The Tower of Hanoi and finite automata

TL;DR

This paper surveys automata-based solutions to the Tower of Hanoi puzzle, explores variations, and introduces new results on morphisms generating classical and lazy versions of the puzzle.

Contribution

It provides a comprehensive survey of finite automata approaches and presents novel findings on morphisms related to Tower of Hanoi variants.

Findings

Automata can solve Tower of Hanoi without memory.

New morphisms generate classical and lazy Tower of Hanoi.

Survey includes variations and automata algorithms.

Abstract

Some of the algorithms for solving the Tower of Hanoi puzzle can be applied "with eyes closed" or "without memory". Here we survey the solution for the classical Tower of Hanoi that uses finite automata, as well as some variations on the original puzzle. In passing, we obtain a new result on morphisms generating the classical and the lazy Tower of Hanoi.