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HAT GUESSING GAMES

机译：帽子猜游戏

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摘要

Hat problems have become a popular topic in recreational mathematics. In a typical hat problem, each of n players tries to guess the color of the hat he or she is wearing by looking at the colors of the hats worn by some of the other players. In this paper we consider several variants of the problem, united by the common theme that the guessing strategies are required to be deterministic and the objective is to maximize the number of correct answers in the worst case. We also summarize what is currently known about the worst-case analysis of deterministic hat guessing problems with a finite number of players.
机译：帽子问题已成为休闲数学中的热门话题。在一个典型的帽子问题中，n个玩家中的每一个试图通过查看其他一些玩家所戴帽子的颜色来猜测他或她所戴帽子的颜色。在本文中，我们考虑了该问题的几种变体，并结合了共同的主题，即猜测策略必须是确定性的，目标是在最坏的情况下最大化正确答案的数量。我们还总结了当前有关有限数量的参与者的确定性帽子猜测问题的最坏情况分析的已知信息。

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  • 来源
    《SIAM Journal on Discrete Mathematics》 |2008年第2期|592-605|共14页
  • 作者

    STEVE BUTLER; MOHAMMAD T. HAJIAGHAYI; ROBERT D. KLEINBERG; TOM LEIGHTON;

  • 作者单位

    Department of Mathematics, University of California, San Diego, La Jolla, CA 92093;

    Department of Mathematics and Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 32 Vassar Street, Cambridge, MA 02139;

    Computer Science Division, University of California, Berkeley, Berkeley, CA 94720, Department of Computer Science, Cornell University, Ithaca, NY 14853 Department of Mathematics and Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 32 Vassar Street, Cambridge, MA 02139;

    Akamai Technologies, Eight Cambridge Center, Cambridge, MA 02139 Department of Mathematics and Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 32 Vassar Street, Cambridge, MA 02139;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    hat game; deterministic strategies; sight graph; Tutte-Berge formula; hypercube;

    机译：帽子游戏;确定性策略;视线图Tutte-Berge公式;超立方体;

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