Editing Knight's tour (section)

==History==
[[File:Turk-knights-tour.svg|right|thumb|250px|The knight's tour as solved by [[Mechanical Turk|the Turk]], a chess-playing machine hoax. This particular solution is closed (circular), and can thus be completed from any point on the board.]]

The earliest known reference to the knight's tour problem dates back to the 9th century AD. In [[Rudrata]]'s {{lang|sa-Latn|Kavyalankara}}<ref>
{{cite book
|author = Satyadev, Chaudhary
|title = Kavyalankara of Rudrata (Sanskrit text, with Hindi translation);
|publisher = Parimal Sanskrit Series No. 30
|location = Delhitraversal
|title-link = Rudrata#Kavyalankara
}}
</ref> (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 ({{lang|sa-Latn|citra-alaṅkāra}}) called the {{lang|sa-Latn|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|Indic writing systems]] used for Sanskrit are syllabic, each syllable can be thought of as representing a square on a chessboard. Rudrata's example is as follows:

{| style="border:0; text-align:center;"
|-
|से||ना||ली||ली||ली||ना||ना||ली
|-
|ली||ना||ना||ना||ना||ली||ली||ली
|-
|न||ली||ना||ली||ले||ना||ली||ना
|-
|ली||ली||ली||ना||ना||ना||ना||ली
|}

transliterated:
{| style="border:0; text-align:center;"
|-
|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 the 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.

The [[Sri Vaishnavism|Sri Vaishnava]] poet and philosopher [[Vedanta Desika]], during the 14th century, in his 1,008-verse magnum opus praising the deity [[Ranganatha]]'s divine sandals of [[Ranganathaswamy Temple, Srirangam|Srirangam]], [[Paduka Sahasra]]m (in chapter 30: ''Chitra Paddhati'') has composed two consecutive [[Sanskrit]] verses containing 32 letters each (in [[Anuṣṭubh|Anushtubh]] meter) where the second verse can be derived from the first verse by performing a Knight's tour on a {{nowrap|4 × 8}} board, starting from the top-left corner.<ref>{{cite web |url=https://www.iiitb.ac.in/CSL/projects/paduka/paduka.html|title=Indian Institute of Information Technology, Bangalore|website=www.iiitb.ac.in|access-date=2019-10-11}}</ref> The transliterated 19th verse is as follows:
{| class="wikitable"
|sThi
<small>(1)</small>
|rA
<small>(30)</small>
|ga
<small>(9)</small>
|sAm
<small>(20)</small>
|sa
<small>(3)</small>
|dhA
<small>(24)</small>
|rA
<small>(11)</small>
|dhyA
<small>(26)</small>
|-
|vi
<small>(16)</small>
|ha
<small>(19)</small>
|thA
<small>(2)</small>
|ka
<small>(29)</small>
|tha
<small>(10)</small>
|thA
<small>(27)</small>
|ma
<small>(4)</small>
|thA
<small>(23)</small>
|-
|sa
<small>(31)</small>
|thpA
<small>(8)</small>
|dhu
<small>(17)</small>
|kE
<small>(14)</small>
|sa
<small>(21)</small>
|rA
<small>(6)</small>
|sA
<small>(25)</small>
|mA
<small>(12)</small>
|-
|ran
<small>(18)</small>
|ga
<small>(15)</small>
|rA
<small>(32)</small>
|ja
<small>(7)</small>
|pa
<small>(28)</small>
|dha
<small>(13)</small>
|nna
<small>(22)</small>
|ya
<small>(5)</small>
|}
The 20th verse that can be obtained by performing Knight's tour on the above verse is as follows:

sThi thA sa ma ya rA ja thpA

ga tha rA mA dha kE ga vi |

dhu ran ha sAm sa nna thA dhA

sA dhyA thA pa ka rA sa rA ||

It is believed that Desika composed all 1,008 verses (including the special ''Chaturanga Turanga Padabandham'' mentioned above) in a single night as a challenge.<ref>{{cite web |url=http://bridge-india.blogspot.com/2011/08/paduka-sahasram-by-vedanta-desika.html|title=Bridge-India: Paduka Sahasram by Vedanta Desika|last=Bridge-india|date=2011-08-05|website=Bridge-India|access-date=2019-10-16}}</ref>

A tour reported in the fifth book of Bhagavantabaskaraby by Bhat Nilakantha, a cyclopedic work in Sanskrit on ritual, law and politics, written either about 1600 or about 1700 describes three knight's tours. The tours are not only reentrant but also symmetrical, and the verses are based on the same tour, starting from different squares.<ref>[[A History of Chess]] by Murray</ref> Nilakantha's work is an extraordinary achievement being a fully symmetric closed tour, predating the work of Euler (1759) by at least 60 years.

[[File:Euler knight tour semimagic square.svg|thumb|A [[semimagic square]] (its diagonals do not sum to its [[magic constant]], 260) also forming a knight's tour &ndash; no fully magic tours exist on an 8x8 board (although they do exist on larger boards)<ref>{{cite web | url=http://mathworld.wolfram.com/news/2003-08-06/magictours/ | title=MathWorld News: There Are No Magic Knight's Tours on the Chessboard }}</ref>]]
After Nilakantha, one of the first mathematicians to investigate the knight's tour was [[Leonhard Euler]]. The first procedure for completing the knight's tour was Warnsdorf's rule, first described in 1823 by H. C. von Warnsdorf.

In the 20th century, the [[Oulipo]] group of writers used it, among many others. The most notable example is the {{nowrap|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 [[World Chess Championship 2010]] between [[Viswanathan Anand]] and [[Veselin Topalov]] saw Anand making 13 consecutive knight moves (albeit using both knights); online commentators jested that Anand was trying to solve the knight's tour problem during the game.