Hamiltonianicity of the towers of Hanoi problem

In this paper we analyze a variant of the n-disk Towers of Hanoi problem with an arbitrary starting and ending configuration using transition graphs representing valid configurations. In particular, we show that starting with any configuration, there is a sequence of moves that goes through each valid configuration exactly once and back to the starting configuration. Also, we show how the original Towers of Hanoi problem can be solved in any number of moves between 2n - 1 and 3n - 1 inclusive.