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 Question from barbara, a teacher: We are a group of 6 golfers. We play in groups of 3 for 5 days. How can I arrange the groups that everybody plays with everybody else at least once? Thanks.

Barbara,

It seems that you can’t. I have a program that checks all of the possible schedules, so long as the number of possibilities is small enough to check by computer in less than a couple of days.

The most balanced schedule for two threesomes over 5 days (according to equalizing the number of times each pair is together) is pasted below.

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

The 6 players are the 6 positions in the lists The numbers indicate the groups on the day. For example, on Day 1 the threesomes are 1, 2, 4 and 3, 5, 6. This schedule is less than perfect: players 1 and 6 are never together, whereas 1 and 2 are together three times.

—Victoria

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