相关论文: New constructions and bounds for Winkler's hat gam…

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…

Assume $n$ players are placed on the $n$ vertices of a graph $G$. The following game was introduced by Winkler: An adversary puts a hat on each player, where each hat has a colour out of $q$ available colours. The players can see the hat of…

The following general variant of deterministic Hats game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the $k$-th sage can have hats of one of $h(k)$ colors. Each sage tries to guess the color of his own…

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 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 analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of $k$ colors. Each sage tries to guess the color of his own hat…

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…

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…

In this note, we give an explicit polynomial-time executable strategy for Peter Winkler's hat guessing game that gives superior results if the distribution of hats is imbalanced. While Winkler's strategy guarantees in any case that $\lfloor…

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.…

We analyze the following version of the deterministic \hats game. We have a graph $G$, and a sage resides at each vertex of $G$. When the game starts, an adversary puts on the head of each sage a hat of a color arbitrarily chosen from a set…

Consider the following hat guessing game: $n$ players are placed on $n$ vertices of a graph, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but…

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…

The hat guessing number of a graph is a parameter related to the hat guessing game for graphs introduced by Winkler. In this paper, we show that graphs of sufficiently large hat guessing number must contain arbitrary trees and arbitrarily…

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…

The hat guessing number $HG(G)$ of a graph $G$ on $n$ vertices is defined in terms of the following game: $n$ players are placed on the $n$ vertices of $G$, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible…

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…

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…

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…

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…