Tournament setup challenge

[tourjay]

You guys/gals are wonderful to have when help is needed.

I've been asked to setup a tournament:

8 couples (8 "teams").  

There are 5 rounds (or occasions of playing).

In the first 4 rounds, each round has 2 locations and 4 teams meet to play at each of the two locations (thus all 8 teams play in each round).  In each round, at each location, each team plays each of the other 3 teams once.)

In the fifth round, all 8 teams meet at one location and each team plays only the two games against the remaining teams that they haven't played twice already (making a total of 14 games played, 2 against each of the other 7 teams).

Can you please help me figure out a playing schedule for the teams

Thank you in advance!

Jay?

[wbport]

It can't be done without some rematches.  Two pairs would have to swap locations between each "round".

[Ian Wakeling]

It is indeed impossible as stated.  But a different tweak to the format of play may also be workable.  Play the first 4 rounds as follows:

round   venue1     venue2
  1   (6 3 2 4)  (8 5 7 1)
  2   (7 4 6 5)  (2 1 8 3)
  3   (1 2 5 6)  (3 8 4 7)
  4   (5 6 3 8)  (4 7 1 2)

If the four teams who meet at a venue are (A B C D), then three sub rounds can be played as follows

sr1 (A v B) (C v D)
sr2 (A v C) (B v D)
sr3 (A v D) (B v C)

For rounds 1 to 3 play all three sub-rounds, however at round 4 omit the sub-round sr1. So by the end of round 4 all teams will have played exactly 11 matches.  The remaining 3 matches of the double round robin can be played at a single venue in round 5 and can be resolved into 3 sub rounds as follows:

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

Hope that helps.

[tourjay]

Ian:

Thank you very much.  It was more complicated than I thought it would be, but you have done it!

Dr. Jay