Math CentralQuandaries & Queries


Question from Doreen:

We have seven people - we want to create a rotating schedule for two people at a time to attend one day a week with each person working the same amount of days in the year.


There are 21 different twosomes that can be formed from seven people. Each person belongs to six of these.

For each person to work the same number of days, the total number of days that are to be worked (by some two people) must be a multiple of 21. If you're talking about one day per week total, then each person would work 12 days over 42 weeks. It is possible to have each person work two days over the next 7 weeks. In the remaining three weeks, one person will not work while the others do.

Good luck!

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