On the number of queries necessary to identify a permutation☆
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Cited by (16)
Bounds for the Static Permutation Mastermind game
2021, Discrete MathematicsQuery complexity of mastermind variants
2018, Discrete MathematicsCitation Excerpt :In 1963 Erdős and Rényi [6] studied the two-color variant of this game, and after the release of Mastermind, Knuth showed that a minimax strategy guarantees guessing the hidden vector in no more than 5 turns [13]. Many authors have since studied algorithms to minimize the number of guesses required in the worst case [4,3,14,9,5,11,2,12,7,8], and almost all of these results will be introduced and discussed at relevant points in this paper. We note here that the work of Jäger and Peczarski [11,12] and Goddard [7,8] deal with finding explicit optimal bounds for small numbers of colors and pegs, whereas we deal with asymptotics when both of these quantities are large.
The worst case number of questions in Generalized AB game with and without white-peg answers
2015, Discrete Applied MathematicsStrategy optimization for deductive games
2007, European Journal of Operational ResearchFinding a needle in a haystack using hints and evolutionary computation: The case of evolutionary MasterMind
2006, Applied Soft Computing JournalCitation Excerpt :This result is consistent with Knuth's, but it is a clear improvement over it. Variants of the MasterMind game have also been researched by Flood [27] and Ko and Teng [28]. Other approaches have also been reviewed in one of our previous papers [29].
Optimal strategies for the static black-peg AB game with two and three pegs
2023, Discrete Mathematics, Algorithms and Applications
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This research was supported in part by the National Science Foundation Grant MCS-8103479A01.