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The Angel of Power 2 Wins

Published online by Cambridge University Press:  01 May 2007

ANDRÁS MÁTHÉ
Affiliation:
Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c, 1117 Budapest, Hungary (e-mail: amathe@cs.elte.huhttp://amathe.web.elte.hu)
Corresponding
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Abstract

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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Copyright
Copyright © Cambridge University Press 2007

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References

[1]Bollobás, B. and Leader, I. (2006) The Angel and the Devil in three dimensions. J. Combin. Theory Ser. A 113 176184.CrossRefGoogle Scholar
[2]Bowditch, B. H. (2007) The angel game in the plane. Combin. Probab. Comput. 16 345362.CrossRefGoogle Scholar
[3]Conway, J. H. (1996) The Angel problem. In Games of No Chance (Nowakowski, R. J., ed.), Cambridge University Press, pp. 312.Google Scholar
[4]Gács, P. (2006) The angel wins. Manuscript.Google Scholar
[5]Kloster, O. (2006) A solution to the Angel Problem. Submitted Theoret. Comp. Sci.Google Scholar
[6]Kutz, M. (2005) Conway's Angel in three dimensions. Theoret. Comput. Sci. 349 443451.CrossRefGoogle Scholar
[7]Kutz, M. and Pór, A. (2005) Angel, Devil, and King. In Computing and Combinatorics, Vol. 3595 of Lecture Notes in Computer Science, Springer, Berlin, pp. 925934.Google Scholar
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