Matchstick games: On removing a matchstick without disturbing the others

Godfried T. Toussaint

doi:10.1007/978-3-030-03577-8_63

Matchstick games: On removing a matchstick without disturbing the others

Godfried T. Toussaint

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

It is shown that given any configuration of n ≥ 3 line segments (matchsticks) in the plane, there exist at least three segments that can each be translated to infinity, without colliding with the other n − 1 segments. In addition, if n ≥ 4, and the line segments are restricted to be parallel to the axes, at least four segments can be moved without disturbing the others. Furthermore, both lower bounds are best possible. The proofs are elementary and suitable for teaching in lower-level undergraduate courses on discrete mathematics.

Original language	English (US)
Title of host publication	Information Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018
Editors	Alvaro Rocha, Mohammed Serrhini
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	580-587
Number of pages	8
ISBN (Print)	9783030035761
DOIs	https://doi.org/10.1007/978-3-030-03577-8_63
State	Published - 2019
Event	2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018 - Fez, Morocco Duration: Oct 25 2018 → Oct 27 2018

Publication series

Name	Smart Innovation, Systems and Technologies
Volume	111
ISSN (Print)	2190-3018
ISSN (Electronic)	2190-3026

Other

Other	2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018
Country/Territory	Morocco
City	Fez
Period	10/25/18 → 10/27/18

Keywords

Artificial intelligence
Collision avoidance
Computational geometry
Discrete mathematics
Line segments
Robotics
Spatial planning
Translation

ASJC Scopus subject areas

Decision Sciences(all)
Computer Science(all)

Access to Document

10.1007/978-3-030-03577-8_63

Cite this

Toussaint, G. T. (2019). Matchstick games: On removing a matchstick without disturbing the others. In A. Rocha, & M. Serrhini (Eds.), Information Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018 (pp. 580-587). (Smart Innovation, Systems and Technologies; Vol. 111). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-03577-8_63

Matchstick games : On removing a matchstick without disturbing the others. / Toussaint, Godfried T.

Information Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018. ed. / Alvaro Rocha; Mohammed Serrhini. Springer Science and Business Media Deutschland GmbH, 2019. p. 580-587 (Smart Innovation, Systems and Technologies; Vol. 111).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Toussaint, GT 2019, Matchstick games: On removing a matchstick without disturbing the others. in A Rocha & M Serrhini (eds), Information Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018. Smart Innovation, Systems and Technologies, vol. 111, Springer Science and Business Media Deutschland GmbH, pp. 580-587, 2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018, Fez, Morocco, 10/25/18. https://doi.org/10.1007/978-3-030-03577-8_63

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abstract = "It is shown that given any configuration of n ≥ 3 line segments (matchsticks) in the plane, there exist at least three segments that can each be translated to infinity, without colliding with the other n − 1 segments. In addition, if n ≥ 4, and the line segments are restricted to be parallel to the axes, at least four segments can be moved without disturbing the others. Furthermore, both lower bounds are best possible. The proofs are elementary and suitable for teaching in lower-level undergraduate courses on discrete mathematics.",

keywords = "Artificial intelligence, Collision avoidance, Computational geometry, Discrete mathematics, Line segments, Robotics, Spatial planning, Translation",

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Matchstick games: On removing a matchstick without disturbing the others

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Keywords

ASJC Scopus subject areas

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