Journal of Mathematical Sciences

, Volume 236, Issue 5, pp 503–520 | Cite as

For Which Graphs the Sages Can Guess Correctly the Color of at Least One Hat

  • K. KokhasEmail author
  • A. Latyshev

Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. Each hat can have one of three colors. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We completely solve the problem of describing all graphs for which the sages win.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Butler, M. T. Hajiaghayi, R. D. Kleinberg, and T. Leighton, “Hat guessing games,” SIAM Rev., 51, 399–413 (2009).MathSciNetCrossRefGoogle Scholar
  2. 2.
    T. Ebert, “Applications of recursive operators to randomness and complexity,” PhD Thesis, University of California, Santa Barbara (1998).Google Scholar
  3. 3.
    M. Gardner, The Scientific American Book of Mathematical Puzzles & Diversions, Simon and Schuster (1959).Google Scholar
  4. 4.
    M. Krzywkowski, “On the hat problem, its variations, and their applications,” Ann. Univ. Paedagog. Cracov. Stud. Math., 9, No. 1, 55–67 (2010).MathSciNetzbMATHGoogle Scholar
  5. 5.
    W. W. Szczechla, “The three-colour hat guessing game on the cycle graphs,” Electron. J. Combin., 24, No. 1, Paper #P1.37 (2017).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.ITMO UniversitySt. PetersburgRussia

Personalised recommendations