I'm throwing an event where every individual is suppose to meet every other individual so I'm trying figure out how to rotate them. My friends say its easy but they have yet to come up with an answer and our event looms closer and closer.
We are shooting for n = 20 but my gut says n has to be a power of 2 for this to work. The first half is easy, you just have the odds stay in their seats and rotate evens. Then take the 10 odds, renumber them, repeat. Then split to 5... oops. you've got an odd number. but thats ok, you've got 4 groups with 5 each so create 2 pairs and you've got 5 sets of 2 pairs.
At this point, my head hurts and it's taking more time to tell my guests who to meet than they spend meeting them.
Is there a simpler answer for n=20?
(edit: lots of questions about the table setup and who they are suppose to meet. Assume whatever table arrangement works, we have a variety. Regardless, i think the long narrow solution below works.)