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       #Post#: 97--------------------------------------------------
       ANTS ON A STICK
       By: eba95 Date: July 29, 2010, 9:01 pm
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       One hundred ants are dropped on a
       meter stick. Each ant is traveling
       either to the left or the right with
       constant speed 1 meter per minute.
       When two ants meet, they bounce
       off each other and reverse direction.
       When an ant reaches an end of the
       stick, it falls off.
       At some point all the ants will have
       fallen off. The time at which this
       happens will depend on the initial
       configuration of the ants.
       Question: over ALL possible initial
       configurations, what is the longest
       amount of time that you would need
       to wait to guarantee that the stick
       has no more ants?
       Presentation Suggestions:
       You might give this at the end of
       lecture one day and present the
       answer the following lecture.
       The Math Behind the Fact:
       The answer is 1 minute! While ants
       bouncing off each other seems
       difficult to keep track of, one key idea
       (fun fact!) makes it quite simple: two
       ants bouncing off each other is
       equivalent to two ants that pass
       through each other, in the sense that
       the positions of ants in each case are
       identical. So, you might as well think
       of all ants acting with independent
       motions. Viewed in this way, all ants
       fall off after traversing the length of
       the stick, i.e., the longest that you
       would need to wait to ensure that all
       ants are off is 1 minute.
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