Combinatorics of JENGA

Detalhes bibliográficos
Autor(a) principal: Carvalho, Alda
Data de Publicação: 2020
Outros Autores: Neto, João, Santos, Carlos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/13577
Resumo: JENGA, a very popular game of physical skill, when played by perfect players, can be seen as a pure combinatorial ruleset. Taking that into account, it is possible to play with more than one tower; a move is made by choosing one of the towers, removing a block from there, that is, a disjunctive sum. JENGA is an impartial combinatorial ruleset, i.e., Left options and Right options are the same for any position and all its followers. In this paper, we illustrate how to determine the Grundy value of a JENGA tower by showing that it may be seen as a bidimensional vector addition game. Also, we propose a class of impartial rulesets, the clock nim games, JENGA being an example of that class.
id RCAP_57e0014fd30348be44606a542ad279da
oai_identifier_str oai:repositorio.ipl.pt:10400.21/13577
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Combinatorics of JENGAGameRulesetGrundy value of a JENGA towerBidimensional vector addition gameJENGA, a very popular game of physical skill, when played by perfect players, can be seen as a pure combinatorial ruleset. Taking that into account, it is possible to play with more than one tower; a move is made by choosing one of the towers, removing a block from there, that is, a disjunctive sum. JENGA is an impartial combinatorial ruleset, i.e., Left options and Right options are the same for any position and all its followers. In this paper, we illustrate how to determine the Grundy value of a JENGA tower by showing that it may be seen as a bidimensional vector addition game. Also, we propose a class of impartial rulesets, the clock nim games, JENGA being an example of that class.Combinatorial Mathematics Society of Australasia (CMSA)RCIPLCarvalho, AldaNeto, JoãoSantos, Carlos2021-07-23T10:13:43Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/13577engCARVALHO, Alda; NETO, João Pedro; SANTOS, Carlos Pereira dos – Combinatorics of JENGA. The Australasian Journal of Combinatorics. ISSN 2202-3518. Vol. 76, N.º 1 (2020), pp. 87-1042202-3518info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:08:34Zoai:repositorio.ipl.pt:10400.21/13577Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:21:29.964517Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Combinatorics of JENGA
title Combinatorics of JENGA
spellingShingle Combinatorics of JENGA
Carvalho, Alda
Game
Ruleset
Grundy value of a JENGA tower
Bidimensional vector addition game
title_short Combinatorics of JENGA
title_full Combinatorics of JENGA
title_fullStr Combinatorics of JENGA
title_full_unstemmed Combinatorics of JENGA
title_sort Combinatorics of JENGA
author Carvalho, Alda
author_facet Carvalho, Alda
Neto, João
Santos, Carlos
author_role author
author2 Neto, João
Santos, Carlos
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Carvalho, Alda
Neto, João
Santos, Carlos
dc.subject.por.fl_str_mv Game
Ruleset
Grundy value of a JENGA tower
Bidimensional vector addition game
topic Game
Ruleset
Grundy value of a JENGA tower
Bidimensional vector addition game
description JENGA, a very popular game of physical skill, when played by perfect players, can be seen as a pure combinatorial ruleset. Taking that into account, it is possible to play with more than one tower; a move is made by choosing one of the towers, removing a block from there, that is, a disjunctive sum. JENGA is an impartial combinatorial ruleset, i.e., Left options and Right options are the same for any position and all its followers. In this paper, we illustrate how to determine the Grundy value of a JENGA tower by showing that it may be seen as a bidimensional vector addition game. Also, we propose a class of impartial rulesets, the clock nim games, JENGA being an example of that class.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2021-07-23T10:13:43Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/13577
url http://hdl.handle.net/10400.21/13577
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv CARVALHO, Alda; NETO, João Pedro; SANTOS, Carlos Pereira dos – Combinatorics of JENGA. The Australasian Journal of Combinatorics. ISSN 2202-3518. Vol. 76, N.º 1 (2020), pp. 87-104
2202-3518
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Combinatorial Mathematics Society of Australasia (CMSA)
publisher.none.fl_str_mv Combinatorial Mathematics Society of Australasia (CMSA)
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799133486086356992

Registros relacionados