  We prove the exact formulae for the expected number of moves to solve several
variants of the Tower of Hanoi puzzle with 3 pegs and n disks, when each move
is chosen uniformly randomly from the set of all valid moves. We further
present an alternative proof for one of the formulae that couples a theorem
about expected commute times of random walks on graphs with the delta-to-wye
transformation used in the analysis of three-phase AC systems for electrical
power distribution.
