By Andreas M. Hinz, Sandi Klavzar, Ciril Petr
This is the 1st entire monograph at the mathematical conception of the solitaire video game “The Tower of Hanoi” which used to be invented within the nineteenth century through the French quantity theorist Édouard Lucas. The e-book contains a survey of the old improvement from the game’s predecessors as much as contemporary study in arithmetic and purposes in computing device technology and psychology. except long-standing myths it includes a thorough, mostly self-contained presentation of the fundamental mathematical evidence with entire proofs, together with additionally unpublished fabric. the most items of study this day are the so-called Hanoi graphs and the comparable Sierpi?ski graphs. Acknowledging the nice acclaim for the subject in desktop technology, algorithms and their correctness proofs shape a vital a part of the ebook. In view of crucial functional functions of the Tower of Hanoi and its variations, particularly in physics, community thought, and cognitive (neuro)psychology, different comparable buildings and puzzles like, e.g., the “Tower of London”, are addressed.
Numerous beautiful integer sequences come up alongside the way in which, but in addition many open questions impose themselves. imperative between those is the famed Frame-Stewart conjecture. regardless of many makes an attempt to choose it and large-scale numerical experiments aiding its fact, it continues to be unsettled after greater than 70 years and therefore demonstrates the timeliness of the subject.
Enriched with complicated 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 ebook is agreeable examining for college students, educators, gamers and researchers alike.