History
The earliest known reference to the Knight's Tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara (5.15), a Sanskrit work on Poetics, the pattern of a knight's tour on a half-board has been presented as an elaborate poetic figure ("citra-alaṅkāra") called the "turagapadabandha" or 'arrangement in the steps of a horse.' The same verse in four lines of eight syllables each can be read from left to right or by following the path of the knight on tour. Since the Indic writing systems used for Sanskrit are syllabic, each syllable can be thought of as representing a square on a chess board. Rudrata's example is as follows:
से ना ली ली ली ना ना ना ली
ली ना ना ना ना ली ली ली ली
न ली ना ली ली ले ना ली ना
ली ली ली ना ना ना ना ना ली
se nā lī lī lī nā nā lī
lī nā nā nā nā lī lī lī
na lī nā lī le nā lī nā
lī lī lī nā nā nā nā lī
For example, the first line can be read from left to right or by moving from the first square to second line, third syllable (2.3) and then to 1.5 to 2.7 to 4.8 to 3.6 to 4.4 to 3.2.
One of the first mathematicians to investigate the knight's tour was Leonhard Euler. The first procedure for completing the Knight's Tour was Warnsdorff's rule, first described in 1823 by H. C. von Warnsdorff.
In the 20th century, the Oulipo group of writers used it among many others. The most notable example is the 10 × 10 Knight's Tour which sets the order of the chapters in Georges Perec's novel Life: A User's Manual. The sixth game of the 2010 World Chess Championship between Viswanathan Anand and Veselin Topalov saw Anand making 13 consecutive knight moves (albeit using both knights) -– online commentors jested that Anand was trying to solve the Knight's Tour problem during the game.
Read more about this topic: Knight's Tour
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