## Tuesday, February 13, 2018

LITERAL SOLUTION TO THE CHESS & KNIGHT PROBLEM.

There is a well-known problem in mathematics called the Chess & Knight problem. Here the challenge is to place a knight in one corner of the chessboard and to cover all 64 squares with the knight, without landing on any square twice. The French Mathematician Euler found a solution to this problem. Since then, it is known as Euler’s chess and knight problem. In ancient India, the Tamil poet Shri Deshikan wrote 1000 verses in Sanskrit in praise of the wooden sandals of Lord Rama. The composition is known as Paadukaasahasram. In one of the chapters, the poet has used a style known as Chitrakaavyam or artistic poetry. In two of the shlokas in this chapter, he has solved the Chess & Knight problem 700 years before Euler.
The first stanza is:
स्थिरागसां सदाराध्या विहताकततामता । सत्पादुके सरासा मा रङ्गराजपदन्नय ।
The meaning of the above stanza is: O sacred sandals of the Brahman! You are always adored by those, who have committed unpardonable sins. You remove all that is sorrowful and unwanted. You create a musical sound. (Be pleased) and lead me to the feet of Lord Rangaraaja (Raama).
The progress has been indicated by arrows and numbers. After the first cycle, it has to be repeated once again. It must be remembered that finding a mathematical solution is much easier than giving a poetical solution.
When this verse is read as per the movement of the knight on the chessboard, it gives the following shloka: स्थिता समयराजत्पागतरा मादके गवि । दुरंहसां सन्नतादा साध्यातापकरासरा ।
The meaning of the above stanza is: The sandals, which protect those who shine by their right attitude; whose place is in the center of the blissful eyes; which destroys the melancholi of the distressed; whose radiance brings peace to those who take refuse in them; which move everywhere; - may those golden and radiating sandals of the Brahman lead me to the feet of Lord Rangaraaja (Raama).