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An Optimal Strategy for Static Black-Peg Mastermind with Three Pegs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Foundations of Language Processing)ORCID iD: 0000-0001-7349-7693
2018 (English)In: SAGT: International Symposium on Algorithmic Game Theory: 11th International Symposium, SAGT 2018, Beijing, China, September 11-14, 2018, Proceedings / [ed] Xiaotie Deng, Springer, 2018, Vol. 11059, p. 261-266Conference paper, Published paper (Refereed)
Abstract [en]

Mastermind is a famous game played by a codebreaker against a codemaker. We investigate its static (also called non-adaptive) black-peg variant. Given c colors and p pegs, the codemaker has to choose a secret, a p-tuple of c colors, and the codebreaker asks a set of questions all at once. Like the secret, a question is a p-tuple of c colors. The codemaker then tells the codebreaker how many pegs in each question are correct in position and color. Then the codebreaker has one final question to find the secret. His aim is to use as few of questions as possible. Our main result is an optimal strategy for the codebreaker for p=3 pegs and an arbitrary number c of colors using ⌊3c/2⌋+1questions.

A reformulation of our result is that the metric dimension of ℤn×ℤn×ℤnis equal to ⌊3n/2⌋.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 11059, p. 261-266
Series
Lecture Notes in Computer Science
Keywords [en]
Mastermind, winning strategy, optimality
National Category
Discrete Mathematics Other Computer and Information Science
Identifiers
URN: urn:nbn:se:umu:diva-151844DOI: 10.1007/978-3-319-99660-8_25OAI: oai:DiVA.org:umu-151844DiVA, id: diva2:1248094
Conference
11th International Symposium on Algorithmic Game Theory, Beijing, China, September 11-14, 2018
Available from: 2018-09-13 Created: 2018-09-13 Last updated: 2019-06-19Bibliographically approved

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Jäger, Gerold

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CiteExportLink to record
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Citation style
  • apa
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