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A modified hat problem

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The topic of our paper is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. There are known many variations of the hat problem. In this paper we consider a variation in which there are n >= 3 players, and blue and red hats. Players do not have to guess their hat colors simultaneously. In this variation of the hat problem players guess their hat colors by coming to the basket and throwing the proper card into it. Every player has got two cards with his name and the sentence ``I have got a red hat'' or ``I have got a blue hat''. If someone wants to resign from answering, then he does not do anything. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. Is there a strategy such that the team always succeeds? We give an optimal strategy for the problem which always succeeds. Additionally, we prove in which step the team wins using the strategy. We also prove what is the greatest possible number of steps that are needed for the team to win using the strategy.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach recenzowanych i innych wydawnictwach ciągłych
Opublikowano w:
Commentationes Mathematicae nr 50, strony 121 - 126,
ISSN: 0373-8299
Język:
angielski
Rok wydania:
2010
Opis bibliograficzny:
Krzywkowski M.: A modified hat problem// Commentationes Mathematicae. -Vol. 50., nr. Iss. 2 (2010), s.121-126
Weryfikacja:
Politechnika Gdańska

wyświetlono 16 razy

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