A theorem of A. Chandra et al. says that the mean number of steps it takes a purely random walk on an undirected graph to complete a cycle from node A to node B and back to A (also known as a "commute) equals 2mR, where R is the electrical resistance between nodes A and B when a one ohm resistor is placed in each edge of the graph and m is the total number of edges in the graph.  Via this theorem and an induction argument that iteratively applies the delta-to-wye transformation of electrical network theory, I obtain Max Alekseyev's formula, (3^n - 1) (5^n -3^n)/[2 * 3^{n-1}] for the mean number of legal moves it takes a randomly moving Hanoi tower with n disks to transfer all of them from peg 1 to peg 3. [Historical notes:  Alekseyev, a UCSD computer science PhD student when he derived the formula in February 2008, is now a professor at U. South Carolina; his formula became immediately famous, at least among a small circle of Hanoi tower devotees.  The delta-to-wye transformation was devised in 1899 by A. E. Kennelly to facilitate analysis of three phase AC power distribution systems; Kennelly also is generally credited with having discovered the ionosphere.]