Two-Player Tower of Hanoi

Autor: Urban Larsson, Akihiro Matsuura, Jonathan Chappelon
Přispěvatelé: Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics [Canada], Dalhousie University [Halifax], School of Science and Engineering [TDU], Tokyo Denki University
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Statistics and Probability
FOS: Computer and information sciences
Economics and Econometrics
Discrete Mathematics (cs.DM)
Combinatorial game theory
MSC2010 : 91A05
91A46
68R99
0102 computer and information sciences
Characterization (mathematics)
Type (model theory)
winning strategy
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
01 natural sciences
scoring game
normal play
Two-player game
Mathematics (miscellaneous)
Computer Science - Computer Science and Game Theory
0101 mathematics
[MATH]Mathematics [math]
Real number
Mathematics
[INFO.INFO-GT]Computer Science [cs]/Computer Science and Game Theory [cs.GT]
010102 general mathematics
ComputingMilieux_PERSONALCOMPUTING
Tower (mathematics)
Recreational mathematics
Tower of Hanoi
weighed Tower of Hanoi
010201 computation theory & mathematics
Statistics
Probability and Uncertainty
Mathematical economics
Algorithm
Social Sciences (miscellaneous)
Computer Science - Discrete Mathematics
Computer Science and Game Theory (cs.GT)
Zdroj: International Journal of Game Theory
International Journal of Game Theory, Springer Verlag, 2018, 47 (2), pp.463-486. ⟨10.1007/s00182-017-0608-4⟩
ISSN: 0020-7276
1432-1270
DOI: 10.1007/s00182-017-0608-4⟩
Popis: The Tower of Hanoi game is a classical puzzle in recreational mathematics (Lucas 1883) which also has a strong record in pure mathematics. In a borderland between these two areas we find the characterization of the minimal number of moves, which is $2^n-1$, to transfer a tower of $n$ disks. But there are also other variations to the game, involving for example real number weights on the moves of the disks. This gives rise to a similar type of problem, but where the final score seeks to be optimized. We study extensions of the one-player setting to two players, invoking classical winning conditions in combinatorial game theory such as the player who moves last wins, or the highest score wins. Here we solve both these winning conditions on three heaps.
Comment: 16 pages, 6 figures, 1 table
Databáze: OpenAIRE
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