The Angel of Power 2 Wins

@article{Mth2007TheAO,
  title={The Angel of Power 2 Wins},
  author={Andr{\'a}s M{\'a}th{\'e}},
  journal={Combinatorics, Probability and Computing},
  year={2007},
  volume={16},
  pages={363 - 374}
}
  • A. Máthé
  • Published 2007
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
We solve Conway's Angel Problem by showing that the Angel of power 2 has a winning strategy. An old observation of Conway is that we may suppose without loss of generality that the Angel never jumps to a square where he could have already landed at a previous time. We turn this observation around and prove that we may suppose without loss of generality that the Devil never eats a square where the Angel could have already jumped. Then we give a simple winning strategy for the Angel. 
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iv, 47 leaves : ill. Thesis (Honors)--Smith College, Northampton, Mass., 2008. Includes bibliographical references (leaf 47)
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References

SHOWING 1-10 OF 11 REFERENCES
A solution to the Angel Problem
TLDR
The Angel Problem is solved, by describing a strategy that guarantees the win of an Angel of power 2 or greater, and it is shown that an Angel following this strategy will always spot a trap early enough to avoid it. Expand
The Angel Game in the Plane
  • B. Bowditch
  • Computer Science, Mathematics
  • Combinatorics, Probability and Computing
  • 2007
We show that in the game of angel and devil, played on the planar integer lattice, the angel of power 4 can evade the devil. This answers a question of Berlekamp, Conway and Guy. Independent proofsExpand
Conway's Angel in three dimensions
TLDR
It is shown that in the three-dimensional analog of the Angel-Devil game the 13-Angel can win and provides an explicit infinite escape strategy. Expand
The angel wins
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.Expand
The Angel Problem
Can the Devil, who removes one square per move from an infinite chessboard, strand the Angel, who can jump up to 1000 squares per move? It seems unlikely, but the answer is unknown. Andreas Blass andExpand
Angel, Devil, and King
TLDR
This work considers Kings, who are Angels that can only walk, not jump, and introduces a general notion of speed for such modified pieces, which allows the Devil to encircle Kings of any speed below 2. Expand
The Angel and the Devil in three dimensions
Our main aim in this paper is to show that, in Conway's Angel and Devil game, an Angel of sufficient speed can always escape in three dimensions. We also prove some related results and make someExpand
Games of No Chance 3: Surveys
TLDR
This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. Expand
The angel wins. Manuscript
  • The angel wins. Manuscript
  • 2006
The Angel problem Games of No Chance 3–12
  • The Angel problem Games of No Chance 3–12
  • 1996
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1
2
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