Matchstick games: On removing a matchstick without disturbing the others

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationInformation Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018
EditorsAlvaro Rocha, Mohammed Serrhini
PublisherSpringer Science and Business Media Deutschland GmbH
Pages580-587
Number of pages8
ISBN (Print)9783030035761
DOIs
StatePublished - Jan 1 2019
Event2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018 - Fez, Morocco
Duration: Oct 25 2018Oct 27 2018

Publication series

NameSmart Innovation, Systems and Technologies
Volume111
ISSN (Print)2190-3018
ISSN (Electronic)2190-3026

Other

Other2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018
CountryMorocco
CityFez
Period10/25/1810/27/18

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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)

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