Morpion Solitaire 5D

A new upper bound of 121 on the maximum score

Akitoshi Kawamura, Yuichi Tatsu, Yushi Uno, Masahide Yamato

Research output: Contribution to journalArticle

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 potential-based analysis.

Original languageEnglish
Pages (from-to)6-10
Number of pages5
JournalInformation Processing Letters
Volume121
DOIs
Publication statusPublished - May 1 2017
Externally publishedYes

Fingerprint

Solitaire
Game
Upper bound
Lattice Points
Line segment
Consecutive
Configuration
Line

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

Cite this

Morpion Solitaire 5D : A new upper bound of 121 on the maximum score. / Kawamura, Akitoshi; Tatsu, Yuichi; Uno, Yushi; Yamato, Masahide.

In: Information Processing Letters, Vol. 121, 01.05.2017, p. 6-10.

Research output: Contribution to journalArticle

Kawamura, Akitoshi ; Tatsu, Yuichi ; Uno, Yushi ; Yamato, Masahide. / Morpion Solitaire 5D : A new upper bound of 121 on the maximum score. In: Information Processing Letters. 2017 ; Vol. 121. pp. 6-10.
@article{15d7f8e0a40d42a3a3157f226d0b0959,
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 potential-based analysis.",
author = "Akitoshi Kawamura and Yuichi Tatsu and Yushi Uno and Masahide Yamato",
year = "2017",
month = "5",
day = "1",
doi = "10.1016/j.ipl.2017.01.003",
language = "English",
volume = "121",
pages = "6--10",
journal = "Information Processing Letters",
issn = "0020-0190",
publisher = "Elsevier",

}

TY - JOUR

T1 - Morpion Solitaire 5D

T2 - A new upper bound of 121 on the maximum score

AU - Kawamura, Akitoshi

AU - Tatsu, Yuichi

AU - Uno, Yushi

AU - Yamato, Masahide

PY - 2017/5/1

Y1 - 2017/5/1

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 potential-based 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 potential-based analysis.

UR - http://www.scopus.com/inward/record.url?scp=85009961465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009961465&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2017.01.003

DO - 10.1016/j.ipl.2017.01.003

M3 - Article

VL - 121

SP - 6

EP - 10

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

ER -