Modified Round Robin

[knorth1979]

I have four teams (we'll call them A, B, C and D).  Each team has from six to eight players.  I need a way to group them so that only one player from each team is grouped with one player from each of the other three teams (i.e. one from A is grouped with one from B, one from C and one from D).  It is ok if the groups are smaller than four members.  For example, let's say that teams A, B and C have 8 members, but team D only has seven members.  After all regroups, ideally I would like to have had each person on each team eventually have played with all people on the other three teams.  I think this is possibly a modified round robin or a type of 4x4 social square.  Can anyone help?

[Ian Wakeling]

With 8 people in each team. then there is a solution using latin squares

        Team A
   M1 M2 M3 M4 M5 M6 M7 M8
R1  1  2  3  4  5  6  7  8
R2  2  1  4  3  6  5  8  7
R3  3  4  1  2  7  8  5  6
R4  4  3  2  1  8  7  6  5
R5  5  6  7  8  1  2  3  4
R6  6  5  8  7  2  1  4  3
R7  7  8  5  6  3  4  1  2
R8  8  7  6  5  4  3  2  1

        Team B
   M1 M2 M3 M4 M5 M6 M7 M8
R1  1  3  5  7  4  2  8  6
R2  2  4  6  8  3  1  7  5
R3  3  1  7  5  2  4  6  8
R4  4  2  8  6  1  3  5  7
R5  5  7  1  3  8  6  4  2
R6  6  8  2  4  7  5  3  1
R7  7  5  3  1  6  8  2  4
R8  8  6  4  2  5  7  1  3

        Team C
   M1 M2 M3 M4 M5 M6 M7 M8
R1  1  4  7  6  8  5  2  3
R2  2  3  8  5  7  6  1  4
R3  3  2  5  8  6  7  4  1
R4  4  1  6  7  5  8  3  2
R5  5  8  3  2  4  1  6  7
R6  6  7  4  1  3  2  5  8
R7  7  6  1  4  2  3  8  5
R8  8  5  2  3  1  4  7  6

        Team D
   M1 M2 M3 M4 M5 M6 M7 M8
R1  1  5  4  8  7  3  6  2
R2  2  6  3  7  8  4  5  1
R3  3  7  2  6  5  1  8  4
R4  4  8  1  5  6  2  7  3
R5  5  1  8  4  3  7  2  6
R6  6  2  7  3  4  8  1  5
R7  7  3  6  2  1  5  4  8
R8  8  4  5  1  2  6  3  7

So for example the matches in round 1 would be:

  Match 1       Match 2       Match 3 
(A1 B1 C1 D1) (A2 B3 C4 D5) (A3 B5 C7 D4) etc...

When you have some teams with less than 8 members, then things will get complicated and I can't see any easy solutions. The only work around would be to use the schedule above and play threesomes whenever the missing eighth player from team D is scheduled to play.

Hope that helps.

[knorth1979]

Thank you so much!  I can use the info you've given me to make things work.  You wouldn't happen to know of any program/software that is based on the latin squares, would you?