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| Math Central | Quandaries & Queries |
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Question from Steve: We have six golfers playing in two threesomes for six rounds of golf. Can you help solve this so that everyone plays with everyone else the same amount of times or close to it? Thanks! |
Steve,
Here is the most balanced schedule found by our computer program that checked all possibilities
Day 1 : (0, 0, 0, 1, 1, 1)
Day 2 : (0, 0, 1, 0, 1, 1)
Day 3 : (0, 0, 1, 1, 0, 1)
Day 4 : (0, 0, 1, 1, 1, 0)
Day 5 : (0, 1, 0, 0, 1, 1)
Day 6 : (0, 1, 0, 1, 0, 1)
The players are the positions, and the number in that position is the threesome they are in (0 or 1). For example on Day 2, the threesomes are 1, 2, 4; 3, 5, 6. The tee times can be assigned so that player 1 is not always off in the first (well, zero-th) group.
Six is a tough number. The best you can do is that some players are together three times. Turns out that it isn't possible to limit it to that. Some players are together four times. Pick them to be friends?
--Victoria
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