Related papers: The Three Hat Problem
Winning probabilities of The Hat Game (Ebert's Hat Problem) with three players and three colors are only known in the symmetric case: all probabilities of the colors are equal. This paper solves the asymmetric case: probabilities may be…
We generalize Ebert's Hat Problem for three persons and three colors. All players guess simultaneously the color of their own hat observing only the hat colors of the other players. It is also allowed for each player to pass: no color is…
This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning…
We study a game puzzle that has enjoyed recent popularity among mathematicians, computer scientist, coding theorists and even the mass press. In the game, $n$ players are fitted with randomly assigned colored hats. Individual players can…
We study a cooperative game in which each member of a team of $N$ players, wearing coloured hats and situated at the vertices of a cycle graph $C_N$, is guessing their own hat colour merely on the basis of observing the hats worn by their…
The Levine hat game requires $n$ players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy…
Several different "hat games" have recently received a fair amount of attention. Typically, in a hat game, one or more players are required to correctly guess their hat colour when given some information about other players' hat colours.…
We consider Lionel Levine's notorious hat puzzle with two players. Each player has a stack of hats on their head, and each hat is chosen independently to be either black or white. After observing only the other player's hats, players…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game,…
N players are randomly fitted with a colored hat (q different colors). All players guess simultaneously the color of their own hat observing only the hat colors of the other N-1 players. The team wins if all players guess right. No…
This paper studies Ebert's hat problem with four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies…
A puzzle about prisoners trying to identify the color of a hat on their head leads to a version where there are k more hats than prisoners. This generalized puzzle is related to the independence number of the arrangement graph A(m, n) and…
This paper studies asymmetric Ebert's Hat Problem with five players where the probability of the colors may be unequal. We obtain maximal winning probabilities and optimal winning strategies using the concept of adequate sets.
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
The prisoners and hats puzzle, or simply the hat puzzle, is a family of games in which a group of prisoners are each assigned a colored hat and are asked to guess the color of their own hat. Various versions of the puzzle arise depending on…
A team of players plays the following game. After a strategy session, each player is randomly fitted with a blue or red hat. Then, without further communication, everybody can try to guess simultaneously his or her own hat color by looking…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
Lionel Levine's hat challenge has $t$ players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are…
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 neighbours without exchanging any information. Each hat can have one of…