These problems are my attempt to give high school students, like you, a glimpse into "real mathematics" by creating a math puzzle which will challenge you to think in ways that you have never thought before. Typically, in your high school math classes, you are given a problem to solve and a fixed step-by-step procedure for solving that type of problem — follow the steps, and you are certain to get an answer. However, "real mathematics" is not like that. When mathematicians work on problems, they often start off with no idea about how to solve the problem. There are lots of math questions that no one yet knows how to solve. I invite you to stretch your mind and take my mathematics challenge. I look forward to see what you come up with.
— Joseph DiMuro, Associate Professor for the Department of Math and Computer Science.
Here we have a 4 by 6 grid of squares. I've divided it into eight identical shapes; each shape has three squares arranged in an L. I'll call this shape the “L-tromino”.
Your task for this month is to find a different rectangular grid of squares that can be completely divided into L-trominoes. The catch is: the length and width of your rectangular grid must both be odd. (In my example, the length is 6 and the width is 4; those are both even numbers.)
Send your answers to this problem to me (Joseph DiMuro) at email@example.com by April 30, 2017.