Skip to main content
×
Home

The Angel Game in the Plane

  • BRIAN H. BOWDITCH (a1)
Abstract

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.

Copyright
References
Hide All
[1]Berlekamp E. R., Conway J. H. and Guy R. K. (1982) Winning Ways, Vol. 2, Academic Press.
[2]Bollobás B. (1998) Modern Graph Theory, Springer.
[3]Bollobás B. and Leader I. (2006) The angel and devil in three dimensions. J. Combin. Theory Ser. A 113 176184.
[4]Conway J. H. (1996) The angel problem. In Games of No Chance (Nowakowski R. J., ed.), Cambridge University Press, pp. 312.
[5]Epstein R. A. (1967) Theory of Gambling and Statistical Logic, Academic Press.
[6]Gardner M. (1974) Cram, crosscram and quadraphage: New games having elusive winning strategies. Sci. Amer. 230 106108.
[7]Kloster O. A solution to the angel problem. To appear in: Theoret Comput. Sci.
[8]Kutz M. (2005) Conway's angel in three dimensions. Theoret. Comput. Sci. 349 443451.
[9]Kutz M. and Pór A. (2006) Angel, devil and king. In Computing and Combinatorics, Vol. 3595 of Lecture Notes in Computer Science, Springer, Berlin, pp. 925934.
[10]Máthé A. (2007) The angel of power 2 wins. Combin. Probab. Comput. 16 363374.
[11]Silverman D. L. (1971) Your Move, McGraw-Hill.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 14 *
Loading metrics...

Abstract views

Total abstract views: 372 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th November 2017. This data will be updated every 24 hours.