I am guessing that your are asking for 4 rounds of golf foursomes for 12 players.
If my guess is right, then it's bad news since it is not possible to arrange that every player plays at least once with every other.
The fact that the number of groups (3 foursomes) is less than the groupsize (4 players) places constraints on the problem that introduce repeated pairings even as soon as the second round.
For example if for the first round you have,
(ABCD) (EFGH) (IJKL)
then for round 2, you take one player each from the brackets above to give the partially completed brackets below,
(AEI?) (BFJ?) (CGK?)
then any way of assigning the remaining players to the unknowns will leave you with 3 repeated pairings. Over 4 rounds this builds up to 18 repeats and the consequence that 12 pairings will not have been covered.
Ian.
Tuesday, November 1 2005, 10:49 am
