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 Question from Claude: Golf Holiday: 7 guys, play a 4-some and a 3-some each day for 10 days. Want to have the best balance of each player playing with every other player the same number of times and each player playing in an equal number of 4-somes and 3-somes.

Claude,

I have a program that will check all possible schedules and choose one that is "most balanced" (has smallest variance in the number of times each pair or players is in the same group). The output is below. The positions are the players, and the numbers are the groups (0 and 1). A flaw is that player 1 is always in the threesome. The software does not handle different group sizes well.

Day 1 : (0, 1, 1, 0, 0, 1, 1)
Day 2 : (0, 0, 1, 1, 1, 0, 1)
Day 3 : (0, 1, 1, 0, 1, 1, 0)
Day 4 : (0, 0, 1, 1, 0, 1, 1)
Day 5 : (0, 1, 0, 0, 1, 1, 1)
Day 6 : (0, 0, 1, 1, 1, 1, 0)
Day 7 : (0, 1, 1, 0, 1, 0, 1)
Day 8 : (0, 1, 0, 1, 0, 1, 1)
Day 9 : (0, 1, 1, 1, 1, 0, 0)
Day 10 : (0, 0, 0, 1, 1, 1, 1)

In the output, the groups for day 1 are 1, 4, 5; 2, 3, 6, 7.

Hope this is useful.
--Victoria

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