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. The 20th verse that can be obtained by performing Knight's tour on the above verse is as follows: The transliterated 19th verse is as follows: The 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 Srirangam, Paduka Sahasram (in chapter 30: Chitra Paddhati) has composed two consecutive Sanskrit verses containing 32 letters each (in Anushtubh meter) where the second verse can be derived from the first verse by performing a Knight's tour on a 4 × 8 board, starting from the top-left corner. Rudrata's example is as follows:įor 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. Since the Indic writing systems used for Sanskrit are syllabic, each syllable can be thought of as representing a square on a chessboard. 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.

In Rudrata'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 earliest known reference to the knight's tour problem dates back to the 9th century AD. This particular solution is closed (circular), and can thus be completed from any point on the board. History The knight's tour as solved by the Turk, a chess-playing machine hoax.

Unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time. The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem. The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory. The numbers on each node indicate the number of possible moves that can be made from that position. Theory Knight's graph showing all possible paths for a knight's tour on a standard 8 × 8 chessboard. Variations of the knight's tour problem involve chessboards of different sizes than the usual 8 × 8, as well as irregular (non-rectangular) boards. Creating a program to find a knight's tour is a common problem given to computer science students. The knight's tour problem is the mathematical problem of finding a knight's tour.

If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed (or re-entrant) otherwise, it is open. I have managed to set them on board and have also tried with getting coordinates from clicking on a piece, then getting coordinates from clicking somewhere on board and assigning the chosen piece those newly acquired coordinates, but nothing seems to work correctly.įor (var k=0 k' + String.Mathematical problem set on a chessboard An open knight's tour of a chessboard An animation of an open knight's tour on a 5 × 5 boardĪ knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. I'm having some problems with my assignment, which was to make chess pieces move freely across the board without the use of ids in native javascript.

Chess horse movement