2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225696I prove that the group of symmetries of the Tower of Hanoi graph with k pegs and n disks, denoted H_n^k, is isomorphic to the group of permutations of k elements, S_k, for all k greater than or equal to 3 and positive n.8 pages, 6 figures; Minor revisions following referees comments. To appear in the American Mathematical MonthlyCombinatoricstext