Problem of the Week: Vacation

By Department of Mathematics

Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a panel of faculty judges, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button.  The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.


The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited! Send solutions to or put solutions in the marked envelope in the hallway outside Glatfelter 215. This problem was posted on Friday, February 22 and solutions are due on Friday, March 1 by 5:00 p.m.


There are five cities that I would like to visit. I have decided, starting this year, to plan my vacations in the following way: every year I will choose one of the five cities at random, and vacation there. In any particular year, I will be equally likely to choose any of the five cities, regardless of which cities I have visited in previous years.

After how many years will it be more likely than not that I have visited all five cities? Can you generalize to n cities?

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Author: Gettysburgian Staff

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