  The angel-devil game is played on an infinite two-dimensional ``chessboard''.
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, vertical or diagonal) to a new white square. Here J is a constant.
The devil wins if the angel does not find any more white squares to land on.
The result of the paper is that if J is sufficiently large then the angel has a
strategy such that the devil will never capture her. This deceptively
easy-sounding result has been a conjecture, surprisingly, for about thirty
years. Several other independent solutions have appeared simultaneously, some
of them prove that J=2 is sufficient (see the Wikipedia on the angel problem).
Still, it is hoped that the hierarchical solution presented here may prove
useful for some generalizations.
