Heirloom wood inlaid chess board.As I remember, the white squares are birch, and the dark squares are walnut. (Photo by the author.) |

A solution of the eight queens puzzle.You can see that no two queens share the same row, column, or diagonal. The eight queens puzzle has been generalized to placing (n-1) queens on an n-by-n chessboard. (Illustration by the author using Inkscape.) |

Uncrossed knight's path on an 8x8 chessboard.(Modified version of a Wikimedia Commons image.) |

As a demonstration of the power of modern computing, an artificial neural network was used to find the knight's tour on a 24-by-24 board shown in the following figure.

NTours1 1 2 0 3 0 4 0 5 1,728 6 6,637,920 7 165,575,218,320 8 (unknown)

Tour de force knights tour.A knight's tour on a 24x24 board. A neural network was used to find this solution. (Illustration by "Pattern86" via Wikimedia Commons.) |

- Joe Verghese, M.D., Richard B. Lipton, M.D., Mindy J. Katz, M.P.H., Charles B. Hall, Ph.D., Carol A. Derby, Ph.D., Gail Kuslansky, Ph.D., Anne F. Ambrose, M.D., Martin Sliwinski, Ph.D., and Herman Buschke, M.D., "Leisure Activities and the Risk of Dementia in the Elderly," New England Journal of Medicine, vol. 348, no. 25 (June 19, 2003), pp. 2508-2516.
- Niklaus Wirth, Algorithms + Data Structures = Programs, Prentice-Hall, 1976, 366 pp. (ISBN 0-13-022418-9, via Amazon).
- The path lengths for the open paths are Sequence A003192 of the On-Line Encyclopedia of Integer Sequences. The path lengths for the closed paths are Sequence A157416 of the On-Line Encyclopedia of Integer Sequences.
- Douglas Main, "Ants Playing Chess Find New Solutions To Old Problem," Popular Science, February 3, 2014.
- P. Hingston and G. Kendall, "Ant Colonies Discover Knight's Tours," Lecture Notes in Computer Science, vol. 3339 (2005), pp. 1213-1218.
- Knight's Tour, Numberphile (http://www.numberphile.com), YouTube video, January 16, 2014.
- Brendan D. McKay, "Knight's Tours of an 8 8 Chessboard," Computer Science Department, Australian National University, Canberra, Australia (PDF file).
- George Jelliss, Knight's Tour Notes, mayhematics.com.
- Ben Hill and Kevin Tostado, "Knight's Tours," December 18, 2004 (PDF file).