Related papers: The Three Hat Problem
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of…
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…
Discuss several tricks for solving twenty question problems which in this paper is depicted as a guessing game. Player tries to find a ball in twenty boxes by asking as few questions as possible, and these questions are answered by only…
Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are…
Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the…
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by…
Geschke, Lubarsky, and Rahn in ``Choice and the Hat Game''~\cite{choice-and-the-hat-game} generalize the classic hat game puzzle to infinitely-many players and ask whether every model of set theory without choice in which the optimal…
We analyze the version of the deterministic Hats game. In this paper, we present new constructors, i.e. theorems that allow built winning strategies for the sages on different graphs. Using this technique we calculate the hat guessing…
In this paper we study a cooperative card game called Hanabi from the viewpoint of algorithmic combinatorial game theory. In Hanabi, each card has one among $c$ colors and a number between $1$ and $n$. The aim is to make, for each color, a…
The multi-armed bandit is a mathematical interpretation of the problem a gambler faces when confronted with a number of different machines (bandits). The gambler wants to explore different machines to discover which machine offers the best…
Benaloh challenge allows the voter to audit the encryption of her vote, and in particular to check whether the vote has been represented correctly. An interesting analysis of the mechanism has been presented by Culnane and Teague. The…
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven…
The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer…
We initiate the study of the hat guessing number of a graph where the adversary is only allowed to provide a proper coloring of the graph. This is the largest number $q$ for which there is a guessing strategy on each vertex that only…
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. Once the knot is fully resolved, the winner is…
The 3x+1 problem is one of the most classical problems in computer science, related to many fields. As it is thought by scientists a highly hard problem, resolving it successfully not only can improve the research in many relating fields,…