Related papers: Corner the Empress
We apply our geometrical theory for counting placements of $q$ nonattacking on an $n\times n$ chessboard, from Parts~I and II, to partial queens: that is, chess pieces with any combination of horizontal, vertical, and $45^\circ$-diagonal…
The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum…
A well-known chessboard problem is that of placing eight queens on the chessboard so that no two queens are able to attack each other. (Recall that a queen can attack anything on the same row, column, or diagonal as itself.) This problem is…
A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…
Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the column at position (0,0). For non-negative integers u,w such…
We play a variation of Nim on stacks of tokens. Take your favorite increasing sequence of positive integers and color the tokens according to the following rule. Each token on a level that corresponds to a number in the sequence is colored…
In combinatorial game theory, there are two famous winning conventions, normal play and mis\`ere play. Under normal play convention, the winner is the player who moves last and under mis\`ere play convention, the loser is the player who…
In 1967, Klarner proposed a problem concerning the existence of reflecting $n$-queens configurations. The problem considers the feasibility of placing $n$ mutually non-attacking queens on the reflecting chessboard, an $n\times n$ chessboard…
The Warden's Game is a 2-player game, played with a row of coins. One player (the prisoner) wants to get all coins to show tails; the other player (the warden) wants to delay that as long as possible. At each turn, one player transfers the…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
In this paper, a quantum variant of chess is introduced, which can be played on a traditional board, without using computers or other electronic devices. The rules of the game arise naturally by combining the rules of conventional chess…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…
We show the chess billiard map, which was introduced in [HM] in order to study a generalization of the $n$-Queens problem in chess, is a circle homeomorphism. We give a survey of some of the known results on circle homeomorphisms, and apply…
We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial…
We introduce a new board game based on the ancient Chinese game of Go (Weiqi, Igo, Baduk). The key difference from the original game is that players no longer alternatively play single stones on the board but instead they take turns placing…
Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move…
The game of \emph{Showcase Showdown} with unlimited spins is investigated as an $n$-players continuous game, and the Nash Equilibrium strategies for the players are obtained. The sequential game with information on the results of the…
In this note we discuss a theory of combinatorial games that involve transmitting the moves through a noisy channel that can introduce errors during the transmission. Players are aware of this interference and incorporate this variable into…
Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…