Math CentralQuandaries & Queries


Question from ken, a parent:

I have 6 golfers alternating playing in a group of 4 each week for 27 weeks.
How can I create a schedule so that each golfer both plays equally and plays against the other golfers an equal amount of time


There are 15 different foursomes one can make from 6 golfers. For everyone to play equally and and play against everyone else an equal number of times you'd need 30 rounds. The best you can do is come close.

I suggest listing the 15 foursomes, actually it is easier to list the two people that don't play, and then arranging them so no one sits out for many consecutive weeks. You might use 12, 34, 56, 13, 25, 46, 14, 26, 45, 16, 23, 45, 36, 24, 15. Use this for the first 15 weeks, and then the first 12 of that same schedule for the next 12 weeks. The three pairs who sit out in the last 2 weeks have no one in common, so this is the best you can do.


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