The problem of determining how many nonattacking knights can be placed on an chessboard. For , the solution is 32 (illustrated above). In general, the solutions are

(1)

giving the sequence 1, 4, 5, 8, 13, 18, 25, ... (Sloane's A030978, Dudeney 1970, p. 96; Madachy 1979).

The minimal number of knights needed to occupy or attack every square on an chessboard is given by 1, 4, 4, 4, 5, 8, 10, ... (Sloane's A006075). The number of such solutions are given by 1, 1, 2, 3, 8, 22, 3, ... (Sloane's A006076).

Dudeney, H. E. "The Knight-Guards." §319 in Amusements in Mathematics. New York: Dover, p. 95, 1970.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 38-39, 1979.

Moser, L. "King Paths on a Chessboard." Math. Gaz. 39, 54, 1955.

Sloane, N. J. A. Sequences A006075/M3224, A006076/M0884, and A030978 in "The On-Line Encyclopedia of Integer Sequences."

Sloane, N. J. A. and Plouffe, S. Figure M3224 in The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 196-197, 1991.

Watkins, J. Across the Board: The Mathematics of Chessboard Problems. Princeton, NJ: Princeton University Press, 2004.

Wilf, H. S. "The Problem of Kings." Electronic J. Combinatorics 2, No. 1, R3, 1-7, 1995. http://www.combinatorics.org/Volume_2/Abstracts/v2i1r3.html.

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Weisstein, Eric W. "Knights Problem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/KnightsProblem.html