Abstract
Consider the following game. There are n players, each wearing a hat colored red or blue. Each player does not see the color of her own hat but does see the colors of all other hats. Simultaneously, each player has to guess the color of her own hat, without communicating with the other players. The players are allowed to meet beforehand, hats-off, in order to coordinate a strategy. We give an explicit polynomial time deterministic strategy which guarantees that the number of correct guesses is at least \(\max\{n_{r}, n_{b}\} - O(n^{1/2})\), where n r is the number of players with a red hat and n b = n − n r . This answers a question of Feige.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aggarwal, G., Fiat, A., Goldberg, A.V., Hartline, J.D., Immorlica, N., Sudan, M.: Derandomization of auctions. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 619–625. ACM, New York (2005)
Doerr, B.: Integral approximation. Habilitationsschrift. Christian-Albrechts-Universität zu Kiel (2005)
Feige, U.: 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)
Winkler, P.: Games people don’t play. In: Wolfe, D., Rodgers, T. (eds.) Puzzlers’ tribute: a feast for the mind, A.K. Peters Ltd., Wellesley (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ben-Zwi, O., Wolfovitz, G. (2010). A Hat Trick. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-13122-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13121-9
Online ISBN: 978-3-642-13122-6
eBook Packages: Computer ScienceComputer Science (R0)