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 RULES:

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 bkennedy@gettysburg.edu 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.

THE PROBLEM:

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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