References
W. Ahrens,Mathematische Unterhaltungen und Spiele, Teubner, Leipzig, 1910 (Vol. 1)and 1918 (Vol. 2).
E. R. Berlekamp, J. H. Conway, and R. K. Guy,Winning Ways, vol. 2, Academic Press, London/New York, 1982.
H. E. Dudeney,Amusements in Mathematics, Dover, New York, 1958, 1970 (reprint of Nelson, 1917).
N. D. Elkies, On numbers and endgames: Combinatorial game theory in chess endgames, in [22], pp. 135-150.
G. Foster, Sliding-block problems, Part 1,The Problemist Supplement 49 (November, 2000), 405–407.
G. Foster, Sliding-block problems, Part 2,The Problemist Supplement 51 (March, 2001), 430–432.
G. Foster, Sliding-block problems, Part 3,The Problemist Supplement 54 (September, 2001), 454.
G. Foster, Sliding-block problems, Part 4,The Problemist Supplement 55 (November, 2001), 463–464.
M. Gardner,Mathematical Magic Show, Vintage Books, New York, 1978.
J. Gik,Schach und Mathematik, MIR, Moscow, and Urania-Verlag, Leipzig/Jena/ Berlin, 1986; translated from the Russian original published in 1983.
B. Hochberg,Chess Braintwisters, Sterling, New York, 1999.
D. Hooper and K. Whyld,The Oxford Companion to Chess, Oxford, Oxford University Press, 1984.
G. P. Jelliss,Synthetic Games, September 1998, 22 pp.
G. P. Jelliss,Knight’s Tour Notes: Knight’s Tours of Four-Rank Boards (Note 4a, 30 November 2001), http://home.freeuk.net/ ktn/4a.htm
T. Krabbé,Chess Curiosities, George Allen & Unwin Ltd., London, 1985.
J. Levitt and D. Friedgood,Secrets of Spectacular Chess, Batsford, London, 1995.
C. D. Locock,Manchester Weekly Times, December 28, 1912.
S. Loyd,Strategy, 1881.
B. McKay, Comments on: Martin Loeb-bing and Ingo Wegener, The Number of Knight’s Tours Equals 33,439,123,484, 294—Counting with Binary Decision Diagrams,Electronic J. Combinatorics, http:// www.combinatorics.org/Volume_3/Com- ments/v3ilr5.html.
J. Morse,Chess Problems: Tasks andRecords, London, Faber and Faber, 1995; second ed., 2001.
I. Newman, problem E 1585 (“What is the maximum number of knights which can be placed on a chessboard in such a way that no knight attacks any other?”), with solutions by R. Patenaude and R. Greenberg,Amer. Math. Monthly 71 no. 2 (Feb. 1964), 210–211.
R. J. Nowakowski, ed.,Games of No Chance, MSRI Publ. #29 (proceedings of the 7/94 MSRI conference on combinatorial games), Cambridge, Cambridge University Press, 1996.
N. J. A. Sloane,The On-Line Encyclopedia of Integer Sequences, on the Web at http://www. research .att.com/~njas/sequences.
L. Stiller, Multilinear Algebra and Chess Endgames, in [22], pp. 151-192.
M. A. Sutherland and H. M. Lommer,1234 Modern End-Game Studies. Dover, New York, 1968.
G. Törnberg, “Knight’s Tour”, http://w1. 859.telia.com/~u85905224/knight/eknig ht.htm.
A. C. White,Sam Loyd and His Chess Problems, Whitehead and Miller, 1913; reprinted (with corrections) by Dover, New York, 1962.
G. Wilts and A. Frolkin,Shortest Proof Games, Gerd Wilts, Karlsruhe, 1991.
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article is available at http://dx.doi.org/10.1007/BF02984828.
Rights and permissions
About this article
Cite this article
Elkies, N.D., Stanley, R.P. The mathematical knight. The Mathematical Intelligencer 25, 22–34 (2003). https://doi.org/10.1007/BF02985635
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02985635