Hat Guessing Games

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 they are 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. Key words: hat game; deterministic strategies; sight graph; Tutte-Berge formula; hypercube AMS Mathematics Subject Classification: 91A12; 05C20

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Steve Butler, Mohammad Taghi Hajiaghayi, Robert D. Kleinberg, Tom Leighton
• Keywords: Deterministic, Hat Problem, SIAMDM 2008, Typical Hat Problem