an exploration of polyominos

Abstract

This paper was inspired by AMS Mathematics Magazine problem #2175 which asks “For which integers \(n\geq 3\) can an \(n\times n\) square grid be colored black and white—using each color at least once—so that every possible placement of a \(W\)-pentomino covers an even number of black squares?” We extend this problem to consider other and more general polyominos in square grids, as well as grids composed of triangles, and present their respective results. We also prove a solution to the original problem that is \(2\leq n\leq 5\).

The paper can be found here.

Now, why not some words about the project! I completed this project with two friends, and I think I had a lot of fun. Thanks!

(30 January, 2025)