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It takes no longer than a minute. For an explanation, I'd like to cite Ken's solution, which I like best:
Suppose each ladybug is carrying a baton (like in a relay race) and each time two ladybugs bounce off each other, they instantaneously exchange batons. Notice that that the batons never change direction; so all the batons now move either left or right until they fall off. At one meter/minute, this has to happen in one minute or less.
We don't even have to consider the ladybugs to have negligible length; if two of them bounce, the baton will just make an instant leap of one ladybug-length, i.e. they will still all fall off after at least a minute. The maximum can only be reached if all go in one directions and on of them starts at one end of the stick, moving towards the other. |
