The Maximum Queens Problem with Pawns

Open access

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.

References

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  • [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.

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

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

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

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

Journal Information


Mathematical Citation Quotient (MCQ) 2016: 0.05

Target Group

researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms

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