Simple Variations on The Tower of Hanoi A Study of Recurrences and Proofs by Induction
The Tower of Hanoi problem was formulated in 1883 by mathematician Edouard Lucas. For over a century, this problem has become familiar to many of us in disciplines such as computer programming, algorithms, and discrete mathematics. Several variations to Lucas' original problem exist today, and...
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| Vydané v: | Teaching Mathematics and Computer Science Ročník 17; číslo 2; s. 131 - 158 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Debrecen
University of Debrecen
24.03.2020
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| Predmet: | |
| ISSN: | 1589-7389, 2676-8364 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | The Tower of Hanoi problem was formulated in 1883 by mathematician Edouard Lucas. For over a century, this problem has become familiar to many of us in disciplines such as computer programming, algorithms, and discrete mathematics. Several variations to Lucas' original problem exist today, and interestingly some remain unsolved and continue to ignite research questions. Nevertheless, simple variations can still lead to interesting recurrences, which in turn are associated with exemplary proofs by induction. We explore this richness of the Tower of Hanoi beyond its classical setting to compliment the study of recurrences and proofs by induction, and clarify their pitfalls. Both topics are essential components of any typical introduction to algorithms or discrete mathematics.
Subject Classification: A20, C30, D40, D50, E50, M10, N70, P20, Q30, R20 |
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| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1589-7389 2676-8364 |
| DOI: | 10.5485/TMCS.2019.0459 |