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Towers of Hanoi

[ iHanoi | Legend | Play | Download]
Objective
     Move all the disks from rod A to rod C, using as many movements is possible, and respecting the next 3 rules.
Rules
    
  1. a greater disk could never be put over a smaller one;
  2. it is allowed to move one disk per time;
  3. all disks must be always on some rod or in movement.
How to play
    
  1. Initially you must select the rod origin, "clicking" near of it, then you must "click" the second rod, to be the destination.
    For instance, if you want to move the disk (on top) or rod B to rod C, first you must "click" on rod B, then on rod C.
  2. To change the number of disks on rods, you must "click" on the desired number of disks using the buttons below the rods (it could be 1 disk until 6 disks.
  3. To start a new session of play, you must "click" on the button Restart.
  4. Once you effectuated some movements, it is possible to "review" them, "clicking" on the button Review (it is necessary to new "click" to see the next movement).
Legend
     The Towers of Hanoi problem was first proposed by the french mathematician Edouard Lucas, in 1883. Lucas created to his "invention" a curious legend about a giant tower, Brahma Tower, that was created since the begining of the world. This tower has three rods with 64 concentric disks. At the same time was created a community of monks whose live duty was to move all disks from rod "A" to rod "C", determining that, the world will came to an ending when the monks complete their task. However, the creator also defined that the monks must allways follow the three rules:
  1. a greater disk could never be put over a smaller one;
  2. it is allowed to move one disk per time;
  3. all disks must be always on some rod or in movement.
Considering this, we must estimate how many more years have we on Earth?
Do do this, initially is necessary to found the rule to effectuate the optimal movements, i.e., the movement using the minimum number of movements, respecting those three rules.
Lets say H(n) is the minimum number of movements to move n disks. If we consider that each movement (to move one disk to any origin rod to any destination rod) take exactly one second, how many years will have the world?
Are you interested in contribute with educational software or want to personalize one version of iHanoi?
     This version of iHanoi was implemented using (pure) JavaScript puro (with no additional framework) to illustrate the ideia of interative Learning Module (iLM).
Any iLM can be seamless integrated to Moodle, if you are interested, please, follow this link.
 
To get a complete copy of iHanoi (inclunding these Web pages), "click" here.
 
To see other free educational software developed by LInE.
Free Software, private data.
 
Prof. Leônidas de Oliveira Brandão
Laboratoy of Informatics in Educacion.

 

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