The angel problem is a question in game theory proposed by John Horton Conway.[1] The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2

lattice). The angel has a power k (a natural number 1 or higher), specified before the games starts. The board starts empty with the angel at the origin. On each turn, the angel jumps to a different empty square which could be reached by at most k moves of a chess king, i.e. the distance from the starting square is at most k in the infinity norm. The devil, on his turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely.
The angel problem is: can an angel with high enough power win?
http://en.wikipedia.org/wiki/Angel_problem