Exchanging disks in the tower of hanoi

We examine a variation of the famous Tower of Hanoi puzzle posed but not solved in a 1944 paper by Scorer et al. [5]. In this variation, disks of adjacent sizes can be exchanged, provided that they are at the top of their respective stacks. We present an algorithm for solving this variation, analyze its performance, and prove that it is optimal. Several exercises are listed at the end, ranging in difficulty from elementary to research level.