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 power k can escape. We show that in the three-dimensional analog of the game the 13-Angel can win. Our proof is constructive and provides an explicit infinite escape strategy. (c) 2005 Published by Elsevier B.V.
infinite games angel and devil combinatorial games