Angel Problem

In a game proposed by J. H. Conway, a devil chases an angel on an infinite chessboard. At each move, the devil can eliminate one of the squares, and the angel can make a leap in any direction, covering a distance of at most  squares. Here,  is a positive integer previously fixed, and is called the "power" of the angel. The devil's aim is to trap the angel on an island surrounded by a hole of width at least .

Can the angel indefinitely escape the devil, if his power is sufficiently high? Can the devil defeat an angel of any finite power? In 2006, Brian Bowditch proved that the 4-angel can win. Later that year, András Máthé proved the 2-angel will win, completely solving the problem.

REFERENCES:

Conway, J. "The Angel Problem." In Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994 (Ed. R. J. Nowakowski.) Cambridge, England: Cambridge University Press, pp. 3-12, 1996. http://www.msri.org/publications/books/Book29/files/conway.pdf.