20 Men For 6 rounds

[IronCityPutter]

I have 20 men going on a 6 day outing and would like to have them play with as many others as possible. I figure we should be able to play with 18 others, but I can not figure it out on paper.  Can anyone make a schedule that will maximize the number interacting? We must play in foursomes due to course restraints.  :question

[Ian Wakeling]

It is possible to play 5 rounds of foursomes where every players plays with 15 different opponents.

(A B C D)  (E F G H)  (I J K L)  (M N O P)  (Q R S T)
(A E I M)  (B J O Q)  (C H N T)  (D G L S)  (F K P R)
(A G K O)  (B I P T)  (C F M S)  (D H J R)  (E L N Q)
(A H L P)  (B K N S)  (C E O R)  (D F I Q)  (G J M T)
(A F J N)  (B L M R)  (C G P Q)  (D E K T)  (H I O S)

However, I think a 6th round will allways introduce repeated pairings and leave other pairings unplayed.  Perhaps you could try something different for the final day?  If you were keeping score, then you could use the rankings after 5 days to select the foursomes for the final day.

[IronCityPutter]

Thanks for the response. Do you have a 6th day schedule even if it has a limited number of repeats?  :-/

[Ian Wakeling]

Adding a 6th day the schedule above is not the best thing to do.  I think we need to start again.

Round 1
  16  13   2  14
  17   8  18   1
   9  10   5   3
  15  20   4   6
   7  19  12  11

Round 2
  10  13  17  11
   7  14   1  15
   4   3  19  16
  12  18   9  20
   2   5   8   6

Round 3
  15  19   8  10
   6  14  11   9
  12   2  17   4
  13  16   7   1
   3   5  20  18

Round 4
  14   4  18  10
   1   9   2  19
  17   3   6   7
   5  12  15  13
  20  11  16   8

Round 5
  20   7  10   2
   8  12  14   3
  16  15   9  17
  11   1   5   4
  18   6  13  19

Round 6
   9   4  13   8
  19  17  14  20
  18   7  16   5
   1  10   6  12
  11   2   3  15

Above there are 16 pairs that don't occur together and 6 pairs that occur twice.  The latter are (1,7) (3,5) (5,18) (7,16) (13,16) (18,20).

[IronCityPutter]

Thanks, this is much improved over anything I worked out.