I agree with Jim's interpretation. I don't remember the exact speeds from the original problem, but I would imagine that they were chosen in such a way that the *only* time both swimmers hit the wall simultaneously was at the very start. This would eliminate the necessity to explain in great detail exactly what a "pass" entailed. At 08:03 PM 11/11/2017, Tom Karzes wrote:
Well, if you perturb it by moving the fast swimmer ahead slightly, then you get (a) the fast swimmer overtaking the slow swimmer on the way up, followed by (b) the swimmers swimming past each other. If you perturb it by moving the slow swimmer ahead slightly, then you get (a) the swimmers swimming past each other, followed by (b) the fast swimmer overtaking the slow swimmer on the way back. In other words, the two types of passes occur in the opposite order. I argue that these disappear entirely if they bounce at the exact same time.
Tom
James Propp writes:
I think both swimmers simultaneous bouncing off the wall should count as a "double pass", since that's what it turns into if you perturb the history of the system ever-so-slightly in either direction (having the slow swimmer reach the wall first or having the fast swimmer reach the wall first).