In this paper, we analyze the recurrence relations generalized from the Tower of Hanoi problem of the form T (n, α, β) = min1≤t≤n{αT (n− t, α, β)+β S(t, 3)}, where S(t, 3) = 2−1 is the optimal solution for the 3-peg Tower of Hanoi problem. It is shown that when α and β are natural numbers and α ≥ 2, the sequence of differences of T (n, α, β)’s, i.e., T (n, α, β) − T (n − 1, α, β), consists of n...

Dijkstra and Scholten have argued that greater use should be made of the associativity of equivalence. This note shows how the property is used in specifying the rotation of the disks in the well-known Towers of Hanoi problem.  2001 Elsevier Science B.V. All rights reserved.

In this work I study a modified Tower of Hanoi puzzle, which I term Magnetic Tower of Hanoi (MToH). The original Tower of Hanoi puzzle, invented by the French mathematician Edouard Lucas in 1883, spans "base 2". That is – the number of moves of disk number k is 2^(k-1), and the total number of moves required to solve the puzzle with N disks is 2^N 1. In the MToH puzzle, each disk has two distin...

The famous Tower of Hanoi puzzle, invented in 1883 by Édouard Lucas (see [21]), consists of three posts and a set of n, typically 8, pierced disks of differing diameters that can be stacked on the posts. The tower is formed initially by stacking the disks onto one post in decreasing order of size from bottom to top. The challenge is to transport the tower to another post by moving the disks one...

Hanoi graphs Hn p model the Tower of Hanoi game with p pegs and n discs. Sierpiński graphs Sn p arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that Sn p embeds as a spanning subgraph into Hn p if and only if p is odd or, trivially, if n = 1. MSC: 05C60

We prove that the solutions to the k-peg Tower of Hanoi problem given by Frame and Stewart are minimal. This paper solves the problem of finding the least number of moves needed to transfer a Tower of Hanoi of n disks, from an initial peg to another one of the k− 1 other pegs. This problem generalizes a well known puzzle proposed and solved in [5] for the case of three pegs. The generalization ...

Designing sound-based interactive entertainment for visually impaired users poses several challenges. This article points out some central issues faced when developing sound-based computer games. The three games described here were developed for the Swedish Library of Talking Books and Braille (TPB), to be published on the TPB Internet site [1]. These games, Towers of Hanoi, Memory and Tag, can...

This study uses minimally invasive technology to monitor the emotional response of a subject during stress inducing psychological tasks. The goal of these tasks is to investigate the possibility of measuring and subsequently categorising the subject’s level of stress using biosignal devices. If a consistent metric of stress can be determined it may be used for many forms of human-machine intera...

By making the moving direction of each disc explicit in the representation, a bit-string so constructed can be used to drive the Tower of Hanoi algorithm. The behaviour of disc moves is further analyzed based on the bit-string representation. It has been shown that the bit-string for moving n discs can be used to generate successively the Gray codes of n bits.

The Tower of Hanoi game is a classical puzzle in recreational mathematics, which also has a strong record in pure mathematics. In a borderland between these two areas we find the characterization of the minimal number of moves, which is 2n−1, to transfer a tower of n disks. But there are also other variations to the game, involving for example move edges weighted by real numbers. This gives ris...