While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of Regina, I decided to bring one of those tasks, "to account for all possible three-tall towers using two colours" (pp. 567, 568), into the pedagogy and mathematics content courses that I was teaching. My goals were simple: to find out how the students thought about combinatorics using a situation that was most likely unique to them, and to inspire them to actually work with some of the plethora of manipulative materials in our "math lab." The actual outcomes, however, went well beyond those goals, as problems related to common words used in relation to combinatorics, connections to Pascal's triangle, and the development of the binomial expansion theorem also emerged during the pre-service teachers' explorations of the two-coloured towers. As the task expanded into a suite of tasks and learnings over time, it also led the students and me to a new conundrum: "How did the permutations captured in the built towers change to combinations in the binomial expansion theorem?" This article reflects on the journey to an answer, while also leading to some questions about the existing literature related to the two-colour-tower tasks.