Math CentralQuandaries & Queries


Question from Jacey, a parent:

I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done?

Hi Jacey,

It can. When the number of people is even, each month everyone meets someone. When it is odd, some person has a month off every so often.

Let's suppose the number of people is even. Number them 0, 1, ..., 2n-2 and infinity. In week 1, the pairs are {infinity, 0}, {1, 2n-2}, {2, 2n-3}, ..., {n-1, n}. For each subsequent week, add one to each number with the two conditions that infinity + 1 = infinity, and (2n-2) + 1 = 0. This will give each possible pairing exactly once over 2n-1 weeks, and then it will repeat.

When the number of people is odd, go up to the next even number, and adopt the rule that whomever is scheduled to meet person 0 has that week off.

Hope this helps.

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