I was just figuring out how to rotate 21 kids through 7 stations in such a way that each kid does each station with a different group. And it just dropped in to try this: 1/3 of the kids advance by 1’s. (If you’re at station 2, move to 3). 1/3 advance by 2’s (e.g. if you’re at 2, move to 4). 1/3 advance by 3’s (if you’re at 2, move to 5.) And it works! I wonder if any group reconstitutes itself along the way somewhere … and what other combinations of kids/stations this or similar patterns work for ….