Lilavati (Leelaavathi)  of Bhaskaraacharya

    Dear Children,

 Let us hear about a young girl, Leelaavathi ,  daughter of Bhaskaraacharya, a famous mathematician of India who lived in 12^th century. One of the books he wrote was named after her , and is famous  as Leelavathi  Ganita .

Bhaskaraacharya II was a great scholar in Mathematics, Astronomy, Astrology and a Sanskrit Poet as well. He adored his young daughter, Leelaavati who was a brilliant student of arithmetic. When she came of marriageable age, he found her an eligible boy. Being a good astrologer, he studied the horoscope of his daughter and, to his horror, found that there was a “Dosha” or defect in her time of birth ,due to which ,she would become a widow soon after marriage.. He used all his skill and fixed an auspicious date and time for marriage such that, she would not become a widow if she was married in that ‘lagna’.

In those days, there were no clocks, .Time was measured in a “water clock” where water was allowed to drip from one part of a vessel into another through a small hole and the level of water in the lower vessel indicated the time.

 Bhaskaraacharya set up the water clock carefully .The time of arrival of the auspicious ‘lagna’ was marked on the vessel to announce the time of marriage. Leelavathi often would come and peep to see the time. Though Bhaskaraacharya had used all his skill to avert the widowhood, Fate could not be hoodwinked! A pearl from the dress of the bride had slipped into the water clock, which nobody noticed. The pearl had clogged the hole. The rate of flow of water had changed and the Auspicious time  of Lagna had passed before the marriage! Leelavathi had to endure the widowhood at a tender age.

Since Leelavathi was fond of arithmetic, her father used to tell her stories and puzzles, in order to cheer her up, and  endure the grief .That is how Leelavathi Mathmatics was born! It became a popular text for children to learn arithmetic without the usual hardship or boredom!

  Here is a puzzle which my teacher used to tell as an example.

  There is a mango grove protected by seven rows of fences, each having a gate, guarded by a gate-keeper. The trees are full of nice juicy fruits. A boy pleads with the gate-keepers to be allowed to pluck some fruits. He   agrees to give the gate-keeper,  half of whatever quantity of fruits  he has at the time of crossing the gate, but pleads that the gate-keeper should give back  one fruit , This, he promises to each of the 7 gate-keepers,to which they agree.

 The boy plucks as many fruits as he wants, passes through all the 7 gates after fulfilling his promise to each of the gate-keepers.  

 When he comes out, he finds he has as many fruits as he had plucked!!! How many, he plucked?

It is desirable if it is answered orally. You may use pen and paper also!

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 Another puzzle which was popular in my school-days:-

Three friends go to a restaurant for snacks. They decide to share the bill equally. Each gives a ten rupee note. The bill is for Rs.25 and the waiter returns five one rupee notes. Each pocket one rupee and leave 2 rupees to the waiter.

On coming out, one of them pauses and says:- We had put ten rupees each, ie Thirty rupees. We got back one each. So, each have spent nine rupees, which makes it 9x3=27. we gave the waiter 2 rupees. It accounts for27+2=29. But, we came with 10x3=30 rupees. Where is the one rupee gone?

Can you find the one rupee which is lost?

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