Q:

18 families and 6 plays

I have to organize a meeting with 18 families. Each family has to play 6 plays. For each play 3 families meet.
How can I combine them, so they always meet different families? 

A:

This is not possible; even a simpler variation with 12 families and 2 families per play is impossible. This is known as the Thirty-six officers problem.

