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The Angel Game in the Plane


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 proofs that work for the angel of power 2 have been given by Kloster and by Máthé.

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[2] B. Bollobás (1998) Modern Graph Theory, Springer.

[10] A. Máthé (2007) The angel of power 2 wins. Combin. Probab. Comput. 16 363374.

[3] B. Bollobás and I. Leader (2006) The angel and devil in three dimensions. J. Combin. Theory Ser. A 113 176184.

[8] M. Kutz (2005) Conway's angel in three dimensions. Theoret. Comput. Sci. 349 443451.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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