams.  Each game includes 4 teams so there are two games happening simultaneously.  Is it possible to make sure each team sees each of the other teams somewhere along the way?  We want to have 4 rounds to accomplish this if possible.  Thanks for any help you can offer.

[Ian Wakeling]

Yes this is possible, but there will be four pairs of teams who see each other three times, below these are (1 7), (2 4), (3 8) & (5 6)

(6 2 5 4) (7 1 3 8)
(2 3 7 6) (1 4 8 5)
(5 6 1 7) (3 8 4 2)
(4 7 2 1) (8 5 6 3)

If you have prior information on team ability, then you could make sure that closely matched teams were the ones that meet three times.

[jwb216]

Thank you!  Am I correct in saying it would not be possible to make sure they all meet every other team at least twice within our four round limit?

[Ian Wakeling]

That's correct, each team meets 3 others in each of 4 rounds, so 12 opponents total and a pool of 7 distinct opponents to choose from - so not all can be seen twice each.  Interestingly it is possible to arrange it so that each team meets six of the others exactly twice each and the other team not at all.

1 2 3 4
5 6 7 8
-------
2 7 8 1
6 3 4 5
-------
3 8 1 6
7 4 5 2
-------
4 1 6 7
8 5 2 3

Above (1 5), (2 6), (3 7) & (4 8) are the pairs that do not meet.

[jwb216]

This is perfect.  Thank you so much!!