Thirty-three ladybugs are sitting on a one meter stick. Suddenly all ladybugs start crawling either to the left or to the right with a constant speed of one meter per minute. When two ladybugs meet, they reverse directions immediately. If one arrives at the end of the stick, it falls off. Considering all possible initial configurations, what is the longest time it can take until all ladybugs have fallen off?
One minute. 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.
Solution
