Take the tour ×  As an amusement at the start of this talk,
Moshe Rosenfeld poses the following question.  Suppose that
there are n salmon which begin at distinct points on a unit
circle, each facing either clockwise or counterclockwise. On a
signal, each salmon moves around the circle in its chosen
direction at a constant speed (the same for all salmon). When
two salmon meet, they both instantly reverse directions. If any
salmon ever returns to its starting point, it dies. (If two
salmon meet at one of their starting points, there is a death
and no change of direction; as Rosenfeld says, "Death comes
first.")    1. Is it true that all the salmon will eventually
die?   2. (assuming the answer to part 1 is yes) Give an
algorithm to find the last survivor.  I spent a certain amount
of time on buses and planes tinkering with this. It's quite easy
to show that every configuration is preperiodic, as a start. I
have some ideas about how one might finish. Eventually I decided
just to look for more information on the