Angel, Devil, and King
نویسندگان
چکیده
منابع مشابه
Conway's Angel in three dimensions
The Angel-Devil game is an infinite game played on an infinite chess board: In each move the Angel, a generalized chess king, jumps from his current square to some location at distance at most k, while his opponent, the Devil, blocks squares trying to strand the Angel. The Angel wins if he manages to fly on forever. It is a long-standing open question whether some Angel of sufficiently large po...
متن کاملThe Angel wins
The angel-devil game is played on an infinite two-dimensional “chessboard” Z. The squares of the board are all white at the beginning. The players called angel and devil take turns in their steps. When it is the devil’s turn, he can turn a square black. The angel always stays on a white square, and when it is her turn she can fly at a distance of at most J steps (each of which can be horizontal...
متن کاملThe Angel Problem, Positional Games, and Digraph Roots
Preface This thesis is about combinatorial games—mostly. It is also about graphs, directed graphs and hypergraphs, to a large extent; and it deals with the complexity of certain computational problems from these two areas. We study three different problems that share several of the above aspects, yet, they form three individual subjects and so we treat them independently in three self-contained...
متن کاملThe Angel Game in the Plane
The angel game, as described in [BeCG], has two players the “angel” and the “devil” who play alternately on the 2-dimensional integer lattice, Z. We refer to lattice points as vertices, and write o = (0, 0) for the origin. The angel has a certain fixed power p. (We refer to it as a p-angel .) It starts the game at the origin, and at each play moves to another vertex so that the change in each c...
متن کاملThe Angel of Power 2 Wins
We solve Conway’s Angel Problem by showing that the Angel of power 2 has a winning strategy. An old observation of Conway is that we may suppose without loss of generality that the Angel never jumps to a square where he could have already landed at a previous time. We turn this observation around and prove that we may suppose without loss of generality that the Devil never eats a square where t...
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