In this talk, I will outline a combinatorial problem that has journeyed with me from Berkeley City College to Cornell. I will describe how a small curiosity posed to me by a mentor turned into a research project driven by curiosity and collaboration. Along the way, we will encounter probabilities, permutation patterns, powers of two, ordered partitions and a Pascal-esque recurrence relation. All of this work is joint with Ben Thompson and Gabe Udell.