- In December 1914, Ramanujan was asked by his friend P.C. Mahalanobis to solve a puzzle that appeared in Strand magazine as “Puzzles at a Village Inn”. The puzzle stated that n houses on one side of the street are numbered sequentially starting from 1. The sum of the house numbers on the left of a particular house having the number m, equals that of the houses on the right of this particular house. It is given that n lies between 50 and 500 and one has to determine the values of m and n. Ramanujan immediately rattled out a continued fraction generating all possible values of m without having any restriction on the values of n. List the first five values of m and n.
- Ramanujan had posed the following problem in a journal:
, find x. Without receiving an answer from the readers, after three months he gave answer as 3. This he could say because he had an earlier general result stating
is true for all x. Prove this result, then
will give the answer to Ramanujan’s problem.
Try try until you succeed!!
Nalin Pithwa.
