Math CentralQuandaries & Queries


Question from Julie:

We have 8 people on our team, but only 4 can play every week. We have 32 weeks, total. How can we divide this so everyone plays evenly ?


It depends what you mean by "evenly". If you mean "everybody plays the same amount", it's as simple as "ABCD play one week, EFGH next week, repeat sixteen times!" This is also the only scheme that never keeps anybody off for more than one week.

If you want, for social reasons, every pair of players to be on together equally often, it cannot be done. There are 28 (8x7/2x1) pairs, and 32 weeks, with 6 pairs (4x3/2x1) playing per week,and 28 does not divide 192 (= 32x6) which is the total number of pairs who play together.

Any sixteen random choices for who plays in weeks 1,3,5,... with the other four always playing the next week will come reasonable close (and guarantee nobody ever sits out more than two weeks.)

Good Hunting!

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