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}
}