1,4

J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. ACM, 18 (1975), 651-656.

J. Freeman, A neural network solution to the n-queens problem, The Mathematica J., 3 (No. 3, 1993), 52-56.

M. Gardner, The Unexpected Hanging, pp. 190-2, Simon & Shuster NY 1969

Jieh Hsiang, Yuh-Pyng Shieh, and Yao-Chiang Chen, The cyclic complete mappings counting problems, in Problems and Problem Sets for ATP, volume 02-10 of DIKU technical reports, G. Sutcliffe, J. Pelletier, and C. Suttner, eds., 2002.

Kenji Kise, Takahiro Katagiri, Hiroki Honda, and Toshitsugu Yuba: Solving the 24-queens Problem using MPI on a PC Cluster, Technical Report UEC-IS-2004-6, Graduate School of Information Systems, The University of Electro-Communications (2004)

I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.

M. A. Sainte-Lagu\"{e}, Les R\'{e}seaux (ou Graphes), M\'{e}morial des Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, p. 47.

R. J. Walker, An enumerative technique for a class of combinatorial problems, pp. 91-94 of Proc. Sympos. Applied Math., vol. 10, Amer. Math. Soc., 1960.

M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.

Amazing Mathematical Object Factory, Information on the n Queens problem [Broken link?]

Anonymous, N Queens Problem

D. Bill, Durango Bill's The N-Queens Problem [Broken link?]

Patrick GUILLEMIN, N-Queens Challenge [Broken link?]

Patrick GUILLEMIN, N-Queens Challenge [Broken link?]

Patrick GUILLEMIN, N-Queens Challenge [Broken link?]

Kenji KISE, 24-queens.

W. Kosters, n-Queens (Extensive Bibliography)

NQuens@home, Home Page

Objectweb ProActive INRIA Team, Home Page

Objectweb ProActive INRIA Team, Solve the N Queens challenge with ProActive !

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Strong conjecture : there is a constant c around 2.54 such that a(n) is asymptotic to n!/c^n; weak conjecture : lim n -> infinity (1/n) * ln(n!/a(n)) = constant =0.90.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002

a(2) = a(3) = 0, since on 2 X 2 and 3 X 3 chessboards there are no solutions.

See A140393 for another version. Cf. A002562, A065256.

Sequence in context: A029673 A054790 A140393 this_sequence A038216 A027626 A096668

Adjacent sequences: A000167 A000168 A000169 this_sequence A000171 A000172 A000173

nonn,hard,nice

njas

Terms for n=21-23 computed by Sylvain PION (Sylvain.Pion(AT)sophia.inria.fr) and Joel-Yann FOURRE (Joel-Yann.Fourre(AT)ens.fr).

a(24) from Kenji KISE (kis(AT)is.uec.ac.jp), Sep 01 2004

a(25) from Objectweb ProActive INRIA Team (proactive(AT)objectweb.org), Jun 11 2005 [Communicated by Alexandre Di Costanzo (Alexandre.Di_Costanzo(AT)sophia.inria.fr)]. This calculation took about 53 years of CPU time.

a(25) has been confirmed by the NTU 25Queen Project at National Taiwan University and Ming Chuan University, led by Yuh-Pyng (Arping) Shieh, Jul 26 2005. This computation took 26613 days CPU time.

Some of the links may be broken. I would appreciate receiving updates to them. - njas, May 01 2006

The NQueens@Home web site gives a different value for a(24), 226732487925864. Thanks to Goran Fagerstrom for pointing this out. I do not know which value is correct. I have therefore created a new entry, A140393, which gives the NQueens@home version of the sequence. - njas, Jun 18 2008