The Trees of Hanoi

TL;DR

This paper generalizes the classic Towers of Hanoi game to binary trees, providing a straightforward solution, a shorter optimized solution, and proving its optimality.

Contribution

It introduces a novel binary tree generalization of the Towers of Hanoi and presents an optimal solution with proof of minimal moves.

Findings

Presented a straightforward solution for the binary tree version.

Developed a shorter, optimized solution.

Proved the optimality of the new solution.

Abstract

The game of the Towers of Hanoi is generalized to binary trees. First, a straightforward solution of the game is discussed. Second, a shorter solution is presented, which is then shown to be optimal.