4-angel (that is, an angel with power k = 4) can win and Máthé and Kloster gave proofs that a 2-angel can win. Basic strategies and why they don't work Many intuitive escape strategies for the angel can be defeated. For example, if the angel tries to run away from near blocks, the devil can make a giant horseshoe far to the north, then prod the angel into the trap by repeatedly eating the square just to the south of the angel. If the angel tries to avoid traps set very far away, the devil can make a small horseshoe to the north, then prod the angel into the trap by eating the squares far to the south. It seems that the angel should be able to win by moving up as fast as he can, combined with occasional zigzags to the east or west to avoid any obvious traps. This strategy can be defeated by noting that this angel's possible future positions lie in a cone, and the devil can build a wall across the cone in the distance in a certain manner, so that when the angel finally arrives at the distance, the devil has created an impenetrable wall, and since the angel insists on moving north, the angel cannot move at all. History The problem was first published in the 1982 book Winning Ways by Berlekamp, Conway, and Guy, under the name "the angel and the square-eater." In two dimensions, some early partial results included: If the angel has power 1, the devil has a winning strategy (Conway, 1982). (According to Conway, this result is actually due to Berlekamp.) This can be read at section 1.1 of Kutz's paper. If the angel never decreases its y coordinate, then the devil has a winning strategy (Conway, 1982). If the angel always increases its distance from the origin, then the devil has a winning strategy (Conway, 1996). In three dimensions, it was shown that: If the angel always increases its y coordinate, and the devil can only play in one plane, then the angel has a winning strategy. If the angel always increases its y coordinate, and the devil can only play in two planes, then the angel has a winning strategy. The angel has a winning strategy if it has power 13 or more. If we have an infinite number of devils each playing at distances then the