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 firstname.lastname@example.org 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.
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
QUESTION: Find three runny 2×2 matrices A, B and C such that AB = C.