BIT Numerical Mathematics

, Volume 22, Issue 1, pp 42–52 | Cite as

Fundamental solutions of the eight queens problem

  • Rodney W. Topor
Part I Computer Science


Previous algorithms presented to solve the eight queens problem have generated the set of all solutions. Many of these solutions are identical after applying sequences of rotations and reflections. In this paper we present a simple, clear, efficient algorithm to generate a set of fundamental (or distinct) solutions to the problem.


eight queens problem fundamental solutions isomorph rejection backtracking group theory 


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  1. 1.
    A. Ahrens,Mathematische Unterhaltungen und Spiele, Leipzig: Teubner, 1910.Google Scholar
  2. 2.
    E. W. Dijkstra,Notes on structured programming, inStructured Programming, O.-J. Dahl, E. W. Dijkstra, and C. A. R. Hoare (eds), Academic Press 1972.Google Scholar
  3. 3.
    J. P. Fillmore and S. G. Williamson,On backtracking: a combinatorial description of the algorithm, SIAM Journal of Computing 3, 1 (March 1974), 41–55.Google Scholar
  4. 4.
    P. Henderson,Functional Programming: Application and Implementation, Prentice-Hall 1980.Google Scholar
  5. 5.
    M. Kraitchik,Mathematical Recreations, Second revised edition, Dover 1953.Google Scholar
  6. 6.
    P. Naur,An experiment in program development, BIT 12 (1972), 347–365.Google Scholar
  7. 7.
    E. M. Reingold, J. Nievergelt, and N. Deo,Combinatorial Algorithms: Theory and Practice, Prentice-Hall 1977.Google Scholar
  8. 8.
    J. S. Rohl,Generating permutations by choosing, The Computer Journal 21, 4 (November 1978), 302–305. See also The Computer Journal 22,2 (May 1979), 191.Google Scholar
  9. 9.
    W. W. Rouse Ball and H. S. M. Coxeter,Mathematical Recreations and Essays, Twelfth edition, University of Toronto Press 1974.Google Scholar
  10. 10.
    N. Wirth,Program development by stepwise refinement, Communications of the ACM 14, 4 (April 1971), 221–227.Google Scholar
  11. 11.
    N. Wirth,Algorithms +Data Structures =Programs, Prentice-Hall 1976.Google Scholar

Copyright information

© BIT Foundations 1982

Authors and Affiliations

  • Rodney W. Topor
    • 1
  1. 1.Department of Computer ScienceMonash UniversityClaytonAustralia

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