Math CentralQuandaries & Queries


Question from Cynthia:

We have 5 employees and need only 2 to work on Saturdays. what is the best way to fairly schedule everyone. PS. from time to time a sixth person will be thrown in to make things really interesting.

Hi Cynthia,

There are 10 possible 2-person pairs you can make from 5 people: 12, 34, 15, 24, 35, 14, 25, 13, 45, 23.

The order they are listed above seems like not a bad schedule. Repeat it every 10 weeks? Fit the sixth person in as you can. Maybe have them replace each individual once before any person is replaced twice?

Hope this makes sense.

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