Problem of the Week: Marbles

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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, September 14 and solutions are due on Friday September 21 by 5:00 p.m.


A jar contains some positive whole number of marbles; each is either green or yellow. Let G be the number of green marbles, and let Y be the number of yellow marbles.

I will reach into the jar and take out two different marbles; the two marbles will of course either be (a) both green; (b) both yellow; or (c) one green and one yellow.

Find values of G and Y so that all three scenarios (a), (b), and (c) above are equally likely, or show that no such values of G and Y exist.

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Author: Joshua Wagner

Josh Wagner '19 is a chemistry and mathematics double major who enjoys bike rides on the battlefield and waving around a red pen as the Gettysburgian's Managing Opinions Editor. When not editing for the Gettysburgian, he can usually be found working in the College Life Office, helping students with calculus as a PLA, or studying in the library.

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