By Andreas M. Hinz, Sandi Klavzar, Uros Milutinovic, Ciril Petr
This can be the 1st accomplished monograph at the mathematical conception of the solitaire online game “The Tower of Hanoi” which used to be invented within the nineteenth century by way of the French quantity theorist Édouard Lucas. The booklet contains a survey of the old improvement from the game’s predecessors as much as fresh examine in arithmetic and purposes in desktop technology and psychology. except long-standing myths it encompasses a thorough, principally self-contained presentation of the basic mathematical evidence with whole proofs, together with additionally unpublished fabric. the most items of analysis this present day are the so-called Hanoi graphs and the comparable Sierpiński graphs. Acknowledging the good acclaim for the subject in desktop technology, algorithms and their correctness proofs shape an important a part of the ebook. In view of crucial sensible functions of the Tower of Hanoi and its versions, specifically in physics, community idea, and cognitive (neuro)psychology, different similar buildings and puzzles like, e.g., the “Tower of London”, are addressed.
Numerous alluring integer sequences come up alongside the best way, but additionally many open questions impose themselves. valuable between those is the famed Frame-Stewart conjecture. regardless of many makes an attempt to choose it and large-scale numerical experiments helping its fact, it is still unsettled after greater than 70 years and hence demonstrates the timeliness of the subject.
Enriched with complex illustrations, connections to different puzzles and demanding situations for the reader within the type of (solved) routines in addition to difficulties for extra exploration, this publication is pleasing analyzing for college students, educators, gamers and researchers alike.