Hinz T.A., Klavžar S., Petr C. The Tower of Hanoi: Myths and Maths

Second Edition — Basel: Birkhäuser, 2018. — 456 p. — ISBN: 978-3-319-73779-9.The solitaire game “The Tower of Hanoi" was invented in the 19th century by the French number theorist Édouard Lucas. The book presents its mathematical theory and offers a survey of the historical development from predecessors up to recent research. In addition to long-standing myths, it provides a detailed overview of the essential mathematical facts with complete proofs, and also includes unpublished material, e.g., on some captivating integer sequences. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms, together with their correctness proofs, form an essential part of the book. In view of the most important practical applications, namely in physics, network theory and cognitive (neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and its variants.The updated second edition includes, for the first time in English, the breakthrough reached with the solution of the “The Reve's Puzzle" in 2014. This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.Foreword by Ian StewartThe Beginning of the World
The Chinese Rings
The Classical Tower of Hanoi
Lucas’s Second Problem
Sierpiński Graphs
The Tower of Hanoi with More Pegs
Variations of the Puzzle
The Tower of London
Tower of Hanoi Variants with Restricted Disc Moves
Hints, Solutions and Supplements to Exercises
The End of the WorldName Index
Subject Index
Symbol Index
Файл: векторный PDF-файл с закладками