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| Math Central | Quandaries & Queries |
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Question from Sabrina, a student: I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks! |
Sabrina,
There are 6 pairs per week, and after 11 weeks every two people will have lunched together exactly once. Here is a schedule. The 12 positions in each sequence are the 12 people. The numbers indicate who lunches who with who that lunch day. The zeros lunch together, the ones, etc.
Day 1 : (0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5)
Day 2 : (0, 1, 1, 0, 2, 3, 3, 2, 4, 5, 5, 4)
Day 3 : (0, 1, 2, 3, 0, 1, 4, 5, 2, 3, 4, 5)
Day 4 : (0, 1, 2, 3, 1, 0, 4, 5, 3, 2, 5, 4)
Day 5 : (0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 0, 1)
Day 6 : (0, 1, 2, 3, 3, 2, 4, 5, 5, 4, 1, 0)
Day 7 : (0, 1, 2, 3, 4, 5, 0, 1, 4, 5, 2, 3)
Day 8 : (0, 1, 2, 3, 4, 5, 1, 0, 5, 4, 3, 2)
Day 9 : (0, 1, 2, 3, 4, 5, 2, 3, 0, 1, 4, 5)
Day 10 : (0, 1, 2, 3, 4, 5, 3, 2, 1, 0, 5, 4)
Day 11 : (0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5)
Happy eating!
--Victoria
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