Narzędzia help

Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
cannonical link button

http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BUS8-0012-0003

Czasopismo

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
[1] G. Aggarwal, A. Fiat, A. Goldberg, J. Hartline, N. Immorlica, and M. Sudan, Derandomization of auctions, Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 619-625, ACM, New York, 2005.
[2] J. Aspnes, R. Beigel, M. Furst, and S. Rudich, The expressive power of voting polynomials, Combinatorica 14 (1994), 135-148.
[3] R. Beigel, L. Fortnow, and F. Stephan, Infinitely-often autoreducible sets, SIAM Journal on Computing 36 (2006), 595-608.
[4] Berkeley Riddles, www.ocf.berkeley.edu/ wwu/riddles/hard.shtml.
[5] M. Bernstein, The hat problem and Hamming codes, MAA Focus, November, 2001, 4-6.
[6] W. Blum, Denksport f¨ur Huttr¨ager, Die Zeit, May 3, 2001.
[7] M. Breit, D. Deshommes, and A. Falden, Hats required: perfect and imperfect strategies for the hat problem, manuscript.
[8] E. Brown, K. Mellinger, Kirkman's schoolgirls wearing hats and walking through fields of numbers, Mathematics Magazine 82 (2009), 3-15.
[9] E. Burke, S. Gustafson, and G. Kendall, A Puzzle to challenge genetic programming, Genetic Programming, 136-147, Lecture Notes in Computer Science, Springer, 2002.
[10] S. Butler, M. Hajianghayi, R. Kleinberg, and T. Leighton, Hat guessing games, SIAM Journal on Discrete Mathematics 22 (2008), 592-605.
[11] G. Cohen, I. Honkala, S. Litsyn, and A. Lobstein, Covering Codes, North Holland, 1997.
[12] T. Ebert, Applications of recursive operators to randomness and complexity, Ph.D. Thesis, University of California at Santa Barbara, 1998.
[13] T. Ebert and W. Merkle, Autoreducibility of random sets: a sharp bound on the density of guessed bits, Mathematical foundations of computer science 2002, 221-233, Lecture Notes in Computer Science, 2420, Springer, Berlin, 2002.
[14] T. Ebert, W. Merkle, and H. Vollmer, On the autoreducibility of random sequences, SIAM Journal on Computing32 (2003), 1542-1569.
[15] T. Ebert and H. Vollmer, On the autoreducibility of random sequences, Mathematical foundations of computer science 2000 (Bratislava), 333-342, Lecture Notes in Computer Science, 1893, Springer, Berlin, 2000.
[16] U. Feige, You can leave your hat on (if you guess its color), Technical Report MCS04-03, Computer Science and Applied Mathematics, The Weizmann Institute of Science, 2004, 10 pp.
[17] W. Guo, S. Kasala, M. Rao, and B. Tucker, The hat problem and some variations, Advances in distribution theory, order statistics, and inference, 459-479, Statistics for Industry and Technology, Birkh¨auser Boston, 2007.
[18] N. Immorlica, Computing with strategic agents, Ph.D. Thesis, Massachusetts Institute of Technology, 2005.
[19] H. Lenstra and G. Seroussi, On hats and other covers, IEEE International Symposium on Information Theory, Lausanne, 2002.
[20] J. Poulos, Could you solve this $1 million hat trick?, abcNews, November 29, 2001.
[21] S. Robinson, Why mathematicians now care about their hat color, The New York Times, Science Times Section, page D5, April 10, 2001.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-BUS8-0012-0003
Identyfikatory