Polyominoes are two-dimensional shapes formed by a series of orthogonally connected unit squares on the integer lattice. In this talk, we will investigate the Longest Narrow Path Polyominoes problem: given a fixed collection of polyominoes, what is the maximum possible length of a corridor that can be created by packing them together? The corridor is required to be exactly one square wide and fully enclosed by the polyominoes, with no self-contact or branching. All tiles meet edge to edge, such that each square in the corridor is only adjacent to polyomino tile(s) and the neighboring square(s) of the corridor. After introducing the problem and giving some new results, we will also discuss how this problem can be adapted into an engaging outreach activity.

Links to the slides and material will be available at https://danielhodgins.github.io/pages/research.html