Math Is Fun Forum

This is a real life problem.  I am organizing a networking meeting

85 people will attend
We will seat them at 17 tables with 5 people at each table
At the first seating (while the soup is served) everyone will introduce themselves and present the group with a question or problem they have prepared

After the soup and discussion, everyone will be sent to new tables where salad will be served and each person will again introduce themselves and persent their question

After salad, everyone will again be sent to new tables where the entre will be served and again they will present their question

Finally, everyone will go to a new table for desert and their introduction and question

We want to make sure that no one sits with anyone they have been seated with during the earlier seatings

Is there a formula or system I can use to assign seating so that everyone gets to meet 16  different people (4 seatings with 4 new people each) with no repeats?

Trial and error is just giving me a headache!

Can I use the same formula or system if 90 people show up and we put them at 18 tables of 5?

What if we change our minds and go with tables of 6?

Thanks for any help I can get

JimS