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Recreational Mathematics Magazine

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Mathematical Citation Quotient (MCQ) 2016: 0.05

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2182-1976
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The Maximum Queens Problem with Pawns

Doug Chatham
Published Online: 2016-12-08 | DOI: https://doi.org/10.1515/rmm-2016-0010

Abstract

The classic n-queens problem asks for placements of just n mutually non-attacking queens on an n × n board. By adding enough pawns, we can arrange to fill roughly one-quarter of the board with mutually non-attacking queens. How many pawns do we need? We discuss that question for square boards as well as rectangular m × n boards.

Keywords: chess; n-queens problem; combinatorics

References

  • [1] Bell, J., Stevens, B.“A survey of known results and research areas for n-queens”, Discrete Math, 309, 1-31, 2009.Web of ScienceGoogle Scholar

  • [2] Chatham, R. D., Doyle, M., Fricke, G. H., Reitmann, J., Skaggs, R. , Wolff, M.“Independence and domination separation on chessboard graphs”, J. Combin. Math. Combin. Comput, 68, 3-17, 2009.Google Scholar

  • [3] Chatham, R. D., Fricke, G. H., Skaggs, R. D.“The queens separation problem”, Util. Math, 69, 129-141, 2006.Google Scholar

  • [4] Kosters, W. A. n-Queens bibliography, 2016. http://www.liacs.nl/home/kosters/nqueens/Google Scholar

  • [5] Watkins, J. J. Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, 2004.Google Scholar

  • [6] Zhao, K. The Combinatorics of Chessboards, Ph.D. dissertation, City University of New York, 1998. Google Scholar

About the article

Published Online: 2016-12-08

Published in Print: 2016-12-01


Citation Information: Recreational Mathematics Magazine, Volume 3, Issue 6, Pages 95–102, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2016-0010.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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