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## Commentationes Mathematicae

Tytuł artykułu

### A modified hat problem

Autorzy Krzywkowski, M.
Treść / Zawartość http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN 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.
Słowa kluczowe
 EN hat problem   variation of hat problem
Wydawca Polskie Towarzystwo Matematyczne
Czasopismo Commentationes Mathematicae
Rocznik 2010
Tom Vol. 50, [Z] 2
Strony 121--126
Opis fizyczny Bibliogr. 21 poz.
Twórcy
 autor Krzywkowski, M. Faculty of Applied Physics and Mathematics, Gdansk University of Technology Narutowicza 11/12, 80–233 Gdansk, Poland, fevernova@wp.pl
Bibliografia
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