The Group of Symmetries of the Tower of Hanoi Graph

The classical Tower of Hanoi puzzle, invented by the French mathematician Édourd Lucas in 1883, consists of 3 wooden pegs and n disks with pairwise different diameters. The n disks are initially stacked on a single peg in order of decreasing size, from the largest at the bottom to the smallest at the top. (See Figure 1.) The goal is to move the tower of disks to another peg, moving one topmost disk at a time while never stacking a disk on a smaller one. A sequence of moves realizing this goal in the shortest possible number of moves for any given number of pegs provides a general solution to the Monthly Problem 3918 [1].