ACU Mathematics Problem of the Week
Problem 4 – February 5th, 2018
The Problem of the Week competition, sponsored by Mu Sigma, is now live. This week’s problem can be found below or slips of paper with the problem description can be found on the main bulletin board in the math department. Students have two weeks from issuance of the problem to construct a solution. Simple answers will not suffice for most problems. Your solution must demonstrate a solution method and communicate some understanding of that method to qualify. Students with correct responses will be identified on this blog and the math bulletin board, and the student or students with the most correct responses during the year will be recognized at the departmental dinner each spring. This competition is open to all students regardless of major or affiliation with the department. You may return your solutions to Gaye in the math office any time before noon on the final day.
Issued: Monday, February 5th
Return Solutions By: Monday, February 19th
An Unmagic Square?
Thanks to Dr. Jason Holland for suggesting this problem.
Can a 3×3 matrix with entries from the set {-1, 0, 1} have the sum of all its rows and columns be distinct?
(A more challenging question, and one for which no answer has been attempted to my knowledge, is “Can a 3×3 matrix with entries from the set {n, n+1, n+2} where n is an integer have the sum of all its rows and columns be distinct?”)
Questions like the one above are great examples of problems that start off innocently and can quickly turn into problems suitable for research or presentation. Enjoy!
