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?
The posted solution is not 100% correct.
It says "The maximum can only be reached if all go in one direction and one of them starts at one end of the stick, moving towards the other."
In fact, they do not need to all go in one direction. All that is required is that one of our ladybugs starts at one end of the stick and moves toward the other end. It matters not what the rest of our ladybugs do.
Achieving the maximum
