jasonye wrote:

2) If A taxi drives C, and B taxi drives A, then B will end up hitting C with their drive. So, if D targets A, they will hit B; if they target B, they will hit C; if they target C, they will hit A.

3) If A taxi drives B, and B drives C, then both will hit their intended targets. So, if D targets A, they will hit C; if they target B, they will hit A; if they target C, they will hit B.

Urgh I don't think these two are consistent permutation-wise -- it's saying that (12)(23) and (23)(12) yield the same permutation (easier to see if you swap the roles of A and B in scenario 3 and have B's swap happen before A there), i.e. the order doesn't actually matter. Can you just tell us whether later taxiings get composed on the left or the right?

Actually wait, I guess #1 implies these aren't even actually permutations that are getting composed. Each later drive is being conjugated by the permutation up to there, or something? Or, one of the elements in the transposition is getting transformed before application, and the other isn't. Very confusing; precise mathematical description would be appreciated