Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 05, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Henning Thomas

Mastermind

Most of you probably know the game of Mastermind. In this game, one player (the "codemaker") makes a secret code word m=(m_1, m_2, ..., m_n) over an alphabet of size k. where in the classical board game (n=4, k=6) the symbols are represented by pegs of different colors. The other player (the "codebreaker") has to identify the code word by asking questions of the form q=(q_1, q_2, ..., q_n) over the same alphabet. The codemaker answers a question with a distance measure to the secret code by revealing (i) the number a(m,q) of positions i for which m_i = q_i, in the original board game depicted by black pegs, and (ii) the maximum a(m,q) over all permutations of q, originally depicted by white pegs.
In this talk we present some known upper and lower bounds as well as a new strategy for the case when k=n which improves the currently best-known upper bounds.

This is joint work with Benjamin Doerr, Reto Spöhel and Carola Winzen from MPI Saarbrücken.

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