During couples-group-therapy, where two therapist and multiple couples consisting of two people each are present and we all sit on chairs forming a circle in the middle of the room. We often discuss more than one sensitive topic during a single session. To mentally put some distance between what we just talked about and the next topic, the therapists insists for everyone present to switch places with each other until the following criteria are met before tackling a second topic:
1.) After moving, everyone must have at least one chair between his old and new spot. (You can not just move one chair to the right or left.)
2.) After moving, noone can sit next to a person they sat next to before switching places.
This process tends to take up quite some time, so i thought about it for a while and came up with an algorithm that worked every time for our group consisting of an even number of people, no matter how many additional couples would join therapy - until sadly, one couple got a divorce and stopped coming. At that point i started refusing to change chairs at all, since there was no point in even trying.
Question: How many couples were left in the therapy group?
Bonus Question: How did the algorithm work? (Multiple answers possible)
Super Bonus Question: If all of a sudden just one therapist is with the 2-person-couples (i.e. an uneven number of people), but we assume that at least two new couples joined therapy, how can i change my algorithm to work under the new conditions? (Multiple answers possible)