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Hinz, Andreas M.; Stockmeyer, Paul K. (2019): DISCOVERING FIBONACCI NUMBERS, FIBONACCI WORDS, AND A FIBONACCI FRACTAL IN THE TOWER OF HANOI. In: Fibonacci Quarterly, Vol. 57, No. 5: pp. 72-83
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Abstract

The Tower of Hanoi puzzle, with three pegs and n graduated discs, was invented by Edouard Lucas in 1883, writing under the name of Professor Claus. A simple question about relative distances between various regular states of this puzzle has lead to the discovery of a new occurrence of Fibonacci numbers, a new illustration of the finite Fibonacci words, and a fractal of Hausdorff dimension log(2)(phi), where phi is the Golden ratio.