SOLUTION: Hello, I hope you can help me. This is a real issue, but I believe algebra can solve my question. I have a group of 80 participants, coming from 20 different places. They ha

Question 1025962: Hello, I hope you can help me.
This is a real issue, but I believe algebra can solve my question.
I have a group of 80 participants, coming from 20 different places. They have to be divided into 8 reunion groups of roughly equal size. In each group the number of people from the same place has to be kept to a mininum. It is impossible to know each participant's availability, so each has to be given a certain number of reunion each so they could find one that fits their planning.
I estimated each participant had to be presented at least 3 options and each option would have to presented to at least 12 participants. But I believe algebra will give me a much more definite answer to that.
Thank you
Kasper
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
This problem is difficult to do in general and there is a lot of information we don't know. For example we don't know anything about which places the 80 participants are from (we could have 60 from the same place) or if the groups are distinguishable.

Assigning participants more than one option can also lead to imbalanced groups as well.

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