10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball

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Question from adrian:

Hi,

We are off to Scotland on our yearly golfing trip soon.
Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball.
I would like to ensure that each golfer plays with the other guys an equal amount of times,
guess 3ish? and we share the amount of times each player plays in the 4ball.
Hope you can help?

Adrian,

That computation is a bit too big to solve exactly in less than about a month. But we can give a pretty good solution. Here it is. The positions are the player number, and the entries are the group numbers (0, 1, or 2). For example, the groups on Day 1 would be 1, 4, 8; 2, 6, 7, 9; 3, 7, 10. Renumbering the groups to order the tee times on each day makes no difference.

Day 1 : (0, 1, 2, 0, 1, 1, 2, 0, 1, 2)
Day 2 : (1, 0, 2, 0, 1, 2, 1, 2, 1, 0)
Day 3 : (1, 1, 2, 2, 0, 1, 1, 0, 2, 0)
Day 4 : (1, 2, 0, 1, 1, 0, 2, 2, 0, 1)
Day 5 : (1, 2, 2, 0, 2, 1, 0, 1, 0, 1)
Day 6 : (0, 1, 0, 1, 0, 2, 2, 1, 1, 2)
Day 7 : (0, 0, 0, 1, 1, 1, 1, 2, 2, 2)

—Victoria

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