I remember being at the Barnes Seminar last year about this time and coming up with the following problem. There were probably 150 participants. We convened as a group in the morning and would then split up into breakout sessions of about 6 people. The break sessions were assigned not chosen, and organizers tried to have as little overlap as possible, giving you the opportunity to meet the most number of people. So here is the question, what is the maximum number of breakout sessions until at least two people find themselves in a group again? After you figure that out, what is the maximum number of non-overlapping breakout session of size p chosen from an overall group size of n?
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I have been thinking on and off about this problem ever since it was posed. Since it's about a week old now and I have not been able to solve it I was wondering if you might be able to give us some insight into the solution.
If there are 8 people and you make groups of 3, I come up with 7 groups. I am unable to see any pattern which shows how you can generalize to the number of groups when you have n people and p in a group.
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