The number of pessimistic guesses in Generalized Mastermind

Authors:
Gerold Jäger;Marcin Peczarski
Affiliations:
Institute of Computer Science, Martin-Luther University of Halle-Wittenberg, D-06120 Halle (Saale), Germany;Institute of Informatics, University of Warsaw, ul. Banacha 2, PL-02-097 Warszawa, Poland
Venue:
Information Processing Letters
Year:
2009

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Abstract

Mastermind is a famous two-player game, where the codemaker has to choose a secret code and the codebreaker has to guess it in as few questions as possible. The code consists of 4 pegs, each of which is one of 6 colors. In Generalized Mastermind a general number p of pegs and a general number c of colors is considered. Let f(p,c) be the pessimistic number of questions for the generalization of Mastermind with an arbitrary number p of pegs and c of colors. By a computer program we compute ten new values of f(p,c). Combining this program with theoretical methods, we compute all values f(3,c) and a tight lower and upper bound for f(4,c). For f(p,2) we give an upper bound and a lower bound. Finally, combining results for fixed p and c, we give bounds for the general case f(p,c).