World Cafe seating plan: There are 12 tables each seating 8 people...

richardvahrman

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This is a real world problem that I tried to solve (and only partially succeeded). It is based on a problem solving method called World Cafe used e.g. in large organisations. The example comes exactly from a session my wife ran earlier in the week.

The 96 employees of XYZCo are getting together at Cafe au Lait to discuss the future of the company. They have decided that they need to discuss 4 topics and will spend 15 minutes on each "round". There are 12 tables each seating 8 people: at table A, B and C they will answer topic 1, at tables D, E and F they will answer topic 2 and so on. Each table has one person (the table "host") who will remain at the same table throughout the session. Everyone else has to discuss all 4 topics by moving to different tables at the end of rounds. Employees can discuss topics in any order, in fact, this is vital as no two people should ever sit at the same table more than once. But ...


... is this possible, and if so how to arrange the seating plan for each round?
 
This is a real world problem that I tried to solve (and only partially succeeded). It is based on a problem solving method called World Cafe used e.g. in large organisations. The example comes exactly from a session my wife ran earlier in the week.

The 96 employees of XYZCo are getting together at Cafe au Lait to discuss the future of the company. They have decided that they need to discuss 4 topics and will spend 15 minutes on each "round". There are 12 tables each seating 8 people: at table A, B and C they will answer topic 1, at tables D, E and F they will answer topic 2 and so on. Each table has one person (the table "host") who will remain at the same table throughout the session. Everyone else has to discuss all 4 topics by moving to different tables at the end of rounds. Employees can discuss topics in any order, in fact, this is vital as no two people should ever sit at the same table more than once. But ...


... is this possible, and if so how to arrange the seating plan for each round?

Hmmm. Reminiscent of Contract Bridge movements but not quite. Just to be clear, after being a a particular table, you never return to any of the three tables in that topic group and, if possible, also never sit at any table with someone when you have been at the same table before?
 
Exactly right. I got close to an answer by assigning everyone to one of the 24 ways you could answer 4 questions ABCD, ABDC etc (so 4 people to each group, less the 12 table hosts) and then tried to randomise each of the 4 people so that they didn't sit with each other - it worked well enough for the exercise, but I was peeved that I couldn't come up with a formula. I feel that you should be able to assign a unique number to each person that would tell them which question order and which table to prevent any repeats but the more I thought about it, the more my head hurt.

My ideal solution would be to input the number of people, the number of questions, and the number of tables and produce a plan for each person
 
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