Speed dating/networking challenge

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I am trying to organise an event with 54 participants.

I want them to participate in 9 different activities at stations around a hall. Obviously this will require 9 sessions to allow the participants to visit each station.

I would also like the participants in groups of 6 at each station.

The problem arises from the fact that I would also like to use this as a networking opportunity. It would be great if someone knew of a method or algorithm to allocate participants to groups so that they only meet other participants once. Two encounters would be acceptable but I don't really want any more than that.

Does anyone know of an algorithm or methodology that would help to produce a timetable?

Thanks - Matt