Pat,

If you play in three threes, then there is a formula where every pair plays together exactly once over four rounds. If you only play three of those, then some pairs won't play together, but nobody plays together twice. The groupings for the four days are ABC DEF GHI, AHF DBI GEC, ADG BEH CFI, AEI BFG CDG. This schedule, and others, are online at http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html. To find more like this, use google and search for "The social golfer problem".

Have fun,
--Victoria