English

Solving the Tower of Hanoi with Random Moves

Combinatorics 2017-12-11 v3 Discrete Mathematics Probability

Abstract

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.

Keywords

Cite

@article{arxiv.1304.3780,
  title  = {Solving the Tower of Hanoi with Random Moves},
  author = {Max A. Alekseyev and Toby Berger},
  journal= {arXiv preprint arXiv:1304.3780},
  year   = {2017}
}
R2 v1 2026-06-21T23:59:03.698Z