Problem of the Week: Run, Run, Run

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, November 9 and solutions are due on Friday, November 16 by 5:00 p.m.

THE PROBLEM: 

Let us say that a 2×2 matrix is runny if there are four consecutive integers that make up — in some order — the entries of the matrix. So, for example, the matrices

POW

are runny.

QUESTION: Find three runny 2×2 matrices A, B and C such that AB = C.

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Author: Gettysburgian Staff

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