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The Angel of Power 2 Wins

Published online by Cambridge University Press:  01 May 2007

ANDRÁS MÁTHÉ
ANDRÁS MÁTHÉ*
Affiliation:
Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c, 1117 Budapest, Hungary (e-mail: [email protected]://amathe.web.elte.hu)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 3 , May 2007 , pp. 363 - 374
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 113 176–184.CrossRefGoogle Scholar
[2]Bowditch, B. H. (2007) The angel game in the plane. Combin. Probab. Comput. 16 345–362.CrossRefGoogle Scholar
[3]Conway, J. H. (1996) The Angel problem. In Games of No Chance (Nowakowski, R. J., ed.), Cambridge University Press, pp. 3–12.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. 349 443–451.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. 925–934.Google Scholar