Mahaviracharya/Ganita Sara Samgraha/Chapter IV/17-22

: Chapter $\text {IV}$: Miscellaneous Problems (on Fractions): Problem $17$ to $22$
One night, in a month of the spring season, a certain young lady ... was lovingly happy along with her husband ... on the floor of a big mansion, white like the moon, and situated in a pleasure-garden with trees bent down with the load of bunches of flowers and fruits, and resonant with the sweet sounds of parrots, cuckoos and bees which were all intoxicated with the honey obtained from the flowers therein.

Then on a love-quarrel arising between the husband and the wife, that lady's necklace made up of pearls became sundered and fell on the floor.


 * One-third of that necklace reached the maid-servant there;
 * One-sixth fell on the bed;
 * then one-half of what remained
 * (and one-half of what remained thereafter and again one-half of what remained thereafter)
 * and so on, counting six times [in all] fell all of them everywhere;
 * and there were found to remain (unscattered) $1,161$ pearls;

and if you know ... give out the measure of the pearls.

The translation by remarks:
 * Certain epithets here have not been considered fit for translation.

I don't know what he means.

Solution
Improbably, there were in fact $148, 608$ pearls in that necklace.

Proof
Let $n$ be the number of pearls in the necklace.

After $\frac 1 6$ and $\frac 1 3$ have fallen to the maid-servant and on the bed, there are $\frac 1 2$ remaining.

One-half and half again, and so on, counting $6$ times in all, means $\dfrac 1 {2^6} \times \dfrac 1 2$ remain.

Hence $n \times 1 {128} = 1,161$ and the result follows.