The Knight's Tour Problem and Rudrata's Verse

摘要

If a chess-knight is moved on a vacant chess-board [8 ?? 8 square] such that it visits each one of the 64 squares once and once only, the knight is said to execute a Knighta??s Tour. Solution to the knighta??s tour problem was known in India as early as the 9th century AD as a demonstration of wizardry in composing 32-syllable verses in Sanskrit. A pair of meaningful verses is composed in such a manner that when one verse is written serially (left to right and top to bottom) one syllable a square to ???ll up 8 ?? 4 cells a?? half of a chess board a?? the other verse appears as the Knighta??s Tour. The earliest example of this skill in poetry-composition is given in a Sanskrit treatise on poetics, k??vy??laá1?k??ra written by Rudraá1-a who lived around the ninth century A.D. Knighta??s Tour as a mathematical problem was ???rst noticed and discussed in the West by Leonard Euler in the eighteenth century. After providing the back ground to the subject as a puzzle on the chess-board, a problem in mathemat-ics and as a challenge in verse-composition, the article discusses the special characteristic of Rudrataa??s example where the pair of verses reduces to a single verse.