Math CentralQuandaries & Queries


Question from Tricia:

I have 70 people to go around to 10 tables with 7 at each table. only 6 from each table will rotate each time. There is 1 table monitor that always stays at same table. How do I make the rotation so everyone moves and gets to see all 70 people at the networking event?

You cannot; no table monitor will ever get to see another table monitor.

If we relax that, you will need at least 12 rounds, because each moving person meets six others per round and there are 69 other people to meet (more than 6 x 11). But in a twelve-round event each X must meet two table monitors twice or one three times, leaving exactly one other moving person that X can meet twice. This is a pretty strong constraint! I suspect that the true number of rounds needed is at least 13, maybe more.

At the moment I cannot think of any other obvious approaches - sorry!

Good Hunting!

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