By Andreas M. Hinz, Sandi Klavzar, Ciril Petr
This is the 1st accomplished monograph at the mathematical conception of the solitaire video game “The Tower of Hanoi” which used to be invented within the nineteenth century by means of the French quantity theorist Édouard Lucas. The booklet contains a survey of the old improvement from the game’s predecessors as much as contemporary examine in arithmetic and purposes in machine technological know-how and psychology. except long-standing myths it encompasses a thorough, mostly self-contained presentation of the basic mathematical proof with whole proofs, together with additionally unpublished fabric. the most items of analysis this day are the so-called Hanoi graphs and the similar Sierpi?ski graphs. Acknowledging the nice approval for the subject in machine technology, algorithms and their correctness proofs shape an important a part of the booklet. In view of crucial sensible functions of the Tower of Hanoi and its versions, particularly in physics, community conception, and cognitive (neuro)psychology, different comparable constructions 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. vital between those is the famed Frame-Stewart conjecture. regardless of many makes an attempt to make your mind up it and large-scale numerical experiments assisting its fact, it is still unsettled after greater than 70 years and therefore demonstrates the timeliness of the subject.
Enriched with intricate illustrations, connections to different puzzles and demanding situations for the reader within the type of (solved) workouts in addition to difficulties for extra exploration, this e-book is pleasing examining for college students, educators, gamers and researchers alike.