Hostname: page-component-5b777bbd6c-gtgcz Total loading time: 0 Render date: 2025-06-19T17:00:06.228Z Has data issue: false hasContentIssue false
  • English
  • Français

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: amathe@cs.elte.huhttp://amathe.web.elte.hu)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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