Math CentralQuandaries & Queries


Question from Adam, a teacher:

We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice.

We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this?

I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group.



It is easier to do when the number involved is a perfect square. Please locate a book on combinatorial designs and look up the construction of the affine plane on 81 points; unfortunately it isn’t quick to describe. The points will be the students and the lines will be the groups. If you just delete points 78 through 81 wherever they occur, this will be the design you want.

Good luck,

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