“On
another occasion, I went to his room to have lunch with him. The
Fist World War had started sometime earlier. I had in my hand
a copy of the monthly Strand Magazine which at that time used
to publish a number of puzzles to be solved by readers. Ramanujan
was stirring something in a pan over the fire for our lunch. I
was sitting near the table, turning over the pages of the Magazine.
I got interested in a problem involving a relation between two
numbers. I have forgotten the details; but I remember the type
of the problem. Two British officers had been billeted in Paris
in two different houses in a long street; the door numbers of
these houses were related in a special way; the problem was to
find out the two numbers. It was not at all difficult. I got the
solution in a few minutes by trial and error.
MAHALANOBIS: (In a joking way), Now
here is a problem for you.
RAMANUJAN: What problem, tell me.
(He went on stirring the pan).I read out the question from the
Strand Magazine.
RAMANUJAN: Please take down the solution.
(He dictated a continued fraction).The first term was the solution
which I had obtained. Each successive term represented successive
solutions for the same type of relation between two numbers, as
the number of houses in the street would increase indefinitely.
I was amazed.
MAHALANOBIS: Did you get the solution
in a flash?
RAMANUJAN: Immediately I heard the
problem, it was clear that the solution was obviously a continued
fraction; I then thought, “Which continued fraction?”
and the answer came to my mind. It was just as simple as this.