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 Question from Fred: We have 10 golfers playing 4 rounds: one 4-some and two 3-somes each round. Can you suggest the best distribution of players?

Fred,

This might be too late to be useful. Sorry about that. Another computation had to complete before I could use my program to find the schedule below, and it took 2 weeks.

The program finds a “most balanced” schedule in terms of the number of times each pair of players is together. What was found is pasted below. The positions are the players and the numbers indicate the groups. A flaw is that player 1 is always in group 0, which is a foursome.

Day 0 : (0, 0, 0, 0, 1, 1, 1, 2, 2, 2)
Day 1 : (0, 0, 1, 2, 0, 1, 2, 0, 1, 2)
Day 2 : (0, 1, 0, 2, 0, 2, 1, 2, 1, 0)
Day 3 : (0, 1, 1, 2, 2, 0, 0, 0, 2, 1)

A way around that flaw is to have 11 players in 2 foursomes and a threesome, and then delete player 1 from the foursome he appears in. Here is the 11 player schedule.

Day 0 : (0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2)
Day 1 : (0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2)
Day 2 : (0, 1, 0, 2, 2, 1, 0, 2, 2, 0, 1)
Day 3 : (0, 1, 2, 2, 2, 0, 1, 0, 1, 0, 2)

—Victoria

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