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Journal Article

Conway's Angel in three dimensions


Kutz,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Kutz, M. (2005). Conway's Angel in three dimensions. Theoretical Computer Science, 349, 443-451.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2624-C
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.