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An Optimal Strategy for Static Mastermind with Two Pegs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: Proceedings of 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2016), Springer Berlin/Heidelberg, 2016, 670-682 p.Conference paper, Published paper (Refereed)
Abstract [en]

Mastermind is a famous two-player game which has attracted much attention in literature within the last years. In this work we investigate the static (also called non-adaptive) variant of Mastermind. The principal rule is that the codemaker has to choose a secret consisting of p pegs and c colors for each peg and the codebreaker may give a number of guesses at once, where for each guess he receives information from the codemaker. Using this information he has a final guess for the correct secret. The aim of the game is to minimize the number of guesses. Whereas Goddard has investigated the static version of original Mastermind in 2003, we do such an investigation of its black-peg variant, where the received information consists only of a number of black pegs which corresponds to the number of pegs matching in the corresponding question and the secret. As main result we present a strategy for this game for p=2 pegs and arbitrarily many colors c≥3 colors and prove its feasibility and optimality. Furthermore, by computer search we found optimal strategies for 9 other pairs (pc).

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2016. 670-682 p.
Series
Lecture Notes in Computer Science (LNCS), ISSN 0302-9743 ; 10043
Keyword [en]
Game theory, Logic game, Strategy, Static Mastermind
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-125916DOI: 10.1007/978-3-319-48749-6_48OAI: oai:DiVA.org:umu-125916DiVA: diva2:972707
Conference
10th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2016)
Available from: 2016-09-22 Created: 2016-09-22 Last updated: 2016-12-15Bibliographically approved

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Jäger, Gerold
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf