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. 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. Nilakantha's work is an extraordinary achievement being a fully symmetric closed tour, predating the work of Euler (1759) by at least 60 years. 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 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. Existence Schwenk proved that for any board with m ≤ n, a closed knight's tour is always possible unless one or more of these three conditions are met: m and n are both odd m = 1, 2, or 4 m = 3 and n = 4, 6, or 8. Cull et al. and Conrad et al. proved that on any rectangular board whose smaller dimension is at least 5, there is a (possibly open) knight's tour. Number of tours On an board, there are exactly 26,534,728,821,064 directed closed tours (i.e. two tours along the same path that travel in opposite directions are counted separately, as are rotations and reflections). The number of undirected closed tours is half this number, since every tour can be traced in reverse. There are 9,862 undirected closed tours on a board. Finding tours with computers There are