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From: Brent Hugh on 31 Jul 2010 21:51
An interesting question was posted on Metafilter here:

http://ask.metafilter.com/161031/Dont-meet-the-same-person-twice-involves-math-somehow#2311544

I'm wondering if anyone knows the answer or a good approach.

Slightly re-stated from that forum, here is the problem:

36 people total, meeting in groups of 6. After 5 minutes, the groups
shuffle into completely new groups. Repeat this every five minutes.

Is it possible to arrange the meetings in such a way that after 7 sets
of meetings, each person has been in a group with each of the other 36
people exactly once?

Interestingly there is a pretty simple solution for groups of 4, 9,
16, 25, 49 and all other squares of primes (see the link above for
details).

But how about squares of non-prime numbers, like groups of 36?

Is a solution possible? Is there some general method for finding it?
Any thoughts in general? (I find it hard to believe that this type of
problem hasn't been studied already . . . )
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