Morpion solitaire 5D: A new upper bound of 121 on the maximum score

Akitoshi Kawamura; Takuma Okamoto; Yuichi Tatsu; Yushi Uno; Masahide Yamato

Morpion solitaire 5D: A new upper bound of 121 on the maximum score

Akitoshi Kawamura, Takuma Okamoto, Yuichi Tatsu, Yushi Uno, Masahide Yamato

Research output: Contribution to conference › Paper › peer-review

Abstract

Morpion Solitaire is a pencil-and-paper game for a single player. A move in this game consists of putting a cross at a lattice point and then drawing a line segment that passes through exactly five consecutive crosses. The objective is to make as many moves as possible, starting from a standard initial configuration of crosses. For one of the variants of this game, called 5D, we prove an upper bound of 121 on the number of moves. This is done by introducing line-based analysis, and improves the known upper bound of 138 obtained by potentialbased analysis.

Original language	English
Pages	25-29
Number of pages	5
Publication status	Published - 2013
Externally published	Yes
Event	25th Canadian Conference on Computational Geometry, CCCG 2013 - Waterloo, Canada Duration: Aug 8 2013 → Aug 10 2013

Other

Other	25th Canadian Conference on Computational Geometry, CCCG 2013
Country/Territory	Canada
City	Waterloo
Period	8/8/13 → 8/10/13

All Science Journal Classification (ASJC) codes

Geometry and Topology
Computational Mathematics

Cite this

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title = "Morpion solitaire 5D: A new upper bound of 121 on the maximum score",

abstract = "Morpion Solitaire is a pencil-and-paper game for a single player. A move in this game consists of putting a cross at a lattice point and then drawing a line segment that passes through exactly five consecutive crosses. The objective is to make as many moves as possible, starting from a standard initial configuration of crosses. For one of the variants of this game, called 5D, we prove an upper bound of 121 on the number of moves. This is done by introducing line-based analysis, and improves the known upper bound of 138 obtained by potentialbased analysis.",

author = "Akitoshi Kawamura and Takuma Okamoto and Yuichi Tatsu and Yushi Uno and Masahide Yamato",

note = "Funding Information: This research is partly supported by Grant-in-Aid for Scientific Re-search ( KAKENHI ), No. 15H00853 , 24106002 and JST CREST Foundations of Innovative Algorithms for Big Data. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.; 25th Canadian Conference on Computational Geometry, CCCG 2013 ; Conference date: 08-08-2013 Through 10-08-2013",

year = "2013",

language = "English",

pages = "25--29",

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TY - CONF

T1 - Morpion solitaire 5D

T2 - 25th Canadian Conference on Computational Geometry, CCCG 2013

AU - Kawamura, Akitoshi

AU - Okamoto, Takuma

AU - Tatsu, Yuichi

AU - Uno, Yushi

AU - Yamato, Masahide

N1 - Funding Information: This research is partly supported by Grant-in-Aid for Scientific Re-search ( KAKENHI ), No. 15H00853 , 24106002 and JST CREST Foundations of Innovative Algorithms for Big Data. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - Morpion Solitaire is a pencil-and-paper game for a single player. A move in this game consists of putting a cross at a lattice point and then drawing a line segment that passes through exactly five consecutive crosses. The objective is to make as many moves as possible, starting from a standard initial configuration of crosses. For one of the variants of this game, called 5D, we prove an upper bound of 121 on the number of moves. This is done by introducing line-based analysis, and improves the known upper bound of 138 obtained by potentialbased analysis.

AB - Morpion Solitaire is a pencil-and-paper game for a single player. A move in this game consists of putting a cross at a lattice point and then drawing a line segment that passes through exactly five consecutive crosses. The objective is to make as many moves as possible, starting from a standard initial configuration of crosses. For one of the variants of this game, called 5D, we prove an upper bound of 121 on the number of moves. This is done by introducing line-based analysis, and improves the known upper bound of 138 obtained by potentialbased analysis.

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Y2 - 8 August 2013 through 10 August 2013

ER -

Morpion solitaire 5D: A new upper bound of 121 on the maximum score

Abstract

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All Science Journal Classification (ASJC) codes

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