# Tower of Hanoi: Visualisation of the Bi-colour pentad tower in VRML

Pavitar Kaur Harlochan Singh, (2007) Tower of Hanoi: Visualisation of the Bi-colour pentad tower in VRML. University Malaysia Sabah. (Unpublished)

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## Abstract

The Bi-Colour Pentad Tower is a variation from the Tower of Hanoi game. The Bi-Colour Pentad Tower consists of five pegs, (N = 5) and n discs. There are two different colours of discs. The main aim of this game is to form two towers that consist of two different colours, in this case, to form a blue and red tower of discs on different pegs. The number of minimal moves was studied and a general formula was generated. The formula for 1 â‰¤ n â‰¤ 3 discs is 2(n -1), where n = 2 and 3. When n = 1, only one move is required. The Hanoi Graphs for the Bi-Colour Pentad Tower is drawn for one, two and three discs. The Hanoi Graphs shows all the possible movement of the discs, including the fastest and the longest move to solve the game. The Hanoi Graphs for each number of discs are drawn using Virtual Reality Modelling Language (VRML) in a 3D view. The Hanoi Graphs for the Bi-Colour Pentad Tower forms a pyramid shape. As the number of discs increases, the Hanoi Graphs becomes more complicated. The Hanoi Graphs shows a repetition pattern that consists of pyramids combination. To compare the Hanoi Graphs for the Bi-Colour Pentad Tower and other modifications of the Hanoi Tower game, the Hanoi Graphs for four pegs (N = 4) is drawn using VRML for one, two and three discs. The same recursive pattern of tetrahedrons and pyramids is seen for both N = 4 and N = 5 pegs of the Hanoi Game.

Item Type: Academic Exercise Bi-Colour Pentad Tower, colours of disc, Hanoi Graph, Virtual Reality Modelling Language (VRML) Q Science > QA Mathematics SCHOOL > School of Science and Technology MDM SITI AZIZAH IDRIS 14 May 2014 01:39 13 Oct 2017 03:54 http://eprints.ums.edu.my/id/eprint/9017