Friday, November 4, 2011

Necklace broke in Love-Making

I had just posted "17 Horses and 3 Brothers" (Click here to read it) and within a few minutes one of my middle aged well-wishers taunted me with a Question.  "You have Stories to teach fractions only to children.  Don't you have any story to teach this to older people?  I have to teach a grown-up here!".

Most of the literature is for adults.  Or I should say-grown ups.  It requires more skill, effort and discretion to write for children.

One poet, probably a family man and worshiper of  Shiva and Parvati , visualises and salutes them thus:  "Young Ganesha is siting between Shiva and Parvathi.  They are very pleased by little Ganesha's pranks.  They both turn to Ganesha to plant a kiss on his head.  Sensing this, the mischievous Ganesha ducks at the appropriate moment.  I salute Shiva-Parvati at this moment, sitting in this pose".  If you need to go further, read  Kaalidasa's "Kumara Sambhava".  And many others.

As regards teaching fractions to grown-ups,  I quote a translation of a verse  from Stanza 54, Chapter 3 of the book  "Lilavati" and the English Translation is by Mr. T N Colebrook: 

Whilst making Love, a necklace broke,
A row of pearls mislaid.

One sixth fell to the floor,
One fifth upon the bed,
The young woman saved One third of them,
One tenth were caught by her lover,

If six pearls remained upon the string, 
How many pearls were there altogether?

Bhaskara II (the author of Lilavati) is clear in his question.  There is a young woman and her lover, presumably young too, though she could save a third of the pearls and he could catch only a tenth.  There was a pearl necklace, presumably worn by the woman.  And it broke while making love.  The two of them caught some, some were lying on the bed and some more went farther and fell on the floor. Finally six pearls remained in the broken string.  The mathematical question is how many pearls were in the necklace before it broke?

I leave it to your wide or wild imagination to create the scene in your mind as to why, when and how the necklace broke, while reserving my right to my own imagination and interpretation.  I will only dwell upon the solution of the mathematical problem and not its creation!

We were all taught problems of fractions and LCM and HCF while in school.  It was over five decades ago for me and I have forgotten about it.  However,  the problem can be simplified as under:

Lying on the floor                                                              :     1/6
Lying on the bed                                                                :     1/5
In the hands of the woman (saved by her)                     :     1/3
In the hands of her lover (caught by him)                      :     1/10
Left in the broken string of the necklace                          :      6

If represented in an equation it is :   1/6+1/5+1/3+1/10+6  = total no. of Pearls in the necklace before it broke.

Use  LCM  for  6, 5, 3 and 10.   It will be 30

Then  pearls in different places is 5+6+10+3+6 which makes a total of 30 pearls in the necklace before it broke!  Problem solved!!

I had suggested demonstration to children in the "17 Horses and 3 Brothers" story by replacing horses with Apples or Chocolates for the sake of simplicity, easy availability and generating interest among the children.  I have no such suggestion for this story.


  1. I wish they taught mathematics like that in school! At least our interest would have been guaranteed irrespective of our mathematical skills!

  2. If mathematics was taught to me like this-- perhaps I would have been netter at adding and dividing today ! Another possibility is that I would still have ended up a writer-- writing stories about Maths !

  3. Sirji, aap Math ki classes lete ho kya? I want to apply :-)

  4. this is how learning is made fun and interesting ....

  5. In interesting problem. Such problems/questions motivate to students in mathematics. This process is so good. Also, we may proceed as,
    Let total pearls be x then by question,
    or (5x+6x+10x+3x+180)/30=x
    or 24x+180 =30x
    or 6x=180
    or x=180/6
    Therefor total pearls=30.