Quiet game, where use of non-verbal communication is required to solve the problem
announce that you want everyone lined up across the room by birth-date. Only catch: no talking. Once they are all lined up, ask certain people their birthdays just to be sure.
You can have them do the same thing, but by shoe size, height, month of birthday, etc.
Give everyone a number. They have to arrange themselves in numerical order by communicating with each other without speaking or holding up fingers. They make up their own sub-language or sign-language.