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 Question from Bill: We have 10 golfers scheduled to play over five days on vacation in November. Each day we will play in three groups of three and one foursome. Is there an optimum solution that would assure that every golfer plays with every other golfer at least once while no golfer plays an inordinate number of times with any other golfer or too often in a foursome? Thanks for your help. This has been driving me crazy trying to figure it out.

Bill,

Here is something off the top of my head in case you are in a hurry. There is a good schedule for 9 golfers playing 4 rounds in 3 threesomes, for example see http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html. It looks to me like a good solution for you would be to add player 10 to one of the threesomes on each day. Players 1 through 9 will see each other exactly once. Player 10 will see a couple of others several times, and maybe some players (I think maybe two) zero times. Offhand I don't know if it is possible to do better.

Have fun.
Victoria

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