algebraic puzzle by Bhaskaracharya in sanskrit

Courtesy:Sri.Karthikeyan Madathil

*Bhāskarāchārya* *(1114 -1185 CE)*, has been called the greatest
mathematician of medieval India.
 
He was born in *Bijapur* in Karnataka, and is considered the progenitor of
Differential Calculus - 500 years before Newton and Leibniz.
 
Bhāskarāchārya wrote at least four mathematical treatises in Sanskrit.
One of them, titled Leelavati, contains many algebra-related teasers in
this book, which have become the subject of significant research by
scholars. These teasers are in the form of *shlokas* which pose problems.
 
The shlokas need to be interpreted correctly to decipher the meaning in
order to find the solution.
 
There is one Sloka in it , The direct meaning of this shloka is a question
formulated as follows:
 
During the battle between Arjuna and Karna in Mahabharata, Arjuna released
some arrows. Out of all the released arrows:
 
• Half were consumed in stopping the arrows coming from Karna,
 
• 4 times the squareroot of the arrows were consumed to control the horses
of Karna's chariot.
 
• 6 were for gaining control over Shalya, the charioteer of Karna. (Shalya
was the maternal uncle of Nakula and Sahadeva.)
 
• 3 were used to take on the umbrella of the chariot, flag of the chariot
and bow of Karna.
 
• Finally Karna was killed with a single arrow.
🤔
So how many arrows were released by Arjuna in the battle?
 
Basic algebra easily yields the answer to this question, if the equation is
formulated correctly.
 
Let the total number of arrows be X.
 
The statements above can be reduced to the algebraic form
*X = X/2 + 4√X + 6 + 3 + 1*
 
If we solve this we get the value of X=100 for the number of arrows shot by
Arjuna.
 
However, the fun is not just getting the algebra right. There is so much of
hidden information in this shloka.
 
If we pause to think a little deeper about the hidden meanings:
 
• Even for an atirathi like Arjuna, it took as many as 50 arrows to stop
the arrows of Karna - it tells us about the skills of Karna.
 
• That the horses needed 40 arrows to immobilize the chariot tells us about
the kind of training given to the horses in the battle field.
 
• When even the horses needed 40 arrows, that Shalya the charioteer
surrendered with just 6 tells us that he is favouring Arjuna.
 
• 3 arrows to take the chariot and the bow shows the helplessness of Karna.
 
• Once everything is in control, the enemy should vanquished in just a
single arrow.

पार्थ: कर्णवधाय मार्गणगणं क्रुद्धो रणे संदधे
तस्यार्धेन निवार्य तच्छरगणं मूलैश्चतुभिर्हयान् |
शल्यं षड्भिरथेषुभिस्त्रिभिरपि च्छत्रं ध्वजं कार्मुकम्
चिच्छेदास्य शिरः शरेण कति ते यानर्जुनः संदधे || ७६ ||
 
( गुणकर्म )