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Analysis Of The Tower Of Hanoi

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Introduction A French mathematician called Edouard Lucas invented the Tower of Hanoi also known as “The End of The World Puzzle”, in 1883. It is thought that Lucas designed it based on the legend of a Hindu Temple. The priests in the temple were apparently given a tower of 64 gold discs, each smaller in size than the disc beneath. The priests were to move the discs from one of the three poles to another, one by one, without placing a bigger disc on a smaller one, as the weight of the bigger one would crush the smaller one. It’s said that when the priests were able to successfully transfer all the discs from one pole to another, the world will crumble and disappear. If this were true, would there then be a way of predicting the end of the world? My aim for this mathematical exploration is to put the Tower of Hanoi to the test and find out (if true) how long we have until the end of the world. Finding a Pattern Before finding a pattern it would be wise to familiarise oneself with the task at hand. The task is to find out how many moves it would take to move all 64 discs from one pole to another without placing a bigger disc on a smaller one. Then the task is to work out how many years it would take to move the discs non-stop, each move taking no longer than a second. I will do this by looking for patterns in the Tower of Hanoi. However, first I will look at it using a smaller amount of discs, due to solving the puzzle using less discs would be simpler to analyse and

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