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This is the first comprehensive monograph on the mathematical
theory of the solitaire game "The Tower of Hanoi" which was
invented in the 19th century by the French number theorist Edouard
Lucas. The book comprises a survey of the historical development
from the game's predecessors up to recent research in mathematics
and applications in computer science and psychology. Apart from
long-standing myths it contains a thorough, largely self-contained
presentation of the essential mathematical facts with complete
proofs, including also unpublished material. The main objects of
research today are the so-called Hanoi graphs and the related
Sierpinski graphs. Acknowledging the great popularity of the topic
in computer science, algorithms and their correctness proofs form
an essential part of the book. In view of the most important
practical applications of the Tower of Hanoi and its variants,
namely in physics, network theory, and cognitive (neuro)psychology,
other related structures and puzzles like, e.g., the "Tower of
London", are addressed. Numerous captivating integer sequences
arise along the way, but also many open questions impose
themselves. Central among these is the famed Frame-Stewart
conjecture. Despite many attempts to decide it and large-scale
numerical experiments supporting its truth, it remains unsettled
after more than 70 years and thus demonstrates the timeliness of
the topic. 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.
This is the first comprehensive monograph on the mathematical
theory of the solitaire game "The Tower of Hanoi" which was
invented in the 19th century by the French number theorist Edouard
Lucas. The book comprises a survey of the historical development
from the game's predecessors up to recent research in mathematics
and applications in computer science and psychology. Apart from
long-standing myths it contains a thorough, largely self-contained
presentation of the essential mathematical facts with complete
proofs, including also unpublished material. The main objects of
research today are the so-called Hanoi graphs and the related
Sierpinski graphs. Acknowledging the great popularity of the topic
in computer science, algorithms and their correctness proofs form
an essential part of the book. In view of the most important
practical applications of the Tower of Hanoi and its variants,
namely in physics, network theory, and cognitive (neuro)psychology,
other related structures and puzzles like, e.g., the "Tower of
London", are addressed. Numerous captivating integer sequences
arise along the way, but also many open questions impose
themselves. Central among these is the famed Frame-Stewart
conjecture. Despite many attempts to decide it and large-scale
numerical experiments supporting its truth, it remains unsettled
after more than 70 years and thus demonstrates the timeliness of
the topic. 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.
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