This printout gives students an opportunity to explore a (possibly) real-life situation, empirically determine the minimum number of moves required to accomplish the task, then gather the data and find a pattern to describe it. The activity is completely printable (which also gives students the opportunity to do something with their hands (cutting) and lets them practice fine motor coordination, though if you want to spice it up students could cut discs out of corrugated cardboard (or even real wood).
My favorite aspect of this activity is that it gives a practical opportunity to discuss explicit vs recursive formulas. The explicit vs recursive discussion could tie well to a spreadsheets project. (I base mine on interest rates calculations, because they also fit into the Exponential Functions unit.)